By COMSOL, Inc.
Run a Variety of Structural Analyses Several analysis types are available for predicting structural performance in a virtual environment. The Structural Mechanics Module can be used to answer questions concerning stress and strain levels; deformations, stiffness, and compliance; natural frequencies; response to dynamic loads; and buckling instability, to name a few. Structural Mechanics Module Analyses - Static - Eigenfrequency: Undamped, Damped, Prestressed - Transient: Implicit, explicit, or mode superposition - Frequency response: Direct or mode superposition, Prestressed - Geometric nonlinearity and large deformations - Mechanical contact - Buckling and postbuckling - Response spectrum - Random vibration - Component mode synthesis Parametric Analysis: Compute a model with multiple input parameters to compare results. Optimization: Optimize geometric dimensions, shape, topology, and other quantities with the Optimization Module. The Structural Mechanics Module provides a full suite of modeling tools for various types of structural analyses. Based on the finite element method (FEM), its functionality can be used not only for modeling 3D solids, but also in 2D formulations (to simulate plane stress, plane strain, generalized plane strain, and axial symmetry). The module also provides functionality for modeling shells and plates, membranes, beams, pipes, trusses, and wires and for transitioning between different formulations. There are many options available in the software for the finite element shapes and orders: Triangle, quadrilateral, tetrahedron, hexahedron, prism, and pyramid elements are all available, and users can choose from first-, second-, and higher-order elements, as well as mixed-order elements for multiphysics analysis. The Structural Mechanics Module provides specialized features and functionality for running a variety of structural analyses and works seamlessly in the COMSOL Multiphysics® platform for a consistent model-building workflow. Solid Mechanics: The Solid Mechanics interface can be used for modeling in full 3D, 2D (for plane stress, plane strain, and generalized plane strain), 2D axial symmetry, 1D (for plane stress or plane strain in transverse directions), and 1D axial symmetry. The interface provides the most general approach to analyzing solid structures, with built-in multiphysics couplings. Its wide variety of material models makes it possible to accurately describe solid mechanics problems, and it is easy to extend these features via equation-based modeling. Users can define material properties with constant, spatially varying, anisotropic, or nonlinear expressions; lookup tables; or combinations of these. Elements can be activated and deactivated based on user-defined expressions. It is also possible to assign material models to internal or external surfaces. This functionality can be used to model, for example, glue layers, gaskets, fracture zones, or claddings. Shells, Membranes, and Thin Layers: For thin structures, using shell (in 3D and 2D axisymmetry) and plate (in 2D) elements can be very efficient. The formulations allow for the transverse shear deformations needed to model thick shells. It is also possible to prescribe an offset in the direction normal to a selected surface, which simplifies modeling projects involving a full 3D representation of the geometry. The results from a shell element analysis can be visualized using a solid representation. Very thin structures, such as thin films and fabric, require a formulation with no bending stiffness. This is possible in the Membrane interface, in which curved plane stress elements in 3D or 2D axisymmetry are used to compute in-plane and out-of-plane displacements, including the effects of wrinkling. When studying this type of structure, the ability to start from a prestressed state is used extensively. For membranes that are not prestressed, automatic stabilization is available. With the Nonlinear Structural Materials Module, a variety of nonlinear material models can be applied to internal and external thin layers. This enables accurate representation of interface layers such as adhesives, gaskets, and claddings, using modeling assumptions that range from full 3D behavior to purely in-plane strain formulations. Time-Explicit Dynamics: Functionality specialized for time-explicit dynamic analysis enables efficient simulation of fast, transient, and highly nonlinear events such as impacts, wave propagation, and metal forming. The interfaces Solid Mechanics, Explicit Dynamics and Truss, Explicit Dynamics use explicit time integration optimized for large deformations, high strain rates, and general contact conditions. The formulation supports many of the nonlinear materials of the Nonlinear Structural Materials Module, including hyperelasticity and plasticity. The Elastic Waves, Time Explicit interface can be used to compute the transient propagation of linear elastic waves over large domains containing many wavelengths. It uses a higher-order dG (discontinuous Galerkin)-FEM time-explicit method. The interface is multiphysics enabled and can be seamlessly coupled to fluid domains. Application areas range from micromechanical problems to seismic wave propagation. Material Models: The Structural Mechanics Module provides linear elastic, viscoelastic, and piezoelectric material models. Adding the Nonlinear Structural Materials Module or the Geomechanics Module provides access to a wide range of nonlinear material models, including hyperelastic and elastoplastic models. In addition, there are many capabilities for extending the existing material models or for users to create their own. Expressions that depend on stress, strain, spatial coordinates, time, or fields coming from another physics interface can be entered directly into the input field for a material property. In frequency-domain analyses, complex-valued expressions can be entered. For example, custom differential equations can be added to provide inelastic strain contributions. The material models can accommodate thermal expansion, hygroscopic swelling, initial stresses and strains, and several types of damping. Material properties can be isotropic, orthotropic, or fully anisotropic. Users can also include their own material models by providing external functions coded in the C programming language. Loads and Constraints: The Structural Mechanics Module offers a multitude of different load and constraint options, which facilitates high-fidelity modeling. There are capabilities for defining distributed loads on domains, boundaries, and edges, follower loads, and moving loads. There is also support for specifying a total force, including gravity or added mass, and including rotating frames with centrifugal, Coriolis, and Euler forces. For constraining a model, there are springs and dampers, as well as prescribed displacement, velocity, and acceleration. Periodic boundary conditions, low-reflecting boundaries, perfectly matched layers (PMLs), and infinite elements aid in reducing model size for efficient modeling. Dynamics and Vibration: The Structural Mechanics Module covers transient as well as frequency-response analysis. Frequency-response analysis includes eigenfrequency, damped eigenfrequency, and frequency sweep analyses. In addition, specialized study types are available for random vibration and response spectrum analysis. Random vibration analysis allows for inputs based on power spectral density (PSD) as a function of frequency, including uncorrelated as well as fully correlated loads. Response spectrum analysis is used as an efficient method for determining structural response to short, nondeterministic events like earthquakes and shocks. Component mode synthesis (CMS), also known as dynamic substructuring, reduces linear components to computationally efficient reduced-order models (ROMs) using the Craig–Bampton method. These ROM components can then be used in dynamic or stationary analyses, improving computation time and memory usage. Beams, Pipes, Trusses, and Wires: There are specialized element types for modeling beams, described by their cross-section properties. Formulations for both slender beams (Euler–Bernoulli theory) and thick beams (Timoshenko theory) are available. Predefined couplings make it possible to mix beams with other element types to study reinforcements for solid and shell structures. A library of common cross-section types is available as well as functionality for modeling general cross sections. Additionally, the Structural Mechanics Module enables the modeling of slender structures that can only sustain axial forces (trusses and wires). These elements can also be used for modeling reinforcements. Structural analysis of pipes is similar to that of beams but with the addition of an internal pressure that usually contributes significantly to the stresses in a pipe. Also, in this type of analysis, temperature gradients usually occur through the pipe wall rather than across the entire section. The loads from internal pressure and drag forces can be taken directly from the results of a pipe flow and thermal analysis using the Pipe Flow Module. Contact and Friction: Situations where objects come into contact with each other occur frequently in mechanical simulations. Static and dynamic analyses can include contact modeling, and the objects in contact can have arbitrarily large relative displacements. Additionally, the effects of friction, both sticking and sliding, can be modeled. The contact analysis functionality also includes capabilities for prescribing adhesion and decohesion between objects in contact and modeling removal of material by wear when objects are sliding relative to each other. Fracture Mechanics: Several different approaches for crack modeling are supported. A crack can either be infinitely thin and represented by a single boundary or represented by disjoint surfaces in the geometry. A crack can have any number of branches and corresponding crack fronts. Effects of crack closure, as well as loads on the crack faces, can be included. Stress intensity factors and energy release rates can be computed in 2D and 3D using J-integral or virtual crack extension methods. By adding the Nonlinear Structural Materials Module or the Geomechanics Module, users can model damage and cracking in brittle materials according to various criteria. Engineering Features: The Structural Mechanics Module includes several structural engineering features that enable users to create real-world models more quickly. These features include boundary conditions such as rigid connectors for modeling rigid bodies and kinematic constraints, bolts with pretension, and stress linearization for analysis of pressure vessels, as well as: - Automatic handling of RBE2 elements from NASTRAN® import - Bolt thread contact modeling - Weld evaluation - Mesh-independent spot welds - Fasteners, for example rivets, to automatically connect aligned holes - Evaluation of warpage - Safety factor expressions - Computation of section forces in a cut through a solid - Superposition of load cases - Computation of effective material properties: Uses representative volume elements (RVEs) MEMS: Piezoresistivity, electromechanical deflection due to electrostatic forces, and electrostriction. (Requires the MEMS Module) Multiphysics Couplings for Extended Structural Mechanics Analyses: Easily combine two or more physics interactions, all within the same software environment. - Thermal Stress: Thermal stress and expansion, with a given or computed temperature field, in solids, shells, and pipes. - Fluid–Structure Interaction (FSI): One-way or two-way couplings between a fluid and solid structure, including both fluid pressure and viscous forces. - Metal Processing: Stresses and strains of phase-composition-dependent materials during steel quenching and other heat treatment processes. - Multibody Dynamics: An extensive set of tools for simulating mixed systems of flexible and rigid bodies. - Piezoelectricity: Piezoelectric devices including metallic and dielectric components. - Acoustic–Structure Interaction: Solid–acoustic, acoustic–shell, and piezo–acoustic interactions, as well as vibration and elastic wave propagation. - Poroelasticity: Porous media flow coupled with solid mechanics to model poroelastic effects. - Hygroscopic Swelling: Absorption of moisture and hygroscopic swelling in polymers and batteries. - Electromagnetic Materials: Magnetostrictive, electrostrictive, and ferroelectric elastic devices. - Low-Frequency Electromagnetics: Deformations in electronic devices and electric motors due to electromagnetic forces. - RF and Microwave Components: Mechanical deformation and stress affecting the performance of RF and microwave devices and components such as filters. - Stress-Optical Effects: Stress-induced birefringence in waveguides. - STOP Analysis: Structural-thermal-optical performance (STOP) analysis on optical systems.
The Microfluidics Module is designed specifically for handling momentum, heat, and mass transport with special considerations for fluid flow at the microscale. What Can Be Modeled with the Microfluidics Module: Perform various microfluidics analyses with the COMSOL® software. - Lab-on-a-Chip Devices: Compute the radial pressure distribution and flow rate through a rotating lab-on-a-chip platform. - Microfluidic Channels: Infuse and flush connected pieces of equipment with a fluid. - Micropumps: Model microfluidic systems with applications ranging from biological fluid handling to microelectronic cooling. - Micromixers: Simulate rapid mixing of different fluid streams. - Inkjet Printing: Model the fluid flow in an inkjet to predict optimal inkjet design. - Drug Delivery: Describe the operation of a drug delivery system. - Fuel Cells: Study proton exchange membrane (PEM) fuel cell designs and construction challenges. - Electrowetting Optical Devices: Modify a contact angle by changing the voltage applied to the conducting liquid. - Electrokinetic Valves: Analyze pressure-driven flow and electrophoresis in a 3D microchannel system. - Detection Tests: Study possible symmetries in the spreading of a liquid sample in a test strip. Features and Functionality in the Microfluidics Module: The capabilities of the Microfluidics Module can address multiple simulation problems. - Single-Phase Flow: The Fluid Flow interfaces use physical quantities, such as pressure and flow rate, and physical properties, such as viscosity and density, to define a fluid flow problem. The Laminar Flow interface covers incompressible and weakly compressible flows. This interface also allows for the simulation of non-Newtonian fluid flow. An interface for creeping flow is used when the Reynolds number is significantly smaller than one. This is often referred to as Stokes flow and is appropriate for use when viscous flow is dominant. It is usually applicable to microfluidic devices. - Three-Phase Flow: The Laminar Three-Phase Flow, Phase Field interface is designed to track the interfaces between three immiscible and incompressible fluids. This multiphysics interface couples a Laminar Flow interface to a Ternary Phase Field interface. The flow is assumed to be laminar; that is, the Reynolds number is low to moderate, and the density of each phase is constant. The interface solves the Navier–Stokes equations for the conservation of momentum as well as the continuity equation for the conservation of mass. The interface position is tracked by solving four additional transport equations, two for the phase field variables and two for the generalized chemical potentials. The movement of the surface is determined by the minimization of free energy. - Transport of Species: The Microfluidics Module provides a dedicated interface for transport of diluted species. It is used to simulate chemical species transport through diffusion, convection (when coupled with fluid flow), and migration in electric fields for mixtures where one component — a solvent — is present in excess (90 mol% or greater). It is typically employed to model the performance of mixers and Marangoni effects driven by concentration gradients. For modeling of chemical reactions in microfluidic devices, the Microfluidics Module can be combined with the Chemical Reaction Engineering Module, which also makes available transport of concentrated species with binary diffusion. - Electrokinetic Flow: When modeling the transport of diluted species, the electromigration of ions in a static electric field can be included according to the Nernst–Planck equation. Applications of this functionality include electrophoretic mobility and electroosmotic flow. The Microfluidics Module can be combined with the Chemical Reaction Engineering Module to access the Nernst–Planck interface and Electrophoretic Transport interface, which are dedicated to the modeling of electrolytes and can include the formulations of Poisson’s equation or the electroneutrality condition for the charge balance. The combination of Nernst–Planck and Poisson's equations can be used for modeling charged double layers and electroosmotic flow. - Two-Phase Flow: Three different methods are available in the Microfluidics Module for modeling two-phase flow: level set, phase field, and moving mesh methods. These are used to model two fluids separated by a moving fluid interface, where the interface is tracked in detail, including surface curvature and surface tension forces. The level set and phase field methods use a fixed background mesh and solve additional equations to track the interface location. The moving mesh method solves the flow equation on a moving mesh, and boundary conditions representing the fluid interface are directly applied at the surface. In this case, additional equations are solved for the mesh deformation by means of the arbitrary Lagrangian–Eulerian (ALE) method. All of these methods and their interfaces support both compressible and incompressible laminar flows, where one or both fluids can be non-Newtonian. - Porous Media Flow: Porous media flow can also occur in microscale geometries. When the pore size is in the micron range, the flow is often friction-dominated; in such cases, Darcy’s law can be used to solve the flow. The Microfluidics Module features a dedicated interface for porous media flow based on Darcy's law. In this case, shear stresses perpendicular to the flow are neglected. For intermediate flows, an interface for the Brinkman equations is available. This interface models flow through a porous medium where shear stresses cannot be neglected. There is support for both the Stokes–Brinkman formulation, suitable for very low flow velocities, and Forchheimer drag, which is used to account for effects at higher velocities. The fluid can either be incompressible or compressible, provided that the Mach number is less than 0.3. The formulation allows for free and porous media models, including porous media using the Brinkman equations or laminar flow. These interfaces are appropriate for microfluidic porous media flow. Example applications include paper microfluidics and transport in biological tissue. - Rarefied and Slip Flow: Rarefied gas flow occurs when the mean free path of the molecules becomes comparable with the length scale of the flow. The Knudsen number, Kn, characterizes the importance of rarefaction effects on the flow. As the gas becomes more rarefied (corresponding to how high the Knudsen number is), the Knudsen layer — which is present within one mean free path of the wall — begins to have a significant effect on the flow. For Knudsen numbers below 0.01, rarefaction can be neglected, and the laminar flow interfaces of the Microfluidics Module can be used with nonslip boundary conditions. For slightly rarefied gases (0.01 < Kn < 0.1), the Knudsen layer can be modeled by appropriate boundary conditions at the walls together with the continuum Navier–Stokes equations in the domain. In this instance, a Slip Flow interface is available in the Microfluidics Module. To model higher Knudsen numbers, the Molecular Flow Module is required. Expanded Modeling with the Microfluidics Module: As with the other products in the COMSOL product suite, when the Microfluidics Module is added to COMSOL Multiphysics®, the features and functionality are fully integrated into the modeling workflow and are ready to be used with other modules. For instance, the Microfluidics Module can be combined with the: - Heat Transfer Module to model thermal flows as well as conduction, natural and forced convection, Joule heating, thermophoresis, and Marangoni effects - AC/DC Module to study the effects of magnetophoresis and magnetohydrodynamics - Structural Mechanics Module to perform fluid–structure interaction simulations for fixed and deforming geometries with single-phase or multiphase flow - Chemical Reaction Engineering Module to model chemical reactions and transport of concentrated species and to access advanced capabilities for modeling transport of electrolytes and ions with electric fields as driving forces
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Model transport phenomena and chemical reactions relevant to various industries with the COMSOL® software. What Can Be Modeled with the Chemical Reaction Engineering Module: - Bulk Chemicals: Simulate space-dependent continuous stirred mixers and tank reactors for high flow rates. - Specialty Chemicals: Study reaction kinetics and mass transport to design processes for the fine chemicals industry, such as extraction and distillation processes. - Biotechnology and Pharmaceuticals: Optimize designs and processes for biotech and pharmaceutical applications by modeling the transport and reactions of drugs in tissue and across membranes. - Food Processing: Investigate heat transfer and reactions during pasteurization or study other processes in the food industry, such as drying, cooking, and fermentation. - Petrochemical: Model catalyst deactivation and pressure losses in packed bed reactors. - Environmental Technology: Investigate the elimination of pollutants in effluent streams using separation processes such as adsorption, membrane filtration, and crystallization. - Semiconductors: Study the rate of chemical vapor deposition (CVD) as a function of fluid flow and reaction kinetics in a CVD boat reactor. - Consumer Products: Design static mixers for laminar flow —such as mixers for epoxies, silicones, and acrylic resins — that achieve the desired emulsion properties. - Polymers: Study different aspects of polymer production processes, such as the dissolution of reactants, polymerization reactions, curing reactions, and filtration of the product stream. - Agricultural Chemicals: Investigate optimal process conditions and reactor design for the production of fertilizers, pesticides, and herbicides. Overview of the Modeling Strategy and Workflow: Realistic descriptions of reacting systems in scientific and engineering studies often need to incorporate both transport phenomena and chemical reactions. The Chemical Reaction Engineering Module includes features for following the typical workflow in chemical and chemical engineering investigations, which involves the following incremental steps: - Study reaction mechanisms in ideal, perfectly mixed systems - Calculate kinetic, thermodynamic, and transport properties - Extend the investigations to space-dependent system components that include: Transport of chemical species, Heat transfer, Fluid flow, Electrokinetic effects This workflow can be applied in many different fields that involve chemical reactions and for modeling at different scales, such as for the modeling of nanotechnology and microreactors as well as for environmental studies and geochemistry. The entire process, from defining models to the presentation of the results, is documented in the software for transparency and reproducibility. Features and Functionality in the Chemical Reaction Engineering Module: The Chemical Reaction Engineering Module provides a built-in workflow for simulating perfectly mixed systems in 0D followed by transport phenomena in 2D and 3D. Defining Reaction Kinetics: The first step in modeling any system is to establish the material balances. With the Reaction Engineering interface, chemical equations can be input in order to automatically obtain the material balance equations for the chemical species in the system and the energy balance equations for the system. When a reaction mechanism is added, the kinetic expressions as a function of the species concentrations are derived automatically from the mass action law for elementary steps. Users can also input their own analytical expressions for the reaction rate as a function of the species concentrations and temperature. The material balances and the reaction kinetic expressions give the ordinary differential equations that are formulated automatically by the software. For a perfectly mixed batch reactor, the solution to the equations gives the composition of the reacting mixture over time. Generating Space-Dependent Models: A working model for a perfectly mixed system can be used to automatically define material, energy, and momentum balances for space-dependent systems. The transport properties calculated in the Reaction Engineering interface (for example, heat capacity, thermal conductivity, viscosity, and binary diffusivity) automatically transfer to the physics interfaces for chemical species transport, heat transfer, and fluid flow. This functionality allows for refining kinetics and thermodynamics expressions of chemical reactions before moving to 2D, 2D axisymmetric, and 3D models. Chemical Species Transport: Modeling transport phenomena in reacting systems involves the description of the chemical species in so-called multicomponent transport models. The Chemical Reaction Engineering Module includes sophisticated models for multicomponent transport in the Transport of Concentrated Species interface, which offers the Maxwell–Stefan formulation and the mixture-averaged models for multicomponent transport. For diluted solutions, the Transport of Diluted Species interface is available, which treats cases where the interactions in the solution are dominated by solute–solvent interactions. The Dispersed Two-Phase Flow with Species Transport interface can be used to describe chemical species transfer between two immiscible fluid phases. The chemical species transport equations are also available for including Knudsen diffusion in, for example, porous media. The dusty gas diffusion model is also included. The formulation of the mass balance model as well as the transport properties can be obtained directly from chemical equations when generating a space-dependent model from the Reaction Engineering interface. Electrokinetic Effects: When modeling the transport of diluted or concentrated species, electric fields can be included as driving forces for transport for the modeling of electrolytes and ions. The Nernst-Planck and Electrophoretic Transport interfaces are dedicated to the modeling of electrolytes and can include the formulations of Poisson’s equation or the electroneutrality condition for the charge balance in the electrolyte. Applications of this functionality include electrokinetic valves, electroosmotic flow, and electrophoresis. Thermodynamic Properties Database: The Chemical Reaction Engineering Module contains a thermodynamic properties database, which can be used to calculate properties for gas mixtures, liquid mixtures, gas–liquid systems at equilibrium (flash calculations), liquid–liquid systems, and gas–liquid–liquid systems at equilibrium. There is a variety of thermodynamic models that can be used to calculate density, heat capacity, enthalpy of formation, enthalpy of reaction, viscosity, thermal conductivity, binary diffusivity, activity, and fugacity. Read more about this functionality on the Liquid & Gas Properties Module page, which is included in the Chemical Reaction Engineering Module. The thermodynamic properties database can be used to create a so-called property package for a specific reacting system by selecting the chemical species present in the system, the desired properties, and the thermodynamic model. When defining reaction mechanisms, the reactants and products can be matched with the chemical species in the property package defined by the thermodynamic properties database. This matching automatically links the functions and equations generated by the property package to the model of the reacting system. Parameter Estimation: Analysis of systems of chemical reactions and reaction mechanisms usually rely on parameter estimation of frequency factors, activation energies, and other parameters that may quantitatively describe experimental observations. The Chemical Reaction Engineering Module includes dedicated features for parameter estimation, designed to optimize these parameters using data from multiple experiments. The typical workflow for the estimation of model parameters is as follows: First, the model parameters to estimate (such as the rate constants) are selected, and the initial values and scales for the parameters are defined. Then, the experimental data is imported and data columns are correlated with model variables by entering the proper variable names or expressions. Next, an optimization method is chosen and computed. The progress of the optimization can be inspected during computation. Once the optimal parameter values have been found, the results can be compared with experimental measurements. Fluid Flow: The fluid flow functionality included the Chemical Reaction Engineering Module can handle laminar and porous media flow. Additionally, when combined with the CFD Module, there are ready-made couplings for the modeling of chemical species transfer in turbulent flow. The formulation of the fluid flow model as well as the viscosity and density can be obtained directly from chemical equations when generating a space-dependent model from the Reaction Engineering interface. Heat Transfer: The heat transfer functionality included in the Chemical Reaction Engineering Module can account for heat transfer by conduction, convection, and radiation. The radiation term is given by surface-to-ambient radiation, while the Heat Transfer Module is required for surface-to-surface radiation and radiation in participating media. The heat transfer capabilities of the Chemical Reaction Engineering Module include heat transfer in fluids, solids, and porous media. The formulation of the heat transfer model, as well as the thermodynamic and transport properties, can be obtained directly from chemical equations when generating a space-dependent model from the Reaction Engineering interface. Surface Reactions and Heterogeneous Catalysis: Surface reactions are typical for heterogeneous catalysis as well as for surface deposition processes such as chemical vapor deposition. They are found in the bulk chemicals industry, such as in the Haber–Bosch process for the production of ammonia and in microsensors for the detection of very low amounts of tracers that can adsorb on surfaces and be detected by, for example, a change in electrical properties. In transport-reaction models, surface reactions can be treated as boundary equations coupled to the boundary conditions for the transport and reaction equations in the bulk. This would be typical for models below or up to the microscopic scale. Alternatively, in porous media, these reactions are treated in a similar fashion as homogeneous reactions but include the specific surface area (area per unit volume of the porous material) and the effective transport properties. This would be typical for models both in the microscopic scale and the macroscopic scale — so-called multiscale models. The Chemical Reaction Engineering Module includes ready-made formulations for heterogeneous catalysis for surface reactions on boundary faces as well as surface reactions distributed over a homogenized porous catalyst. For porous catalysts, multiscale models are predefined to describe bimodal pore structures. Such structures may consist of microporous pellets packed to form a macroporous pellet bed.
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Model Low-Temperature Plasma Sources with the Plasma Module What Can Be Modeled with the Plasma Module Simulate the behavior of plasmas subject to a variety of electromagnetic excitations. Inductively Coupled Plasmas Investigate how power couples to the plasma in an ICP reactor. Capacitively Coupled Plasmas Model CCP reactors using a dedicated interface that directly solves the time-periodic steady state. Inductively Coupled Plasmas with RF Bias Investigate how an inductively coupled RF bias influences an ICP reactor. Nonisothermal Plasma Flow Couple a plasma model with fluid flow and heat transfer. Electron Cyclotron Resonance (ECR) Plasma Sources Couple a plasma model with magnetic fields and electromagnetic waves to model an ECR plasma source. Microwave-Excited Plasmas Investigate the effects of microwave heating in a plasma. Direct Current Discharges Simulate discharges sustained by a DC voltage or current. Corona Discharges Compute the spatial distribution of charged species in corona discharges. Electric Breakdown Detect if a high-voltage DC system can cause gas breakdown. Electrostatic Precipitators Track charged particle trajectories and compute the transmission probability of an electrostatic precipitator. Plasma Arcs Simulate the temperature distribution in a plasma arc and surrounding materials. ICP Torches Investigate the electrical and thermal characteristics of an ICP torch at atmospheric pressure. Plasma Global Models Model plasma reactors using global models for fast parameterizations and complex chemistries, including the Boltzmann equation. Electron Energy Distribution Functions (EEDFs) Compute EEDFs and obtain electron transport parameters and source terms for use in fluid plasma models. Optimization for Plasma Uniformity Optimize the coil design and positioning of an ICP reactor to obtain plasma uniformity. Ion Energy Distribution Function Compute the ion energy distribution function at surfaces. Etching and Deposition Simulate etching and growth rates along a surface. Features and Functionality in the Plasma Module The Plasma Module provides specialized tools for modeling low-temperature and thermal plasmas. Nonequilibrium Plasmas The Plasma Module provides built-in interfaces for modeling low-temperature plasma reactors that are sustained by a static or time-varying electric field. These interfaces each define sets of domain equations, boundary conditions, initial conditions, predefined meshes, and predefined studies with solver settings for steady and transient analyses, as well as predefined plots and derived values. Transport equations for all species (electrons, ions, and neutrals) are solved self-consistently with Poisson's equation. The electrons' mean energy equation can also be solved by modeling how the electrons gain energy from the electric field and lose energy in collisions with the background gas. Plasma Chemistry Reactions The plasma chemistry is extremely important for obtaining realistic simulation results. The Plasma Module can be used to define electron impact reactions, reactions between heavy species, and surface reactions. The plasma chemistry dictates how electrons lose or gain energy in collisions with the background gas. The Plasma Module offers dedicated features for modeling electron impact reactions that can result in ionization, excitation, and attachment. Electron impact reactions can be defined from cross-section data, and source terms can be obtained by suitable integration over electron energy distribution functions. Multiphysics Interface for Modeling ICP Reactors The Inductively Coupled Plasma multiphysics interface is used to study discharges that are sustained by induction currents. This multiphysics interface connects the plasma conductivity from the Plasma interface to the Magnetic Fields interface and couples the resulting electron heating due to the induction currents back to the Plasma interface. The magnetic field is solved for in the frequency domain and the plasma is solved for in the time domain. Multiphysics Interfaces for Modeling Equilibrium Discharges The Plasma Module includes interfaces for modeling plasmas in thermodynamic equilibrium. In thermodynamic equilibrium, electrons and heavy species have the same temperature, and the plasma can be characterized by a single temperature. To model plasmas in such conditions, the Plasma Module offers several Equilibrium Discharges interfaces that couple electromagnetics, fluid flow, and heat transfer, incorporating Lorentz force, electromotive force, enthalpy transport, Joule heating, and radiation loss. Multiphysics Interface for Modeling Microwave Plasmas The Microwave Plasma multiphysics interface is used to study discharges that are sustained by electromagnetic waves (wave-heated discharge). When this interface is selected, a Plasma interface and an Electromagnetic Waves interface are automatically generated, as well as multiphysics couplings. The Plasma Conductivity Coupling feature couples the plasma conductivity to the Electromagnetic Waves interface, and the Electron Heat Source feature couples the resulting electron heating back to the Plasma interface. The electromagnetic waves are solved for in the frequency domain and the plasma is solved for in the time domain. Boundary Conditions for Plasma–Surface Interactions As a part of the built-in interfaces within the Plasma Module, there are a variety of boundary conditions to describe how a plasma interacts with a surface. For example, electron density and energy fluxes at a surface are easily defined by applying the Wall feature. This feature introduces losses by transport to the electron transport equations. Additional flux sources can be included, such as secondary electron emission and generic electron fluxes at a surface. Fluxes of charged particles are automatically computed at electrodes and can be added to model external circuits. If a dielectric is in contact with the plasma, the surface charge accumulation can be computed from the fluxes of charged species at the surface. Surface Chemistry Reactions The Plasma Module includes a range of functionality for modeling etching and deposition processes in semiconductor fabrication processes. It solves plasma transport equations fully coupled with surface reaction kinetics, enabling the dynamic exchange of species between the surface and the gas phase. Surface site occupancy models can be used to accurately capture self-limiting reaction mechanisms. Furthermore, surface reaction rates can be specified with energy-dependent reaction yield models, facilitating detailed simulation of mechanisms such as ion-enhanced etching and energy-selective surface modifications. Multiphysics Interfaces for Modeling ICP Reactors with RF Bias The Inductively Coupled Plasma with RF Bias interface is used to study discharges that are sustained by induction currents and by an RF bias. This multiphysics interface connects the plasma conductivity from the Plasma, Time Periodic interface to the Magnetic Fields interface and couples the electron heating resulting from the induction currents back to the Plasma, Time Periodic interface. The magnetic field is solved for in the frequency domain and the plasma is solved for in the time domain. Multiphysics Interfaces for Modeling Fluid Flow and Heat Transfer of Background Gases The Nonisothermal Plasma Flow interfaces combine plasma, fluid flow, and heat transfer interfaces to model background gas flow and heating in a plasma reactor. The heat transfer in the materials surrounding a plasma can also be simulated. The Nonisothermal Plasma Flow multiphysics feature automatically computes the heat source resulting from plasma reactions and inputs it into heat transfer interfaces as a volume heat source. Fluid and thermodynamic properties like viscosity and thermal conductivity are computed in the Plasma interface and passed automatically to fluid flow and heat transfer interfaces. Physics Interface for Modeling CCP Reactors The Plasma Module includes a specialized numerical method for modeling CCP with significantly faster computation times than traditional methods. Instead of solving in the time domain, the periodic steady-state solution is computed by adding an extra dimension to the underlying mathematical equations. This extra dimensional equation represents one RF cycle and enforces periodic boundary conditions. This avoids having to solve for tens or hundreds of thousands of RF cycles, which typically takes a long time before the plasma reaches the periodic steady-state solution. This approach maintains all the nonlinearity of the model while dramatically reducing computation time.
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LiveLink™ for MATLAB® provides the necessary tools for maximizing the use of COMSOL Multiphysics® and MATLAB® in combination. Run Multiphysics Simulations from MATLAB® LiveLink™ for MATLAB® provides commands in the MATLAB® scripting language, sent from MATLAB® to COMSOL Multiphysics®, that initiate simulations in COMSOL Multiphysics®. This can be used for automating modeling steps as well as integrating COMSOL Multiphysics® models with calculations performed in MATLAB®. LiveLink™ for MATLAB® uses the COMSOL application programming interface (API), which has all the necessary functions and methods for implementing models from scratch or updating settings in existing models. All aspects of COMSOL Multiphysics® modeling can be controlled using MATLAB® through the API, which is tightly integrated with the MATLAB® environment. LiveLink™ for MATLAB® enables users to perform geometry and mesh operations, change physics settings, run parametric studies, control solvers, and postprocess the results. Results can be extracted as numerical data and MATLAB® figures. Utility Tools for Managing Models from MATLAB® All COMSOL® model settings are available from the command line in MATLAB®. To help get acquainted with the model data structure and the model settings, LiveLink™ for MATLAB® comes with two utility tools for navigating and searching the model contents: the Model Navigator and Model Search tools. The Model Navigator provides an overview of the model structure in a model tree together with the model settings and the commands that can be executed for each part of the model. Using this tool, it is easy to extract commands for setting and finding model properties to use in custom scripts. The Model Search tool will search the COMSOL Multiphysics® model from the MATLAB® interface, helping to find expressions and variables used in a model. Several filters and search settings are provided to narrow the search. Furthermore, a model from MATLAB® and the COMSOL Desktop® can be accessed simultaneously. This way, the workflow that is best suited for the task at hand can be used. It may be preferable to perform some tasks using the command line and scripting, while other tasks may be more convenient to perform using the COMSOL Multiphysics® user interface. Manage and Create Geometry Models and Meshes from MATLAB® Running COMSOL Multiphysics® from MATLAB® provides a lot of flexibility when handling geometry models and meshes. From MATLAB® programs and the MATLAB® command-line interface, it is possible to: - Generate geometry objects with inputs from MATLAB® - Import and export CAD models in a range of industry-leading file formats 1 - Run simulations based on imported CAD models - Create, import, and export surfaces on the STL, 3MF, and PLY file formats - Plot geometry objects in MATLAB® figures - Obtain geometry information for points, edges, surfaces, and domains, e.g., for adjacency, curvature, distances, etc. - Convert an image to a 2D geometry - Generate meshes - Plot meshes in MATLAB® figures - Retrieve mesh information such as mesh statistics and other mesh data - Import and export mesh data Call MATLAB® Functions from the COMSOL Desktop® LiveLink™ for MATLAB® provides a direct connection to MATLAB® while running COMSOL Multiphysics®. It is possible to call MATLAB® functions from the COMSOL Multiphysics® user interface to define material properties, boundary conditions, and more. These MATLAB® functions can be evaluated while the model is solving. Additionally, a COMSOL simulation app can contain MATLAB® calls, in which case MATLAB® will automatically start when called during runtime. Integrate with Existing MATLAB® Programs For MATLAB® users, COMSOL Multiphysics® simulations can easily be integrated into existing code bases. A model that has been set up in the COMSOL Multiphysics® user interface can be saved to an M-file. This M-file then contains COMSOL® API calls, in MATLAB® syntax, for running COMSOL Multiphysics® functionality. This provides a quick and convenient way of automatically generating COMSOL® modeling code, which can be used as a starting point for further integration into MATLAB® programs. Using the automatic code generation tools provides a quick way to learn the COMSOL® API for MATLAB®, which is included in LiveLink™ for MATLAB®. The COMSOL® API is easy to learn and has an intuitive structure similar to the steps used when setting up models in the COMSOL Multiphysics® user interface using the Model Builder. Existing code that is based on MATLAB® toolboxes or custom code integrates easily with COMSOL Multiphysics® simulations. Users can even call COMSOL Multiphysics® from user interfaces that have been created using MATLAB®. This makes it possible to, for example, use MATLAB® for data preparation and postprocessing and COMSOL Multiphysics® for structural, fluid, electromagnetics, or other physics or multiphysics modeling. Simulations can then be carried out using a mix of programs and models created with MATLAB®, COMSOL Multiphysics®, and even other tools. Generate Plots in MATLAB® and Extract Data from COMSOL Multiphysics® All COMSOL Multiphysics® plots can be recreated in MATLAB®. All plot types can be generated as regular MATLAB® plots and can be saved or exported and manipulated like any other MATLAB® plot. From MATLAB® programs, COMSOL Multiphysics® expressions can be evaluated either locally at a few points or for larger portions of a model, such as along the edges, on surfaces, or in volumes. Users can access the raw solution data or processed data based on arbitrary expressions, including maximum, minimum, average, and integral values. The COMSOL Multiphysics® unit handling is fully supported for any type of extracted data, which means that it is possible, for example, to use unit handling in custom programs for unit conversion. Any numerical data from COMSOL Multiphysics® simulations can be retrieved and assigned to MATLAB® variables for further analysis. Low-level information that is directly related to mesh and shape function data can be extracted, as well as sensitivities and time and spatial derivatives. 1. Requires one of the following add-on products: the CAD Import Module, the Design Module, LiveLink™ for SOLIDWORKS®, LiveLink™ for Inventor®, LiveLink™ for Solid Edge®, LiveLink™ for AutoCAD®, or LiveLink™ for Revit®
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