Outline COMSOL Multyphysics: • Basic concepts and modeling paradigm Overview of software package • Overview of capabilities and capabilities • Steps in setting-up a model • Hands on: assembling and running sample Lecture 5 models • Next time: Brief literature survey of Special Topics: problems/results Device Modeling COMSOL Multiphysics COMSOL: Physics-based Introduction modeling (main program) • Partial differential equation solver package with front-end developed for visual input and output • Electrostatics, and electric currents • Most used through different “modules” with • Heat transfer in solids and fluids predefined “physics”, greatly simplifying modeling • Joule heating of device geometry, governing equations, boundary • Laminar flow conditions, etc. • Pressure acoustics – Also takes input in terms of user-defined equations • Solid mechanics • Available across platforms (Windows, MAC, • Transport of diluted species Linux); since version 5 can create modeling apps • Additional physics interfaces through modules COMSOL Multiphysics: modules COMSOL Multiphysics: modules 1 COMSOL Multiphysics: COMSOL modeling flow available modules • Select the appropriate model attributes (Wizard) – Dimension 3D vs.2D vs. 1D, etc. – Choose physics elements • Draw or import the model geometry, add materials • Set up the subdomain equations (satisfied internally within geometry) and boundary conditions • Mesh geometry Modules available in P&A computer • Solve the model room for the • Apply postprocessing, plot results duration of course Creating a new model Creating a new model • The two main components of the COMSOL Desktop environment are the • When open COMSOL Multiphysics model or Model Builder and Application Builder create a new model, you follow the Model Builder • The Model Builder is the tool where tree: here you add nodes, populate parameters, and you define the model and its control all program settings components; accomplished by building a model tree • Start with Model Wizard: select model dimension, • The Application Builder allows you to physics elements, and study type (stationary, time- create an application (with a specialized dependent, etc.) user interface) based on a model • Alternatively, start with Blank model and add created with the Model Builder components, physics, study type, etc. to the tree Adding global parameters Setting up geometry • Global Definitions (top of the Model Builder tree) • Select model dimension first • Specify parameters applicable to the whole model • Create geometry in COMSOL – Parameterizing geometric dimensions – Work Plane with 2D geometry modeling – Specifying mesh element sizes – Defining parametric sweeps • Or import geometry file – Specify value, units in [] – will be converted to the standard units (e.g., – The DXF (2D), VRML (3D), and STL (3D, used for 3D degF – degree on the Fahrenheit scale, standard unit of T is K, Kelvin) printing) file types are available for import without any • All expressions are evaluated before a simulation begins, add-on products therefore may not depend on the dependent variables for – Other CAD files are supported with add-on CAD Import which your equations are solving (including time and Module and LiveLink products for CAD; expand coordinates) import/processing functionality 2 Setting up geometry Adding materials Creating geometry in COMSOL from the Work Plane: • Material can be added from Materials library (either • Start with 2D geometry modeling, then use extrude, global, or local) revolve, sweep to convert to 3D – Each material is specified in terms of relevant parameters, e.g., thermal expansion coefficient • Primitive solid objects: block, cone, cylinder, sphere, – Properties required by the physics but missing in the etc.; parametric helix, curves, surfaces material are marked with a warning sign • Interpolation curves; boolean operations union, – Blank material with user-defined properties can be added intersection, difference, and partition • Extended Material library can be added as a module • Hybrid modeling with solids, surfaces, curves, and (2,500 materials) points Applying physics to your model Meshing • Connect geometry (domains and sub-domains) • Free tetrahedral meshing with governing equations • Swept mesh with prism and hex elements • If use different physics (e.g., electrical currents • Boundary layer meshing and heat transfer), add Multyphysics node, • Free triangular meshing of 3D surfaces and 2D models containing coupled physics features (e.g., electromagnetic heat source term) • Mapped and free quad meshing of 3D surfaces and 2D models • Specify boundary conditions (initial values) for each physics input; verify default assignments, • Copy mesh operation; virtual geometry operations override as needed • Mesh partitioning of domains, boundaries, and edges Solving your model Results • Choose study type: stationary, time-dependent, • Visualization: surface, isosurface, arrow, slice, eigenvalue, etc. streamline, and contour plots • Corresponding solver will be utilized • Export graphs as images and data (not straight- • Specify solver configuration information: which forward for 3D plots) physics interface and geometry to use, which • Post-processing variables to solve for, and which solvers to use for – Integration, average, max, and min of arbitrary the type of study to perform quantities over volumes, surfaces, edges, and points • May want to examine initial values – Custom mathematical expressions including field variables, their derivatives, spatial coordinates, time, • Compute the model – switch to the Results node and complex-valued quantities 3 Report generation Connecting to other packages • To document your models, the COMSOL Report • COMSOL provides access to scripting Generator provides a comprehensive report of the environment through LiveLinks (up to version 3.4 entire model, including graphics and parameters of there was an internal scripting language) the geometry, mesh, physics parameters, boundary • In addition to CAD-type programs, LiveLink conditions, and postprocessing quantities interfaces are available for Excel and Matlab • You can save the report as an HTML (with all • Data processing (e.g., statistical analysis), access links) or Word (with TOC) file for viewing and to modeling tools from Excel/Matlab interface further editing Connecting to other packages COMSOL Multiphysics • The native COMSOL model file format is *.MPH – Full MPH-files include all meshes and solutions (can be huge) – Compact MPH-files include all settings but has no built meshes and solution data to save space; can open these to study the settings, to mesh and re-solve • COMSOL can save a model as *.java,*.vba or *.m file – Compile Java files and run as separate applications – Use with Excel’s VBA (Visual Basic for Applications) Use topic-based help: – Edit with Matlab scripting environment press F1 click ? access from File->Help Model for hands-on: Electrical Some drawbacks of COMSOL Heating in a Busbar • The error messages are often obscure • Example 2 from • Model inconsistencies are difficult to Introduction to COMSOL Multiphysics, ver. 5.2 identify (user-related mostly) • The resistive (ohmic) • Backward compatibility is problematic heating Qe due to the electric current • Inter-module+main program compatibility • Solve for electric potential is problematic (do not add physics from and temperature modules if not necessary) • Potential applied to Bolt 1; Bolts 2a,b are at ground • Busbar is in air, cooled by convection 4 Model for hands-on: Electrical Model for hands-on: Electrical Heating in a Busbar Heating in a Busbar • Governing equations: • Solver does Laplace equation for electric (k T ) Q e Q 0 0 potential with boundary conditions Q 0 h(Text T ) • From V – finds E, from E finds J, from J·E – heat source Q Q e J E e 2 J 0, J sE , E V V 0 • Next, heat transfer equation is solved: Poisson Parameters: equation for temperature with Qe heat source and Heat source Qe due to the electric current; heat sink Q0 due to convection heat sink convection; solid thermal conductivity k, temperature T, electric conductivity s; J - current density (A/m2), E - electric field strength (V/m) Model for hands-on: Electrical Summary Heating in a Busbar • COMSOL Multiphysics is a versatile • Introduction to COMSOL Multiphysics commercial PDE solver provides step-by-step guide • A number of sample models available for • Extension of the electrical heating problem: each module – Add structural mechanics: solve for Joule heating and thermal expansion • Well-developed run-time (through Excel, – Add cooling by airflow: solve for fluid flow MatLab) and post-processing facilities and Joule heating • Capabilities to develop apps with desired user interface for model distributions References • Introduction to COMSOL Multiphysics, www.comsol.com • W. B. J. Zimmerman, Multiphysics modelling with finite element methods, World Scientific, 2008 5.