COMSOL PDE方程应用.pdf

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Equation-Based Modeling © Copyright 2014 COMSOL. COMSOL, COMSOL Multiphysics, Capture the Concept, COMSOL Desktop, and LiveLink are either registered trademarks or trademarks of COMSOL AB. All other trademarks are the property of their respective owners, and COMSOL AB and its subsidiaries and products are not affiliated with, endorsed by, sponsored by, or supported by those trademark owners. For a list of such trademark owners, see www.comsol.com/trad emarks

Multiphysics and Single-Physics Simulation Platform • Mechanical, Fluid, Electrical, and Chemical Simulations • Multiphysics - Coupled Phenomena – Two or more physics phenomena that affect each other with no limitation on • which combinations • how many combinations • • Single Physics – One integrated environment – different physics and applications – One day you work on Heat Transfer, next day Structural Analysis, then Fluid Flow, and so on – Same workflow for any type of modeling Enables cross-disciplinary product development and a unified simulation platform

Highly Customizable and Adaptable • Create your own multiphysics couplings • Customize material properties and boundary conditions – Type in mathematical expressions, combine with look-up tables and function calls • User-interfaces for differential and algebraic equations • Parameterize on material properties, boundary conditions, geometric dimensions, and more • High-Performance Computing (HPC) – Multicore & Multiprocessor: Included with any license type – Clusters & Cloud: With floating network licenses

Product Suite – COMSOL 4.4

When is Equation-Based Modeling Needed? • Try to avoid equation-based modeling if possible! – Using built-in physics interfaces enables ready-made postprocessing variables and other tools for faster model setup with much lower risk of human error • Applications that previously required equation-based modeling but now has a dedicated physics interface: – Fluid-Structure Interaction (Structural Mechanics Module, MEMS Module) – Surface adsorption and reactions (Chemical Reaction Engineering Module, Plasma Module) – Shell-Acoustics and Piezo-Acoustics (Acoustics Module) – Thermoacoustics (Acoustics Module) – and many more…

When is Equation-Based Modeling Needed? • Try to avoid equation-based modeling if possible! • But: we don’t have every imaginable physics equation built- into COMSOL (yet!). So there is sometimes a need for custom modeling.

Custom-Modeling in COMSOL • COMSOL Multiphysics® allows you to model with PDEs or ODEs directly: – Use one of the equation-template user interfaces • You do *not* need to write “user-subroutines” in COMSOL to implement your own equation! – Benefit: COMSOL’s nonlinear solver gets all the nonlinear info with gradients and all. Faster and more robust convergence.

Customization Approaches • Four modeling approaches: 1. Ready-made physics interfaces 2. First principles with the equation templates 3. Start with ready-made physics interface and add additional terms. 4. Start with a ready-made physics interface and add your own separate equation (PDE,ODE) to represent physics that is not already available as a ready-made application mode • Also: – The Physics Builder lets you create your own user interfaces that hides the mathematics for your colleagues and customers

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