![]() Using two scalar Coefficient Form PDE interfaces is very similar to using predefined physics interfaces. ![]() Joule Heating as a System of Two Scalar Coefficient Form PDE Interfaces Using Coefficient Form PDE, there are two ways of entering this equation system: as a system of two scalar Coefficient Form PDE interfaces or as a system of one vector-valued Coefficient Form PDE interface with two vector components, and. We need to compare with the transient version of Coefficient Form PDE: This means that for the stationary version of Coefficient Form PDE: We can identify the first equation as Poisson's equation. For this, we can use what we learned in the Learning Center article on modeling with PDEs for diffusion-type equations. Here, we will focus on using the Coefficient Form PDE interface. To learn more about using the built-in options, see our Learning Center course on defining multiphysics models.Īs an alternative to using the built-in physics interfaces, you could instead define this system of equations using the Coefficient Form PDE interface, General Form PDE interface, or Weak Form PDE interface. There are multiple ways of defining a Joule heating system of equations in COMSOL Multiphysics ®. Note that the Joule heating source term can also be written as: The second equation is the heat transfer equation with a Joule heating source term. The first equation is that of conservation of currents. Where is the electric conductivity, is the density, is the heat capacity, and is the thermal conductivity. When the equation system represents Joule heating, the system of PDEs can be written as: ![]() Joule Heating and Variables that Represent Different Physics In this article, we will look more closely at the case of Joule heating, a system of type 1, as mentioned here. In such cases, the dependent variables frequently represent the components of a vector or tensor field, such as the displacement field components for structural mechanics. When the variables represent the same physics.One example of this is Joule heating where the dependent variables are the voltage,, and the temperature. When the variables represent different physics.There are several different types of equation systems that can be modeled using the equation-based, or Mathematics, interfaces. For a complete description of what options are available for modeling systems of equations, see the COMSOL Multiphysics Reference Manual documentation, specifically the Multiple Dependent Variables - Equation Systems section of the chapter, Equation-Based Modeling. Modeling with Multiple Dependent VariablesĪll PDE interfaces and equation forms support the use of multiple dependent variables in a system of PDEs, which can be coupled in several different ways. However, learning how to set up the corresponding equation system from scratch will prepare you for setting up more general systems, including systems that are not available as a built-in option in the COMSOL Multiphysics ® software. Using the predefined multiphysics interface for Joule heating is, of course, much easier and quicker for this type of modeling compared to implementing this by hand. As an example, we will use the Coefficient Form PDE interface to recreate the built-in functionality available in the Joule Heating multiphysics interface, available from the Model Wizard. In Part 6 of this course on modeling with partial differential equations (PDEs), we will learn how to use the PDE interfaces to model systems of equations. Modeling with PDEs: Multiphysics Systems of Equations
0 Comments
Leave a Reply. |
Details
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |