Solving PDE Models in Modelica

Modelica is a new object-oriented multi-domain modeling and simulation language and used for solving large, complex, and heterogeneous physical systems with differential-algebraic equations (DAEs). Presently there is no simulation support available in Modelica for solving partial differential equations (PDEs) problems. This paper describes how to solve the PDE models in Modelica and provides a preliminary PDE support for the language. The definition of PDE model in Modelica is briefly described. The method of lines, which transforms a PDE into a system of coupled DAEs, has been implemented with C++ language. The resulting DAE model can be solved by MWorks, which is a Modelica-based platform, without any syntax change of the Modelica language and is therefore very straightforward. To illustrate the applicability of our method, an example of two-dimension heat conduction problem is presented and solved in MWorks environment.