Extending Modelica for Partial Differential Equations

Currently, Modelica only supports models containing constants, time-dependent variables, and time-derivatives of variables, i.e. ordinary differential and algebraic equations. In this article, we present how the Modelica language can be extended to support object-oriented modeling with partial differential equations (PDEs), in order to solve initial and boundary value problems. The techniques we present have fairly general applicability to 1D, 2D or 3D domains, although we focus mostly on 2D domains in this paper. We also describe the architecture of a prototype implementation where the PDE problem is translated and passed to an external mesh generator and a PDE solver for solution using the finite element method. An example of a stationary heat conduction problem is included together with execution results.