PDEModelica1: a Modelica language extension for partial differential equations implemented in OpenModelica

Abstract

Modelica is a language for modeling complex physical systems. It supports algebraic and ordinary differential equations. This paper presents a Modelica language extension for one-dimensional evolutionary partial differential equations (PDE) called PDEModelica1, which is based on earlier extensions, establishes several enhancements, and its support is implemented in OpenModelica. PDEs are solved using the method of lines. In this paper, we discuss changes to and enhancements of previous extensions as well as the numerical methods used. To conclude, we present a counter-current heat exchange model with results to demonstrate the applicability of our extension.

Keywords:

• Modeling
• simulation
• partial differential equations
• Modelica
• language extension
• numerical methods
• counter-current heat exchange

Acknowledgment

We thank to Ivan Nagy and Peter Fritzson for help with preparing this manuscript, Kim Pederson and Veronika Sýkorová for proof reading it, and Klára Ulčová for preparing the art work.

Notes

1. OpenModelica (www.openmodelica.org) is a free, open-source project developed by the Open Source Modelica Consortium. Dymola is a commercial product of Dassault Systèmes. Several other Modelica tools exist.

2. First Faculty of Medicine, Charles University in Prague.

3. www.hummod.org.

4. www.physiomodel.org.

5. www.wolfram.com/mathematica.

6. The website for the project is: en.tongyuan.cc. We tried to simulate example models from papers in the demo version. MWorks was not able to translate them. The extension seems to be unknown to the compiler. The authors have not responded to our email communications, so the current status is unknown.

7. Personal communication with Peter Fritzson.