PDEModelica - Towards a High-Level Language for Modeling with Partial Differential Equations

Abstract: This thesis describes initial language extensions to the Modelica language to define a more general language called PDEModelica, with built-in support for modeling with partial differential equations (PDEs). Modelica® is a standardized modeling language for objectoriented, equation-based modeling. It also supports component-based modeling where existing components with modified parameters can be combined into new models. The aim of the language presented in this thesis is to maintain the advantages of Modelica and also add partial differential equation support.Partial differential equations can be defined using a coefficient-based approach, where a predefined PDE is modified by changing its coefficient values. Language operators to directly express PDEs in the language are also discussed. Furthermore, domain geometry description is handled and language extensions to describe geometries are presented. Boundary conditions, required for a complete PDE problem definition, are also handled.A prototype implementation is described as well. The prototype includes a translator written in the relational meta-language, RML, and interfaces to external software such as mesh generators and PDE solvers, which are needed to solve PDE problems. Finally, a few examples modeled with PDEModelica and solved using the prototype are presented.