Support for Dymola in the Modeling and Simulation of Physical Systems with Distributed Parameters

Farid Dshabarow
Institute of Computational Science
ETH Zürich
CH-8092 Zürich
Switzerland
Email: DFarid@Student.ETHZ.CH

Abstract

The thesis title ”Support for Dymola in the Modeling and Simulation of Physical Systems with Distributed Parameters” could appear a little bit confusing. In short, the goal of the master thesis is to provide Dymola with a Partial Differential Equations (PDE) Package, with which it will be possible to simulate physical systems for example. The PDE area is huge and it is therefore not possible to implement everything. For instance, the methods of solving PDEs are many, ranging from analytical to semianalytical to fully numerical. The methods implemented in PDE Package are Method of Lines (MOL) and Finite Volume Methods (FVM). Among many types of PDEs we considered only time-dependent PDEs, because Dymola was conceived mainly to simulate the quantities in time. Recently, however, a time independent problem, the Poisson equation, was also implemented and works well. The PDE Package provides necessary blocks for the implementation of PDEs, such as integrators and space derivatives blocks. Many examples were implemented with both MOL and FVM to show the use of PDE Package. Some examples are implemented together with the corresponding analytical solution so that the user can see the error of the approximation. To make everything transparent to the user the methods are implemented in such a way that user must not understand the details of the numerical methods that solve the PDEs. What is required from the user is that he knows the complete problem (PDE, initial condition, ...) that he wants to implement. The blocks necessary for the implementation of the problem are provided, and explanations of how to use them is described in the corresponding documentation. As already said, many PDEs, ranging from simple, like advection equation, to more complex, like Euler equations, are implemented to show the user the correct use of the package.

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