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

Description

Unfortunately, Dymola offers until now almost no support in the modeling of systems with distributed parameters. Although it is always possible to discretize partial differential equations by means of the method of lines [2] in such a way that a set of ordinary differential equations results, such models can then not be conveniently assembled in a graphical fashion. Furthermore, the resulting code is frequently not suitable for simulation.

In particular, the numerical simulatability of partial differential equations of the hyperbolic type depends heavily on the selected discretization method. For this reason, the user is forced to deal with problems that he or she usually knows little about.

An old demand in the software support of modeling tasks is that the user may concentrate on the physics of the system that he or she is trying to model, whereas the details of the numerics of the underlying algorithms, i.e., of the differential equation solver, can be relegated to the software.

In the modeling of systems with distributed parameters, we are still miles away from satisfying this demand.

The proposed MS research project shall provide a contribution to the satisfaction of this demand.

Tasks to be tackled

In particular, we wish to study the algorithm of discretizing the spatial axis using finite differences (method of lines) while applying the upwind discretization technique [2,4]. Also, we wish to study the method of finite volumes [5] with logarithmic reconstruction [3]. Finally, we shall also look at a method of spatial discretization by means of finite differences with adaptive grid width control.

Try to discover the communalities of the three methods, so that the three algorithms are being combined in a single code controlled by a method selection parameter. The code should be programmed as much as possible in an object-oriented fashion.

Design an appealing graphic surface that supports the modeling of systems with distributed parameters and that protects the user as much as possible from having to understand the details of the numerics of the underlying algorithms.

References

1. Brück, D., H. Elmqvist, H. Olsson, S.E. Mattsson (2002), Dymola for Multi-Engineering Modeling and Simulation, Proc. 2^nd International Modelica Conference, Oberpfaffenhofen, Germany, pp. 55:1-55:8.

2. Cellier, F.E. and E. Kofman (2006), Continuous System Simulation, Springer-Verlag, New York.

3. Díaz López, J. (2006), "Shock Wave Modeling for Modelica.Fluid Library Using Oscillation-free Logarithmic Reconstruction," Proc. 5^th International Modelica Conference, Vienna, Austria, Vol. 2, pp. 641-649.

4. Carver, M.B., D.G. Stewart, J.M. Blair, W.N. Selander (1978), The Forsim VI Simulation Package for the Automated Solution of Arbitrarily Defined Partial and/or Ordinary Differential Equation Systems, Atomic Energy of Canada, Chalk River Nuclear Laboratories.

5. Levecque, R.J. (2002), Finite Volume Methods for Hyperbolic Problems, Cambridge Texts in Applied Mathematics, Cambridge University Press.