The goal of this project is to investigate, design and evaluate the extensions to the Modelica language that are needed to support modeling with PDE and specification of problems containing PDE, such as initial and boundary value problems. Also, the connection mechanism in Modelica will be generalized to support multi-dimensional connections. Furthermore, connections between DAE-based models that already are supported in Modelica, and PDE-based models will be defined, in order to support integrating PDE models with already existing Modelica models.
PDEs that can be specified should have generic form, for instance, where some components can be zeroes.
In order to specify models containing partial differential equations, the concept of domains and domain boundaries are needed in the language. A domain can be defined by describing its boundary. A new kind of Modelica class can be used to represent domains, with a section called boundary that describes its boundary using lines and parametric curves. A construct for composing separately defined boundaries is also needed, in order to describe more complex domains and also to assign boundary conditions to specific boundary parts. For example, an arc that can be used when defining domains can be written as follows:
domain Arc parameter Real r=1, a=1; boundary curve(r*cos(a*u), r*sin(a*u)) where u in (0,2*PI); end Arc;A domain consisting of an arc an a line can then be defined as:
domain HalfCircle Arc arc(a=0.5, r=2); Line line(x0=-2, y0=0, x1=2, y1=0); boundary composite(arc, line); end Arc;
model PDEModel HalfCircle mydomain; ... equation mydomain.line.bc = isolated; mydomain.arc.bc = conducting; end HalfCircle;Software we use for solution:
- Papers are available from the author's home page.
- Supported by VISP (Vinnova)
- Contact: Levon Saldamli,
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Last updated: 2012-05-07