The Method of Solving PDE and DAE Coupling System

Modelica is a multi-domain unified modeling language for modeling and simulation of large and complex physical systems.However, it deals only with differential-algebraic equation (DAE) and no partial differential equation (PDE) .A method of solving PDE and DAE coupling system was presented.The unknown field function of PDE was first approximated with a radial basis function with the form of temporal-spatial variables separation.Then the space variables of PDE were discretized by the collocation method and thus, the PDE was transformed into a series of DAEs.The coupling system was finally solved by the mature DAE solver in MWorks platform based on Modelica.The value of field function at any time-space point was obtained.Resultsshow that this method realizes the consistent solution of PDE and DAE coupling system under the premise of not changing the Modelica grammar, and has high accuracy, good stability, and the convenience of dealing with boundary conditions.