Consistent Representation of PDE and DAE Problems in Modelica

Modelica is an object-oriented equation based language for modeling of large,complex,and heterogeneous physical systems.It has been relatively mature for modeling and simulation of differential-algebraic equations(DAEs) systems,while lacks effective modeling of partial differential equations(PDEs) problems.Based on the object-oriented idea,a method of consistent representation of PDE and DAE problems was proposed,Modelica language was extended to support modeling of three-dimensional PDE problems.Then the PDE model was transferred into DAE model with the method of lines,and was solved in MWorks platform based on Modelica.To illustrate the application of our method,a heat conduction problem was modeled and simulated in Modelica.