Strategies for mesh-handling and model specification within a highly flexible simulation framework Original Research Article

We describe an approach to solving a general system of coupled, nonlinear partial differential equations and their associated boundary conditions, by means of general discretization schemes, on an arbitrary triangular/rectangular mesh with emphasis on the techniques used to make the specification of the equations as simple as possible on a very general class of mesh. Both the mesh and the system of partial differential equations are specified in input files. Software has been implemented which permits a simple mesh-labeling system to be employed in the equation specification. The mesh can be divided into named regions and the labeling allows the equation specification to simply state by name to which region the equation applies without any restrictions. This greatly simplifies the setting up and modification of the geometrical and physical aspects of the problem specification. In addition, we show how complicated discretization schemes may easily be implemented as user-defined functions which the software can symbolically differentiate and symbolically manipulate as necessary for use during the solution procedure.