Mathematical Modeling and Analysis
Mathematical Modeling and Analysis
As mathematical modeling of fluid flow becomes more sophisticated, the need for discretization methods handling meshes with mixed types of elements is arisen. Practice experiences show that the most effective discretization methods preserve and mimic the underlying properties of original continuum differential operators. Conservation laws, solution symmetries, and the fundamental identities and theorems of vector and tensor calculus are example of such properties.
We developed a new family of mimetic discretizations for diffusion-type equations (e.g. pressure equation in porous medium applications) on general polygonal meshes. The discretizations are locally conservative and use discrete flux and divergence operators which preserve the symmetry property of continuous operators, i.e. they are adjoint to each other. The discretizations are exact for uniform flows, second order accurate for general flows and result in symmetric positive definite coefficient matrix.
