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My research is centered around the Conservation Element and Solution Element (CESE) method.
The CESE Method
The CESE method is a time-accurate numerical algorithm for systems of first-order hyperbolic partial differential equations (PDEs). The CESE method intrinsically uses unstructured mesh for spatial discretization, and can easily handle complex geometry.
A big category of physical phenomena is governed by first-order PDEs, and usually referred as conservation laws. They include Euler equations, Navier-Stokes equations, Maxwell equations, elasto-dynamic equations, etc. Since the CESE method targets the mathematical form of the equations, it can easily adapt to various physical models.
In order to better exploit the multi-physics and easy-to-parallelize nature of the CESE method, I am working on a software framework (Solvcon) for the method, using 2/3D unstructured mesh of mixed elements. You can contact me if you are interested in it.