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A Finite Volume Method For Solving Parabolic Equations On Logically Cartesian Curved Surface Meshes, Donna Calhoun, Christiane Helzel
A Finite Volume Method For Solving Parabolic Equations On Logically Cartesian Curved Surface Meshes, Donna Calhoun, Christiane Helzel
Donna Calhoun
We present a second-order, finite-volume scheme for the constant-coefficient diffusion equation on curved, parametric surfaces described via smooth or piecewise smooth mappings on logically Cartesian meshes. Our method does not require analytic metric terms, shows second-order accuracy, can be easily coupled to existing finite-volume solvers for logically Cartesian meshes and handles general mixed boundary conditions. We present numerical results demonstrating the accuracy of the scheme, and then use the scheme to solve advection-reaction-diffusion equations modeling biological pattern formation on surfaces.