A New Adaptive Numerical Solver for Heat Conduction Equation with Discontinuous Diffusion Coefficient
SONG Shuhong1, WANG Shuanghu1,2,3
1. Institute of Applied Physics and Computational Mathematics, Beijing 100094;2. National Key Laboratory of Computational Physics, Beijing 100088;3. Center for Applied Physics and Technology, University of Peking University, Beijing 100871
In this paper, a high accuracy numerical simulative method is studied for heat conduction equations with discontinuous diffusion coefficient on large fluid distortion grids. This method applies a so-called "twin-fitting" approximate method proposed in this paper to the calculation of fluxes on edges, then improves calculational accuracy of fluxes on edges with discontinuous diffusion coefficient, at last is given some related error analysis. In two dimension case, an adaptive and high accuracy method is constructed to calculate fluxes on edges, here the "adaptive" means to determine the stencils and the weights adaptively. Numerical experiments show that this method can be accommodated to large fluid distortion grids and the difficult case of discontinuous diffusion coefficient.