A small modification of interpolation method for diffusion coefficients at boundary interfaces

Abstract

In this paper, a small modification of interpolation method for diffusion coefficients at boundary interfaces is presented. A one dimension steady source-free diffusion equation with variable diffusion coefficient is taken as an example to verify the effectiveness of the modification. The existing interpolation method used in literatures for computing diffusion coefficients at boundary interfaces is analyzed, the existing method seems reasonable in physics but not in mathematics, and it is accurate only if diffusion coefficients are constant or weakly nonlinear. The conclusion that diffusion coefficients at boundary interfaces should be specified by interior nodes near the boundary, is thus derived, such as λb should be specified by λP. The modification is evaluated by solving several diffusion problems with non-linear diffusion coefficients. Numerical tests show that the modification proposed in this paper can obviously improve the accuracy of non-linear diffusion coefficients problems numerical solution. More reasonable solutions can be obtained through the modified method, Especially for the problem IX the average error is reduced from 24.94 to 9.94e−1.