The compatibility of a nine-point difference scheme is studied in this paper.Based on this result, a new nine-point difference scheme is suggested for the nu-merical solution of nonlinear diffusion equation. The new scheme keeps the same advantages of the original one, i.e., simple in computation and easy to be imple-mented. Furthermore, the new scheme is more accurate than the original one if the mesh is non-smooth and high skewed, which is most important for Lagrange method in computational fluid dynamics.
Two dimensional three temperatures energy equation is a kind of very impor-tant partial differential equation. In general, we discrete such equation with full implicit nine points stencil on Lagrange structured grid and generate a non-linear sparse algebraic equation including nine diagonal lines. This paper will discuss the iterative solver for such non-linear equations. We linearize the equations by fixing the coefficient matrix, and iteratively solve the linearized algebraic equation with Krylov subspace iterative method. We have applied the iterative method presented in this paper to the code Lared-Ⅰ for numerical simulation of two dimensional threetemperatures radial fluid dynamics, and have obtained efficient results.
