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.
In this paper, an adaptive mesh refinement technique is presented in numeri-cal solution of partial differential equations. Mainly including scanning function,refining/ derefine, and the method has been implemented based on unstructuregrid and in Lagrangian or in Eulerian. Results are very helpful to the study of thenumerical simulation of detonation and study of explosive performances.
