Kershaw scheme is not positivity-preserving. Negative values emerge in numerical simulation for anisotropic diffusion equations on both orthogonal and distorted meshes. A conservative enforcing negative value to zero(CENZ) algorithm is proposed, which is an improvement of traditional method. It not only repairs numerical solution nonnegative, but also keeps local conservation of energy fluxes. Numerical examples demonstrate that the method is not limited by anisotropic ratio of diffusion coefficients. The algorithm can be used for numerical solution of finite volume schemes which violate monotony or positivity-preserving.

A structured grid generation method for domains with complicated boundary is discussed.Based on the Winslow method with variational form,and combined with grid untangling and area averaging technologies,a discrete functional is designed. The minimization of the discrete functional is solved by an optimization algorithm,and good grids are generated.Numerical experiments show that the method is robust and generates grids with good geometric qualities on complicated domains.This method inherits advantages of the Winslow method and overcomes some faults.

Combining reference Jacobian method(RJM) with advancing-front method,we present a strategy named advancing reference Jacobian method(ARJM).It advances the optimization process step by step from one part of the computational region boundary to the remaining parts.In each step,two neighboring rows(or columns) are taken as the boundaries of the sub-region and the rear row(column) nodes are the optimized ones and the middle row(or column) is optimized by RJM. Analyses and numerical experiments show that the ARJM is much faster than RJM.The geometric qualities of rezoned grids by ARJM are equal to or even better than those by RJM.The rezoned grids obtained by ARJM are closer to Lagrangian grids than those by RJM.

A scheme for unstructured quadrilateral mesh generation based on Delaunay triangulation is presented.With a front edge definition we mark a triangle mesh in the front edge.According to triangle mesh shape and directionality two triangular meshes are merged into a quadrilateral mesh. A 100% quadrilateral mesh obtained converts a quad-dominant to an allquad mesh with mesh conversion templates.Numerical results are shown.