Based on physical flux Kershaw scheme is extended to multi-block glids and algorithms for degenerative connection or strong connection unstructured points are shown.Flux continuity condition is met in the extended Kershaw scheme on multi-block girds which keeps energy conservation.Three numerical examples show good agreement with exact solutions. It validates accuracy and robustness of the extended Kershaw scheme on multi-block grids.

Over the past two decades there have been many research activities in the design and application of high order accurate numerical methods in computational fluid dynamics (CFD). High order methods are especially desirable for simulating flows with complicated solution structures. We give a review on the development and application of several classes of high order schemes in CFD, mainly concentrating on the simulation of compressible flows. An important feature of the compressible flow is the existence of shocks, interfaces and other discontinuities and often also complicated structure in the smooth part of the solution. This gives a unique challenge to the design of high order schemes to be non-oscillatory and yet still maintaining their high order accuracy. We concentrate our discussion on the essentially non-oscillatory (ENO), weighted ENO (WENO) finite difference,finite volume schemes and discontinuous Galerkin (DG) finite element methods. We attempt to describe their main properties and their relative strength and weakness. We also briefly review their developments and applications, concentrating mainly on the results over the past five years.

A nine-point rezone strategy is presented,which improves geometric quality of computational grids and keeps the rezoned grids close to Lagrangian meshes.The scheme is proved an approximation to elliptic equation with spherical symmetry.Numerical examples demonstrate robustness and effectiveness of the scheme in ALE (Arbitrary Lagrangian Eulerian) calculation of high speed impact and denotation driving.

A parallel unstructured mesh generation method is studied. Lohner's advancing front domain-splitting algorithm is improved so that the subgrids and their boundaries are more favorable for grid generation. An optimization strategy of subdomain's boundary is presented to improve the smoothness of the boundaries and the quality of grids. The conditions for receiving new points and elements are developed in the course of grid generation in subdomains. And a new strategy which receives new elements and refuses new points during the interface grid generation is presented,which saves calculation time.

How to calculate turbulent flow by solving Navier-Stokes equations on unstructured grids is investigated.The cell-center finite volume method is used to solve N-S equations.Baldwin-Barth one equation turbulence model is chosen to calculate turbulent flow which is especially suitable to unstructured meshes.The model consists of a single advection-diffusion equation with a source term.In order to solve this model equation on irregular grids,an explicit finite-volume scheme is delivered,and its time step limiting condition is obtained by analyzing stability of the scheme which possesses a source term.At the end,the numerical examples,such as turbulent flow around flat,RAE-2822 foil and multi-element foil,are given which verify the validation of the computational method.

A new method for adaptive refinement of 2D unstructured grids generated by advancing front technique is presented.Some small triangle units are arranged on the place where mesh needs to be refined,and all the sides of these units are regarded as a part of the initial front.During the advancing process,near the above mentioned units,the cells are naturally generated from small to large.For the flow with shock,in the mesh graph,a quite clear shock picture is formed.