A general high-order unstructured-grid finite volume method based on least-square reconstruction and WENO limiter is presented.Some of the neighboring cells are employed to construct high-order polynomials.a least-square method is used tO solve overdetermined problem.The number of neighboring cells can be reduced with a general method,which saves memory and computing time. To achieve uniform accuracy and depress non-physical oscillation of conservation laws,a WENO limiter and rotated Riemann solver are employed.Two classical cases are provided to show resolution differences between high-order schemes and the second order scheme based on gradient reconstruction and Bath and Jesperson limiter.

A second-order rotational upwind transport scheme for multidimensionul compressible Euler equations on unstructured meshes is presented. Cell-centered FVM is employed in which gradient calculation is node-based with more neighbor cells. Slope limiter schemes are constructed for unstructured meshes. Numerical fluxes are evaluated by solving two Riemann problems in two upwind directions, including velocity-difference vector and perpendicular direction. The scheme eliminate shock instabilities or carbuncle phenomena in flux-difference splitting type schemes completely. A hybrid rotated Riemann solver is employed to form an economical numeric flux function and base Riemann solvers employ HLL and Roe FDS.

An algorithm with unstructured girds is introduced in which coupling of density and temperature is considered.Static enthalpy equation is employed to construct relation between temperature correction and pressure correction.As in Rhie-Chow method,temperature and pressure corrections of grid interfaces are interpolated by static enthalpy equation and omitting neighbour temperature correction as in the velocity-pressure coupling in SIMPLEC.CGNS is taken as I/O in the in-house unstructured FVM code.For combustion simulation,Arrinius-Eddy dissipation model is employed.

An unstructured hybrid grid computational method is proposed,in which CGNS API(CFD General Notation System Application Programming Interface) is taken as pre- and post-processing and FVM(Finite Volume Method) is taken as a PDE(Partial Differential Equation) solver.In the pre-processing,the interior mesh faces and boundary mesh faces are indexed with hash table method for the requirment of the FVM solver.The results of the solver are written into original CGNS files with which the post-processing is dealt with by post-processing softwares,such as tecplot,fluent and CFX.For the solver,a cell centered FVM is applied to solve the coupled pressure and velocities with the SIMPLEC(Semi Implicit Method for Pressure Linked Equation Consistent).Two numerical examples are shown.