With a fifth-order weighted compact nonlinear scheme(WCNS-E-5),flow field of a 65° delta wing with sharp leading edges at high angles of incidence is simulated.The target is checking WCNS's ability for vortex flow at high angles of incidence and vortex breakdown location with shock-vortex interaction.We focus on sudden jump in breakdown towards apex.Unsteady Reynolds averaged Navier-Stokes(URANS) method is available including a high-order weighted compact nonlinear scheme and an SST turbulence model.It is shown that the high order scheme(WCNS-E-5) with minimum numerical dissipation and could capture discontinuities for high angles of incidence transonic flow of delta wing and the results are matched satisfactorily with experiments.Shock-vortex interaction in transonic freestream explains sudden movement of vortex breakdown as the angle of incidence is increased.

With study of finite volume(FV) methods and discontinuous Galerkin(DG) method,"static reconstruction" and "dynamic reconstruction" are proposed for high-order numerical schemes.Based on the concept of "hybrid reconstruction",a new class of hybrid DG/FV schemes is presented for two-dimensional(2D) unstructured grids to solve the 2D conservation law,including 2D scalar equations and Euler equations.In the hybrid DG/FV schemes,lower-order derivatives of the piecewise polynomial are computed locally in a cell by a traditional DG method(called "dynamic reconstruction"),and the higher-order derivatives are reconstructed by the "static reconstruction" of the FV method by using lower-order derivatives in the cell and immediate neighbour cells.Typical 2D cases are given,and accuracy study is carried out.Numerical results show that the hybrid DG/FV scheme reaches desired order of accuracy.In addition,the hybrid DG/FV scheme saves great CPU time and memory compared with same order DG schemes.

Based on the fifth order dissipative compact spatial finite difference scheme(DCS5) and the seven stage Runge-Kutta time integration scheme, with the principle that numerical amplification factor approaches the real amplification factor optimally, an optimal methodology for time integration scheme is proposed and a seven stage fifth order LDDRK scheme is obtained. Numerical results of onedimensional wave propagation obtained by convection equation and linearized Euler equations show that the proposed LDDRK scheme has lower dissipation than standard Runge-Kutta schemes.

Spectrum characteristic of linear dissipative compact schemes and corresponding fully-discrete forms based on m-order Runge-Kutta algorithm are investigated by Fourier analysis.A 5-th order scheme is empolyed to study propagation of a classical high-frequency wave and eigen-value problem of a supersonic plane Couette flow as well as its boundary value stability.Numerical results demonstrate favorable spectrum characteristic of dissipative compact schemes.

In a model for interaction between one atmosphere uniform glow discharge plasma (OAUGDP)and air proposed by Shyy,electric field and electric forces acting on air as body force are obtained.The electric field is calculated with electric potential equation. The influence of OAUGDP on flows around a NACA0015 airfoil at low speed is investigated by solving N-S equation with a body force term.Plasma located upstream of the separation point damps the flow separation around the airfoil efficiently,while plasma located downstream of the separation point has little effect on the flow.It agrees with experimental observations. Effect of plasma on aerodynamics of airfoil and pressure distribution on airfoil surface are investigated.

With a high-order weighted compact nonlinear scheme(WCNS) for space discretization,several different implicit methods,including LU-SGS,Gauss-Seidel point-relaxation,line-relaxation and GMRES(generalized minimal residual),are compared in the simulation of hypersonic viscous flows.Both point and line relaxations with analytical Jacobian matrix converge faster than those of LU-SGS.GMRES obtains a faster convergence rate combined with line relaxation.