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.