In order to increase the computation efficiency, artificial dissipation, variable time step and enthalpy damping acceleration techniques are used in the five-step Runge-Kutta time stepping.

The cell-centered symmetric finite volume arithmetic and Runge-Kutta time stepping scheme are performed to solve Euler equation. The two order and four order artificial dissipation is introduced for stability, local time stepping and implicit residual smoothing technique is applied to save computer time.

In order to prevent odd-even decoupling of the solution and oscillations near the shock waves, a blend of adaptive second- and fourth-order artificial dissipation is added.

The main numerical method of this code is coming from scheme (Jameson, Schimit and Turkel): using cell-centered finite volume method as spatial discretization tools, and a system of ordinary differential equations for time variable is obtained, which is solved by utilizing five-step Runge-Kutta scheme as time marching method , introducing artificial dissipation to damp high frequency oscillations near the shock and stagnation point.

To ensure the numerical dissipation much smaller than the physical viscous terms, directional scaling of the artificial dissipation is achieved and proper boundary conditions are also introduced in this term.

The LU-ADI algorithm is employed in this paper, in order to control the numerical stability, the second-order and fourth-order artificial dissipation are added to the basic algorithm.

Finite Volume Method (FVM) is used to calculate the 3-D viscous flow in the vectoring exhaust nozzle. The artificial dissipation and its boundary condition are improved to quicken the convergence and upgrade the precision of the numerical simulation.

In order to get smooth convergence for transonic, viscous flows, the artificial dissipation has been modified by using the time step for advective and diffusive equations.

A modified artificial dissipation based on the time-step limit for convective and diffusive equation has been used for numerical stability.

Only a fourth order artificial dissipation has been used here for global stability of the solution.

Artificial dissipation terms for finite difference approximations of linear hyperbolic problems with variable coefficients are determined such that an energy estimate and strict stability is obtained.

Conservative Finite Difference Formulations, Variable Coefficients, Energy Estimates and Artificial Dissipation

Compressible flow around an NACA 0012 airfoil at high angle of attack is numerically simulated by solving the two-dimensional Navier-Stokes equations in a body-fitted system, the grid system is C-type grid generated algebraically. The LU-ADI algorithm is employed in this paper, in order to control the numerical stability, the second-order and fourth-order artificial dissipation are added to the basic algorithm. By using the Baldwin-Lomax turbulent model, the formation of the leading edge separation bubble,...

Compressible flow around an NACA 0012 airfoil at high angle of attack is numerically simulated by solving the two-dimensional Navier-Stokes equations in a body-fitted system, the grid system is C-type grid generated algebraically. The LU-ADI algorithm is employed in this paper, in order to control the numerical stability, the second-order and fourth-order artificial dissipation are added to the basic algorithm. By using the Baldwin-Lomax turbulent model, the formation of the leading edge separation bubble, as well as the convection of vortex along the airfoil surface and unsteady phenomena of vortex are simulated at high angle of attack. For some Mach numbers and angles of attack, the NACA 0012 airfoil turbulent solutions are periodie. By the comparison, the results in this paper agree with experiments and results received by other method.

The new idea of making implicit scheme is developed on the basis of analyzing model equation inthis paper. By putting the above idea into Flux Vector Splitting, an Implicit Flux Vector Splitting(IFVS), which can avoid approximate factorization or block-bidiagonal, is provided to solve the timeaverage Navier-Stokes equations. A single-step three-node upwind difference scheme for vector fluxand central difference approximation for viscous terms are adapted.As a result,IFVS has no two-or-der numerical dissipation...

The new idea of making implicit scheme is developed on the basis of analyzing model equation inthis paper. By putting the above idea into Flux Vector Splitting, an Implicit Flux Vector Splitting(IFVS), which can avoid approximate factorization or block-bidiagonal, is provided to solve the timeaverage Navier-Stokes equations. A single-step three-node upwind difference scheme for vector fluxand central difference approximation for viscous terms are adapted.As a result,IFVS has no two-or-der numerical dissipation or artificial dissipation.It has obvious superiority in aspects of accuracy, robustness and little calculation.In the case of two-dimensional transonic cascade flows, shock wave exactly captured,and results are satisfied.

In this paper,three-dimensional Supersonic inlet flowfields have been calculated.The governing equations are nonsteady compressible Navier-Stokes equations. The discretization was Jameson's Runge-Kutta finite volume method. Modified Baldwin-Lomax algebraic eddyviscosity turbulent model and the wall function law were used. A new viscous terms discretization in the frame of finite volume method was adopted. For convergence acceleration,local time stepping,implicit residual average and artificial dissipation...

In this paper,three-dimensional Supersonic inlet flowfields have been calculated.The governing equations are nonsteady compressible Navier-Stokes equations. The discretization was Jameson's Runge-Kutta finite volume method. Modified Baldwin-Lomax algebraic eddyviscosity turbulent model and the wall function law were used. A new viscous terms discretization in the frame of finite volume method was adopted. For convergence acceleration,local time stepping,implicit residual average and artificial dissipation techniques were also used.A aircraft inlet flowfields of several flight states were calculated. The mean total pressure recovery and total pressure distortion across the engine face were obtained. These results were compared with experiment data and were proved to be satisfactory.