An AUSM-based third-order compact scheme for solving Euler equations

In this paper, a third-order compact upwind scheme is given for calculating flows containing discontinuities. The scheme utilizes the AUSM flux splitting method and a third-order compact upwind space discretization relation for calculating third-order numerical flux function. TVD shock capturing properties of the scheme are achieved through a minmod flux limiter. A multistage TVD Runge-Kutta method is employed for the time integration. Computations are performed for two typical one-dimensional problems containing shocks, namely, the steady flow in a divergent nozzle and the unsteady shock tube problem. First-order and third-order numerical results are presented in comparison with the exact solutions. Computed results with KFVS method are also presented.

[1]  B. Leer,et al.  Flux-vector splitting for the Euler equations , 1997 .

[2]  Xiaolin Zhong,et al.  High-Order Finite-Difference Schemes for Numerical Simulation of Hypersonic Boundary-Layer Transition , 1998 .

[3]  Miguel R. Visbal,et al.  High-Order-Accurate Methods for Complex Unsteady Subsonic Flows , 1999 .

[4]  S. Lele.  Compact finite difference schemes with spectral-like resolution , 1992 .

[5]  P. Roe.  Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes , 1997 .

[6]  John Ekaterinaris,et al.  Implicit High-Order-Accurate-in-Space Algorithms for the Navier-Stokes Equations , 2000 .

[7]  S. Basri,et al.  A High-Resolution Compact Upwind Algorithm for Inviscid Flows , 2003 .

[8]  John A. Ekaterinaris,et al.  Regular Article: Implicit, High-Resolution, Compact Schemes for Gas Dynamics and Aeroacoustics , 1999 .

[9]  K. S. Ravichandran.  Higher Order KFVS Algorithms Using Compact Upwind Difference Operators , 1997 .

[10]  Bernardo Cockburn,et al.  Nonlinearly stable compact schemes for shock calculations , 1994 .

[11]  H. C. Yee.  Upwind and Symmetric Shock-Capturing Schemes , 1987 .

[12]  J. Steger,et al.  Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods , 1981 .

[13]  S. M. Deshpande,et al.  New Developments in Kinetic Schemes , 1998 .

[14]  Hiroshi Maekawa,et al.  Compact High-Order Accurate Nonlinear Schemes , 1997 .

[15]  M. Liou,et al.  A New Flux Splitting Scheme , 1993 .

[16]  S. Osher,et al.  Regular ArticleUniformly High Order Accurate Essentially Non-oscillatory Schemes, III , 1997 .

[17]  C. Hirsch,et al.  Numerical Computation of Internal and External Flows. By C. HIRSCH. Wiley. Vol. 1, Fundamentals of Numerical Discretization. 1988. 515 pp. £60. Vol. 2, Computational Methods for Inviscid and Viscous Flows. 1990, 691 pp. £65. , 1991, Journal of Fluid Mechanics.

[18]  S. Osher,et al.  Uniformly high order accurate essentially non-oscillatory schemes, 111 , 1987 .