Application of point implicit Runge–Kutta methods to inviscid and laminar flow problems using AUSM and AUSM⁺ upwinding

References

• Jameson , A. , Schmidt , W. and Turkel , E. Numerical solutions of the Euler equations by finite volume methods using Runge–Kutta time-stepping schemes . AIAA Paper 1981-1259 .
   Google Scholar
• Kroll , N. and Radespiel , R. 1993 . An improved flux vector split discretization scheme for viscous flows, DLR Forschungsbericht. Technical report , Cologne : German Aerospace Center (DLR) . DLR-FB 93-53
   Google Scholar
• Langer , S. 2010 . Investigation and application of point implicit Runge–Kutta methods to inviscid flow problems . International Journal for Numerical Methods in Fluids (submitted) ,
   Google Scholar
• Liou , M.S. 1995 . A sequel to AUSM: AUSM+ . Journal of Computational Physics , 129 : 364 – 382 .
   Web of Science ®Google Scholar
• Liou , M.S. and Steffen , J . 1993 . A new flux splitting scheme . Journal of Computational Physics , 107 : 23 – 29 .
   Web of Science ®Google Scholar
• Mavriplis , D.J. 1997 . Directional coarsening and smoothing for anisotrpoic Navier–Stokes Problems . Electronic Transactions on Numerical Analysis , 6 : 182 – 197 .
   Google Scholar
• Mavriplis , D.J. 1998a . Directional agglomeration multigrid techniques for high-Reynolds number viscous flows , Hampton, VA : ICASE . Report No. 98-7
   Google Scholar
• Mavriplis , D.J. 1998b . Multigrid strategies for viscous flow solvers on anisotropic unstructured meshes . Journal of Computational Physics , 145 ( 1 ) : 141 – 165 .
   Web of Science ®Google Scholar
• Moinier , P. 1999 . Algorithm developments for an unstructured viscous flow solver Thesis (PhD). University of Oxford
   Google Scholar
• Moinier , P. , Müller , J.-D and Giles , M.B . Edge-based multigrid and preconditioning for hybrid grids . AIAA Paper 1999-3339 .
   Google Scholar
• Pierce , N.A. and Giles , M.B. 1997 . Preconditioned multigrid methods for compressible flow calculations on stretched meshes. Technical Report . Journal of Computational Physics , 136 : 425 – 445 .
   Web of Science ®Google Scholar
• Roe , P. 1981 . Approximate Riemann solvers, parameter vectors, and difference schemes . Journal of Computational Physics , 43 : 357 – 372 .
   Web of Science ®Google Scholar
• Schwamborn , D. , Gerhold , T. and Heinrich , R. The DLR TAU-Code: recent applications in research and industry . Proceedings of ECCOMAS CFD 2006 Conference . Edited by: Wesseling , P. , Oate , E. and Priaux , J. The Netherlands
   Google Scholar
• Swanson , R.C. and Turkel , E. 1992 . On central difference and upwind schemes . Journal of Computational Physics , 101 : 292 – 306 .
   Web of Science ®Google Scholar
• Swanson , R.C. , Turkel , E. and Rossow , C.-C. 2006 . Convergence acceleration of Runge–Kutta schemes for solving the Navier–Stokes equations . Journal of Computational Physics , 224 : 365 – 388 .
   Web of Science ®Google Scholar
• Turkel , E. Improving the accuracy of central difference schemes . 11th international conference on numerical methods in fluid dynamics, Lecture Notes in Physics . Edited by: Dwoyer , D.L and Hussaini , M.Y. Vol. 323 , Berlin : Springer-Verlag .
   Google Scholar
• Turkel , E. and Vatsa , V.N. 1994 . Effect of artificial viscosity on three-dimensional flow solutions . AIAA Journal , 32 : 39 – 45 .
   Web of Science ®Google Scholar
• Van Leer , B. 1982 . Flux-vector splitting for the Euler equations , Hampton, VA : ICASE, Report 82-30 .
   Google Scholar
• Van Leer , B. Characteristic time-stepping or local preconditioning of the Euler equations . AIAA Paper 1991-1552-CP .
   Google Scholar
• Venkatakrishnan , V. On the accuracy of limiters and convergence to steady state solutions . AIAA Paper 1993-0880 .
   Google Scholar
• Wada , Y. and Liou , M.S. A flux splitting scheme with high-resolution and robustness for discontinuities . AIAA Paper 1994-0083 .
   Google Scholar