A Unified Method for Computing Incompressible and Compressible Flows in Boundary-Fitted Coordinates

Journal of Computational Physics

Volumn 141, Issue 2, 1998, Pages 153-173

  Bijl, Hester ^a   Wesseling, Pieter ^a  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Boundary fitted coordinates; Euler equations compressible flow; Finite volume method; Subsonic flow; Supersonic flow; Transonic flow

Indexed keywords

AERODYNAMICS; COMPRESSIBLE FLOW; EFFICIENCY; FINITE VOLUME METHOD; INCOMPRESSIBLE FLOW; MACH NUMBER; NAVIER STOKES EQUATIONS; SUPERSONIC FLOW;

BOUNDARY-FITTED COORDINATES; DISCRETIZATIONS; EULER EQUATION COMPRESSIBLE FLOW; EULER'S EQUATION; FINITE-VOLUME METHOD; NON-STATIONARY FLOWS; PRESSURE-BASED; STAGGERED-GRIDS; STATIONARY FLOW; UNIFIED METHOD;

EULER EQUATIONS;

EID: 0002544437     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1998.5914     Document Type: Article

References (53)

1. Arora M., Roe P. L. A well-behaved TVD limiter for high-resolution calculations of unsteady flow. J. Comput. Phys. 132:1997;3.
2. Briley W. R., McDonald H., Shamroth S. J. A low Mach number Euler formulation and application to time-iterative LBI schemes. AIAA J. 21:1983;1467.
3. Chenoweth D. R., Paolucci S. Natural convection in an enclosed vertical air layer with large horizontal temperature differences. J. Fluid Mech. 169:1986;173.
4. Choi Y.-H., Merkle C. L. The application of preconditioning in viscous flows. J. Comput. Phys. 105:1993;207.
5. Davidson L., Hedberg P. Mathematical derivation of a finite volume formulation for laminar flow in complex geometries. Int. J. Num. Meth. Fluids. 9:1989;531.
6. Demirdžić I., Lilek Z., Perić M. A collocated finite volume method for predicting flows at all speeds. Int. J. Num. Meth. Fluids. 16:1993;1029.
7. Eidelman S., Colella P., Shreeve R. P. Application of the Godunov method and its second-order extension to cascade flow modelling. AIAA J. 22:1984;1609.
8. A. G. Godfrey, R. W. Walters, B. van Leer, Preconditioning for the Navier-Stokes equations with finite rate chemistry, 1993.
9. Guerra J., Gustafsson B. A numerical method for incompressible and compressible flow problems with smooth solutions. J. Comput. Phys. 63:1986;377.
10. Harlow F. H., Amsden A. A. Numerical calculation of almost incompressible flows. J. Comput. Phys. 3:1968;80.
11. Harlow F. H., Amsden A. A. A numerical fluid dynamics calculation method for all flow speeds. J. Comput. Phys. 8:1971;197.
12. Harlow F. H., Welch J. E. Numerical calculation of time-dependent viscous incompressible flow of fluid with a free surface. The Physics of Fluids. 8:1965;2182.
13. Harten A. High resolution schemes for hyperbolic conservation laws. J. Comput. Phys. 49:1983;357.
14. Harten A., Engquist B., Osher S., Chakravarty S. R. Uniformly high order accurate essentially non-oscillatory schemes. J. Comput. Phys. 71:1987;231.
15. Hosangadi A., Merkle C. L., Turns S. R. Analysis of forced combusting jets. AIAA J. 28:1990;1473.
16. Ikohagi T., Shin B. R., Daiguji H. Application of an implicit time-marching scheme to a three-dimensional incompressible flow problem in curvilinear coordinate systems. Computers and Fluids. 21:1992;163.
17. Issa R. I., Gosman A. D., Watkins A. P. The computation of compressible and incompressible flows by a non-iterative implicit scheme. J. Comput. Phys. 62:1986;66.
18. Issa R. I. Solution of the implicitly discretised fluid flow equations by operator-splitting. J. Comput. Phys. 62:1986;40.
19. Karimian S. M. H., Schneider G. E. Pressure-based control volume finite element method for flow at all speeds. AIAA J. 33:1995;1611.
20. Karki K. C., Patankar S. V. Pressure based calculation procedure for viscous flows at all speed in arbitrary configurations. AIAA J. 27:1989;1167.
21. Klainerman S., Majda A. Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids. Comm. Pure Appl. Math. 34:1981;481.
22. Klainerman S., Majda A. Compressible and incompressible flows. Comm. Pure Appl. Math. 35:1982;629.
23. Klein R. Semi-implicit extension of a godunov-type scheme based on low mach number asymptotics 1: One-dimensional flow. J. Comput. Phys. 121:1995;213.
24. Koshizuka S., Oka Y., Kondo S. A staggered differencing technique on boundary-fitted curvilinear grids for incompressible flows along curvilinear or slant walls. Computational Mechanics. 7:1990;123.
25. Kreiss H. O., Lorenz J., Naughton M. J. Convergence of the solutions of the compressible to the solutions of the incompressible Navier-Stokes equations. Adv. Appl. Math. 12:1991;187.
26. Majda A. Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables, Applied Mathematical Sciences. 53:1984.
27. McMurtry P. A., Jou W. H., Riley J. J., Metcalfe R. W. Direct numerical simulations of a reacting mixing layer with chemical heat release. AIAA J. 24:1986;962.
28. Merkle C. L., Choi Y.-H. Computation of low-speed compressible flows with time marching procedures. Int. J. Numer. Methods Eng. 25:1988;831.
29. K. Morinishi, Comparison of numerical solutions of pseudocompressible flows and compressible flows at low Mach numbers, 1992.
30. Oran E. S., Boris J. P. Detailed modelling of combustion systems. Prog. Energy Combust. Sci. 7:1981;1.
31. Panton R. L. Incompressible Flow. 1984.
32. Patnaik G., Guirguis R. H., Boris J. P., Oran E. S. A barely implicit correction for flux-corrected transport. J. Comput. Phys. 71:1987;1.
33. Rehm R. G., Baum H. R. The equations of motion for thermally driven buoyant flows. J. Res. Nat. Bur. Stand. 83:1978;297.
34. Rosenfeld M., Kwak D., Vinokur M. A fractional step solution method for the unsteady incompressible Navier-Stokes equations in generalized coordinate systems. J. Comput. Phys. 94:1991;102.
35. Segal A., Wesseling P., van Kan J., Oosterlee C. W., Kassels K. Invariant discretization of the incompressible Navier-Stokes equations in boundary fitted co-ordinates. Int. J. Num. Meth. Fluids. 15:1992;411.
36. Shuen J.-S., Chen K.-H., Choi Y. A coupled implicit method for chemical non-equilibrium flows at all speeds. J. Comput. Phys. 106:1993;306.
37. Shyy W. A numerical study of two-dimensional compressible Navier-Stokes flows. Num. Heat Transfer. 14:1988;323.
38. W. Shyy, M. E. Braaten, Adaptive grid computation for inviscid compressible flows using a pressure correction method, 1988.
39. Shyy W., Chen M.-H., Sun C.-S. Pressure-based multigrid algorithm for flow at all speeds. AIAA J. 30:1992;2660.
40. Shyy W., Tong S. S., Correa S. M. Numerical recirculating flow calculation using a body fitted coordinate system. Numerical Heat Transfer. 8:1985;99.
41. Sod G. A. A survey of several finite difference methods for systems of nonlinear conservation laws. J. Comput. Phys. 27:1978;1.
42. Thompson M. C., Ferziger J. H. An adaptive multigrid technique for the incompressible Navier-Stokes equations. J. Comput. Phys. 82:1989;94.
43. Turkel E. Review of preconditioning techniques for fluid dynamics. Appl. Num. Math. 12:1993;257.
44. E. Turkel, A. Fiterman, B. van Leer, Preconditioning and the limit to the incompressible flow equations, ICASE, 1993.
45. Van Kan J. J. I. M. A second-order accurate pressure correction method for viscous incompressible flow. SIAM J. Sci. Stat. Comput. 7:1986;870.
46. van Leer B. Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method. J. Comput. Phys. 32:1979;101.
47. B. van Leer, W.-T. Lee, P. L. Roe, Characteristic time-stepping or local preconditioning of the Euler equations, 1991.
48. Venkateswaran S., Merkle C. L., Thynell S. T. Analysis of direct solar thermal rocket propulsion. J. Propulsion Power. 8:1992;541.
49. Viviand H. Pseudo-unsteady systems for steady inviscid flow calculations. Numerical Methods for the Euler Equations of Fluid Dynamics. 1985;334.
50. Vuik C. Fast iterative solvers for the discretized incompressible Navier-Stokes equations. Int. J. Num. Meth. Fluids. 22:1996;195.
51. J. P. Withington, J. S. Shuen, V. Yang, A time accurate implicit method for chemically reacting flows at all Mach numbers, 1991.
52. Zijlema M., Segal A., Wesseling P. Finite volume computation of incompressible turbulent flows in general coordinates on staggered grids. Int. J. Num. Meth. Fluids. 20:1995;621.
53. Zijlema M., Segal A., Wesseling P. Invariant discretization of thek. Computers and Fluids. 24:1995;209.