Skew-symmetric form of convective terms and fully conservative finite difference schemes for variable density low-Mach number flows

Journal of Computational Physics

Volumn 229, Issue 2, 2010, Pages 276-300

  Morinishi, Yohei ^a  

^a NAGOYA INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

Advective form; Compact finite difference; Compressible flow; Convective term; Divergence form; Finite difference; Fully conservative; Regular grid system; Secondary conservative; Skew symmetric form; Staggered grid system

Indexed keywords

FINITE DIFFERENCE METHOD; INCOMPRESSIBLE FLOW; MACH NUMBER;

ADVECTIVE FORM; COMPACT FINITE DIFFERENCES; CONVECTIVE TERM; DIVERGENCE FORM; FINITE DIFFERENCE; FULLY CONSERVATIVE; GRID SYSTEMS; REGULAR GRID SYSTEM; REGULAR GRIDS; SECONDARY CONSERVATIVE; SKEW-SYMMETRIC FORMS; STAGGERED GRID SYSTEM; STAGGERED-GRIDS;

COMPRESSIBLE FLOW;

EID: 77955273607     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2009.09.021     Document Type: Article

References (33)

1. Y. Morinishi, T.S. Lund, O.V. Vasilyev, P. Moin, Fully conservative higher order finite difference schemes for incompressible flow, J. Comput. Phys. 143 (1998) 90-124.
2. F.H. Harlow, J.E. Welch, Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Phys. Fluids 8 (1965) 2182-2189.
3. O.V. Vasilyev, High order finite difference schemes on non-uniform meshes with good conservation properties, J. Comput. Phys. 157 (2000) 746-761.
4. Y. Morinishi, O.V. Vasilyev, T. Ogi, Fully conservative finite difference scheme in cylindrical coordinates for incompressible flow simulations, J. Comput. Phys. 197 (2004) 686-710.
5. R.W.C.P. Verstappen, A.E.P. Veldman, Symmetry-preserving discretization of turbulent flow, J. Comput. Phys. 187 (2003) 343-368.
6. F. Nicoud, Conservative high-order finite-difference schemes for low-Mach number flows, J. Comput. Phys. 158 (2000) 71-97.
7. O. Desjardins, G. Blanquart, G. Balarac, H. Pitsch, High order conservative finite difference scheme for variable density low Mach number turbulent flows, J. Comput. Phys. 227 (2008) 7125-7159.
8. A.G. Kravchenko, P. Moin, On the effect of numerical errors in large eddy simulations of turbulent flows, J. Comput. Phys. 131 (1997) 310-322.
9. C.A. Kennedy, A. Gruber, Reduced aliasing formulations of the convective terms within the Navier-Stokes equations for a compressible fluid, J. Comput. Phys. 227 (2008) 1676-1700.
10. W.J. Feiereisen, W.C. Reynolds, J.H. Ferziger, Numerical Simulation of Compressible, Homogeneous Turbulent Shear Flow, Department Mechanical Engineering, Stanford University, Report No. TF-13, 1981.
11. G.A. Blaisdell, N.N. Mansour, W.C. Reynolds, Numerical Simulations of Compressible Homogeneous Turbulence, Stanford University, Report No. TF-50, 1991.
12. G.A. Blaisdell, N.N. Mansour, W.C. Reynolds, Compressibility effects on the growth and structure of homogeneous turbulent shear flow, J. Fluid Mech. 256 (1993) 443-485.
13. F. Ducros, V. Ferrand, F. Nicoud, C. Weber, D. Darracq, C. Gacherieu, T. Poinsot, Large-eddy simulation of the shock/turbulence interaction, J. Comput. Phys. 152 (1999) 517-549.
14. F. Ducros, F. Laporte, T. Souléres, V. Guinot, P. Moinat, B. Caruell, High-order fluxes for conservative skew-symmetric-like schemes in structured meshes: application to compressible flows, J. Comput. Phys. 161 (2000) 114-139.
15. Y. Morinishi, S. Tamano, K. Nakabayashi, A DNS algorithm using B-spline collocation method for compressible turbulent channel flow, Comput. Fluids 32 (2003) 751-776.
16. F.E. Ham, F.S. Lien, A.B. Strong, A fully conservative second-order finite difference scheme for incompressible flow on nonuniform grids, J. Comput. Phys. 177 (2002) 117-133.
17. C.D. Pierce, Progress-variable Approach for Large-eddy Simulation of Turbulent Combustion, Ph.D. Thesis, Stanford University, Stanford, CA, 2001.
18. C. Wall, C.D. Pierce, P. Moin, A semi-implicit method for resolution of acoustic waves in low Mach number flows, J. Comput. Phys. 181 (2002) 545-563.
19. A.E. Honein, P. Moin, Higher entropy conservation and numerical stability of compressible turbulence simulations, J. Comput. Phys. 201 (2004) 531-545.
20. Y. Morinishi, Secondary conservative finite difference scheme of convection for compressible turbulent flow analysis, in: Proceedings of the 22nd SEIKEN TSFD Symposium, Tokyo, 2007, pp. 69-75 (in Japanese).
21. P.K. Subbareddy, G.V. Candler, A fully discrete, kinetic energy consistent finite-volume scheme for compressible flows, J. Comput. Phys. 228 (2009) 1347-1364.
22. P. Roe, Approximated Riemann solvers, parameter vectors, and difference schemes, J. Comput. Phys. 43 (1981) 357-372.
23. S.K. Lele, Compact finite difference schemes with spectral-like resolution, J. Comput. Phys. 103 (1992) 16-42.
24. S. Nagarajan, S.K. Lele, J.H. Ferziger, A robust high-order compact method for large eddy simulation, J. Comput. Phys. 191 (2003) 392-419.
25. J.H. Williamson, Low-storage Runge-Kutta schemes, J. Comput. Phys. 35 (1980) 48-56.
26. D.A. Knoll, D.E. Keyes, Jacobian-free Newton-Krylov methods: a survey of approaches and applications, J. Comput. Phys. 193 (2004) 357-397.
27. P.N. Brown, Y. Saad, Hybrid Krylov methods for nonlinear systems of equations, SIAM J. Sci. Stat. Comput. 11 (1990) 450-481.
28. Y. Saad, M.H. Schults, GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Stat. Comput. 7 (1986) 856-869.
29. Y. Saad, A flexible inner-outer preconditioned GMRES algorithm, SIAM J. Sci. Stat. Comput. 14 (1993) 461-469.
30. R. Samtaney, D.I. Pullin, B. Kosović, Direct numerical simulation of decaying compressible turbulence and shokclet statistics, Phys. Fluids 13 (2001) 1415-1430.
31. N.K. Ghaddar, K.Z. Korczak, B.B. Mikic, A.T. Patera, Numerical investigation of incompressible flow in grooved channels. Part 1. Stability and selfsustained oscillations, J. Fluid Mech. 163 (1986) 99-127.
32. Y. Morinishi, Forms of convection and quadratic conservative finite difference schemes for low-Mach number compressible flow simulations, Trans. JSME 73 (Series B) (2007) 451-458 (in Japanese).
33. M. Vinokur, Conservation equations of gasdynamics in curvilinear coordinate systems, J. Comput. Phys. 14 (1974) 105-125.