Colella, Phillip; Pao, Karen A projection method for low speed flows. (English) Zbl 0935.76056 J. Comput. Phys. 149, No. 2, 245-269 (1999). Summary: We propose a decomposition applicable to low speed, inviscid flows of all Mach numbers less than 1. By using the Hodge decomposition, we may write the velocity field as the sum of a divergence-free vector field and a gradient of a scalar function. Evolution equations for these parts are presented. A numerical procedure based on this decomposition is designed, using projection methods for solving the incompressible variables, and a backward-Euler method for solving the potential variables. Numerical experiments illustrate our algorithm. \(\copyright\) Academic Press. Cited in 31 Documents MSC: 76M20 Finite difference methods applied to problems in fluid mechanics 76N15 Gas dynamics (general theory) Keywords:Hodge decomposition; projection methods; incompressible variables; backward-Euler method; potential variables PDFBibTeX XMLCite \textit{P. Colella} and \textit{K. Pao}, J. Comput. Phys. 149, No. 2, 245--269 (1999; Zbl 0935.76056) Full Text: DOI References: [1] Oran, E. S., Numerical simulation of unsteady combustion, Advances in Combustion Science: In Honor of Ya. B. Zeldovich, Prog. Astronau. Aeronaut., 173, 179 (1997) [2] Lighthill, M. J., On sound generated aerodynamically. I. General theory, Proc. R. Soc. London Ser. A, 211, 564 (1952) · Zbl 0049.25905 [3] Harlow, F.; Amsden, A., Numerical calculation of almost incompressible flow, J. Comput. Phys., 3, 80 (1968) · Zbl 0172.52903 [4] Casulli, V.; Greenspan, D., Pressure method for the numerical solution of transient, compressible fluid flows, Int. J. Numer. Methods Fluids, 4, 1001 (1984) · Zbl 0549.76050 [5] Patnaik, G.; Guirguis, R. H.; Boris, J. P.; Oran, E. S., A barely implicit correction for flux-corrected transport, J. Comput. Phys., 71, 1 (1987) · Zbl 0613.76077 [6] Abarbanel, S.; Duth, P.; Gottlieb, D., Splitting methods for low Mach number Euler and Navier-Stokes equations, Comput. & Fluids, 17, 1 (1989) · Zbl 0664.76088 [7] Gustafsson, B.; Stoor, H., Navier-Stokes equations for almost incompressible flow, SIAM J. Numer. Anal., 28, 1523 (1991) · Zbl 0734.76048 [8] Sesterhenn, J.; Mueller, B.; Thomann, H., Flux-vector splitting for compressible low Mach number flow, Comput. & Fluids, 22, 441 (1993) · Zbl 0779.76077 [9] Klein, R., Semi-implicit extension of a Godunov-type scheme based on low Mach number asymptotics. I. One-dimensional flow, J. Comput. Phys., 121, 213 (1995) · Zbl 0842.76053 [10] C.-D. Munz, S. Roller, R. Klein, K. J. Geratz, The extension of incompressible flow solvers to the weakly compressible regime, 1997; C.-D. Munz, S. Roller, R. Klein, K. J. Geratz, The extension of incompressible flow solvers to the weakly compressible regime, 1997 · Zbl 1042.76045 [11] Pao, K.; Anderson, C., Computation of Flow Noise in Two Dimensions (1994) [12] Klainermann, S.; Majda, A., Compressible and incompressible fluids, Comm. Pure Appl. Math., 35, 629 (1982) · Zbl 0478.76091 [13] Kreiss, H. O.; Lorenz, J.; Naughton, M., Convergence of the solutions of the compressible to the solutions of the incompressible Navier-Stokes equations, Adv. Appl. Math., 12, 187 (1991) · Zbl 0728.76084 [14] Chorin, A.; Marsden, J. E., A Mathematical Introduction to Fluid Mechanics (1979) · Zbl 0417.76002 [15] Anderson, C., Derivation and Solution of the Discrete Pressure Equations for the Incompressible Navier Stokes Equations (1998) [16] Harlow, F.; Welch, J. E., Numerical calculations of time dependent viscous incompressible flow with free surface, Phys. Fluids, 8, 2182 (1965) · Zbl 1180.76043 [17] Colella, P., A multidimensional second order Godunov scheme for conservation laws, J. Comput. Phys., 87, 171 (1990) [18] van Leer, B., Toward the ultimate conservative difference scheme: A second-order sequel to Godunov’s method, J. Comput. Phys., 32, 101 (1979) · Zbl 1364.65223 [19] Bell, J.; Colella, P.; Glaz, H., A second order projection method for the incompressible Navier-Stokes equations, J. Comput. Phys., 85, 257 (1989) · Zbl 0681.76030 [20] Bell, J.; Marcus, D., A second order projection method for variable-density flows, J. Comput. Phys., 101, 334 (1992) · Zbl 0759.76045 [21] Lai, M., A Projection Method for Reacting Flow in the Zero Mach Number Limit (1993) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.