×

zbMATH — the first resource for mathematics

A unified approach to compressible and incompressible flows. (English) Zbl 0845.76040
Summary: We present a finite element formulation for solving the compressible Navier-Stokes equations which accommodates the use of any set of variables. If primitive variables \((p,u,T)\), or entropy variables are used, the incompressible limit is well behaved. Therefore, one formulation can be used to solve both compressible and incompressible flows.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Brooks, A.N.; Hughes, T.J.R., Streamline upwind Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations, Comput. methods appl. mech. engrg., 32, 199-259, (1982) · Zbl 0497.76041
[2] Hughes, T.J.R.; Franca, L.P.; Mallet, M., A new finite element formulation for computational fluid dynamics: I. symmetric forms of the compressible Euler and Navier-Stokes equations and the second law of thermodynamics, Comput. methods appl. mech. engrg., 54, 223-234, (1986) · Zbl 0572.76068
[3] Hughes, T.J.R.; Mallet, M., A new finite element formulation for computational fluid dynamics: III. the generalized streamline operator for multidimensional advective-diffusive systems, Comput. methods appl. mech. engrg., 58, 305-328, (1986) · Zbl 0622.76075
[4] Hughes, T.J.R.; Mallet, M., A new finite element formulation for computational fluid dynamics: IV. A discontinuity-capturing operator for multidimensional advective-diffusive systems, Comput. methods appl. mech. engrg., 58, 329-336, (1986) · Zbl 0587.76120
[5] Hughes, T.J.R.; Franca, L.P.; Hulbert, G., A new finite element formulation for computational fluid dynamics: VIII. the Galerkin/least-squares method for advective-diffusive equations, Comput. methods appl. mech. engrg., 73, 173-189, (1989) · Zbl 0697.76100
[6] Hughes, T.J.R.; Tezduyar, T.E., Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations, Comput. methods appl. mech. engrg., 45, 217-284, (1984) · Zbl 0542.76093
[7] Hansbo, P.; Johnson, C., Adaptive streamline diffusion methods for compressible flow using conservation variables, Comput. methods appl. mech. engrg., 87, 267-280, (1991) · Zbl 0760.76046
[8] Aliabadi, S.K.; Ray, S.E.; Tezduyar, T.E., SUPG finite element computation of viscous compressible flows based on the conservation and entropy variables formulation, University of minnesota supercomputer institute research report UMSI 92/136, (1992) · Zbl 0772.76032
[9] Chalot, F.; Hughes, T.J.R.; Shakib, F., Symmetrization of conservation laws with entropy for high-temperature hypersonic computations, Comput. syst. engrg., 1, 495-521, (1990)
[10] Shakib, F.; Hughes, T.J.R.; Johan, Z., A new finite element formulation for computational fluid dynamics: X. the compressible Euler and Navier-Stokes equations, Comput. methods appl. mech. engrg., 89, 141-219, (1991) · Zbl 0838.76040
[11] Chalot, F.; Hughes, T.J.R., Analysis of hypersonic flows in thermomechanical equilibrium by application of the Galerkin/least-squares formulation, (), 146-159
[12] Hughes, T.J.R., The finite element method: linear static and dynamic finite element analysis, (1987), Prentice Hall Englewood Cliffs, NJ
[13] Ghia, U.; Ghia, K.N.; Shin, C.T., High-re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method, J. comput. phys., 48, 387-441, (1982) · Zbl 0511.76031
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.