Hughes, Thomas J. R.; Mallet, Michel; Mizukami, Akira A new finite element formulation for computational fluid dynamics. II. Beyond SUPG. (English) Zbl 0622.76074 Comput. Methods Appl. Mech. Eng. 54, 341-355 (1986). [For part I see ibid. 54, 223-234 (1986; Zbl 0581.76077; Zbl 0572.76068).] A discontinuity-capturing term is added to the streamline-upwind/Petrov- Galerkin weighting function for the scalar advection-diffusion equation. The additional term enhances the ability of the method to produce smooth yet crisp approximations to internal and boundary layers. Cited in 6 ReviewsCited in 194 Documents MSC: 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics 80A20 Heat and mass transfer, heat flow (MSC2010) 65Z05 Applications to the sciences 76R99 Diffusion and convection Keywords:compressible Navier-Stokes equations; heat conducting effects; entropy variables; finite element methods; second law of thermodynamics; stability; discrete solution; Navier-Stokes equations; discontinuity- capturing term; streamline-upwind/Petrov-Galerkin weighting function; scalar advection-diffusion equation; crisp approximations; boundary layers Citations:Zbl 0587.76120; Zbl 0622.76075; Zbl 0622.76076; Zbl 0622.76077; Zbl 0581.76077; Zbl 0572.76068 PDF BibTeX XML Cite \textit{T. J. R. Hughes} et al., Comput. Methods Appl. Mech. Eng. 54, 341--355 (1986; Zbl 0622.76074) Full Text: DOI OpenURL References: [1] Argyris, J.H.; Doltsinis, J.St.; Pimenta, P.M.; Wüstenberg, H., Natural finite element techniques for viscous fluid motion, Comput. meths. appl. mech. engrg., 45, 3-55, (1984) · Zbl 0541.76004 [2] Brooks, A.N.; Hughes, T.J.R., Streamline upwind/Petrov-Galerkin methods for advection dominated flows, () · Zbl 0449.76077 [3] 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. meths. appl. mech. engrg., 32, 199-259, (1982) · Zbl 0497.76041 [4] Carey, G.F.; Oden, J.T., () [5] Christie, I.; Griffiths, D.F.; Mitchell, A.R.; Zienkiewicz, O.C., Finite element methods for second order differential equations with significant first derivatives, Internat. 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Johnson and J. Saranen, Streamline diffusion methods for the incompressible Euler and Navier-Stokes equations, Math. Comp., to appear. · Zbl 0607.76025 [18] Mizukami, A.; Hughes, T.J.R., A Petrov-Galerkin finite element method for convection-dominated flows: an accurate upwinding technique for satsifying the maximum principle, Comput. meths. appl. mech. engrg., 50, 181-193, (1985) · Zbl 0553.76075 [19] Nävert, U., A finite element methods for convection-diffusion problems, () [20] Rice, J.G.; Schnipke, R.J., A monotone streamline upwind finite element method for convection-dominated flows, Comput. meth. appl. mech. engrg., 48, 313-327, (1985) · Zbl 0553.76073 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.