A new finite element formulation for computational fluid dynamics. IV: A discontinuity-capturing operator for multidimensional advective-diffusive systems. (English) Zbl 0587.76120

Hughes, Thomas J. R.; Mallet, Michel

Comput. Methods Appl. Mech. Eng. 58, 329-336 (1986).

[For part I and II see the authors and L. P. Franca ibid. 54, 223- 234 (1986; Zbl 0572.76068)] and the authors and A. Mizukami, ibid. 54, 341-356 (1986). Part III to appear in ibid]
A discontinuity-capturing operator is developed for the ’streamline’ formulation of advective-diffusive systems extending previous work on the scalar advection-diffusion equation. The operator provides a mechanism for exerting control over strong gradients in the discrete solution which appear, for example, in boundary and interior layers.

MSC:

76N10	Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
65Z05	Applications to the sciences
76N15	Gas dynamics (general theory)
76R99	Diffusion and convection
80A20	Heat and mass transfer, heat flow (MSC2010)

Keywords:

discontinuity-capturing operator; scalar advection-diffusion equation; strong gradients; discrete solution; boundary layers; entropy-variables form; compressible Navier-Stokes equations; symmetric incompletely parabolic systems; interior layers

Citations:

Zbl 0572.76068; Zbl 0581.76077; Zbl 0622.76074; Zbl 0622.76075; Zbl 0622.76077

References:

[1]	Davis, S. F., A rotationally biased upwind difference scheme for the Euler equations, J. Comput. Phys., 56, 65-92 (1984) · Zbl 0557.76067
[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. Meth. 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. Meths. Appl. Mech. Engrg., 58, 305-328 (1986), (this issue). · Zbl 0622.76075
[4]	Hughes, T. J.R.; Mallet, M.; Franca, L. P., Entropy-stable finite element methods for compressible fluids: application to high Mach number flows with shocks, (Bergan, P.; Bathe, K. J.; Wunderlich, W., Finite Element Methods for Nonlinear Problems (1986), Springer: Springer Berlin), 761-773
[5]	Hughes, T. J.R.; Mallet, M.; Mizukami, A., A new finite element formulation for computational fluid dynamics: II. Beyond SUPG, Comput. Meths. Appl. Mech. Engrg., 54, 341-355 (1986) · Zbl 0622.76074