TY - CHAP

T1 - Efficient multigrid computation of steady hypersonic flows

AU - Koren, B.

AU - Hemker, P.W.

PY - 1991

Y1 - 1991

N2 - In steady hypersonic flow computations, Newton iteration as a local relaxation procedure and nonlinear multigrid iteration as an acceleration procedure may both easily fail. In the present chapter,
same remedies are presented for overcoming these problems. The equations considered are the
steady, two-dimensional Navier-Stokes equations. The equations are discretized by an upwind finite
volume method.
Collective point Gauss-Seidel relaxation is applied as the standard smoothing technique. In
hypersonics this technique easily diverges. First, collective line Gauss-Seidel relaxation is applied as
an alternative smoothing technique. Though promising, it also fails in hypersonics. Next, collective
point Gauss-Seidel relaxation is reconsidered and improved; a divergence monitor is introduced and
in case of divergence a switch is made to a local explicit time stepping technique. Satisfactory singlegrid convergence results are shown for the computation of a hypersonic reentry flow around a blunt forebody with canopy.
Unfortunately, with this improved smoothing technique, standard nonlinear multigrid iteration
still fails in hypersonics. The robustness improvements made therefore to the standard nonlinear multigrid method are a local damping of the restricted defect, a global upwind prolongation of the correction and a gIobal upwind restriction of the defect. Satisfactory multigrid convergence results are shown for the computation of a hypersonic launch and reentry flow around a blunt forebody with
canopy. For the test cases considered, it appears that the improved multigrid method performs
significantly better than a standard nonlinear multigrid method. For the test cases considered it
appears that the most significant improvement comes from the upwind prolongation, rather than from the upwind restriction and the defect damping.

AB - In steady hypersonic flow computations, Newton iteration as a local relaxation procedure and nonlinear multigrid iteration as an acceleration procedure may both easily fail. In the present chapter,
same remedies are presented for overcoming these problems. The equations considered are the
steady, two-dimensional Navier-Stokes equations. The equations are discretized by an upwind finite
volume method.
Collective point Gauss-Seidel relaxation is applied as the standard smoothing technique. In
hypersonics this technique easily diverges. First, collective line Gauss-Seidel relaxation is applied as
an alternative smoothing technique. Though promising, it also fails in hypersonics. Next, collective
point Gauss-Seidel relaxation is reconsidered and improved; a divergence monitor is introduced and
in case of divergence a switch is made to a local explicit time stepping technique. Satisfactory singlegrid convergence results are shown for the computation of a hypersonic reentry flow around a blunt forebody with canopy.
Unfortunately, with this improved smoothing technique, standard nonlinear multigrid iteration
still fails in hypersonics. The robustness improvements made therefore to the standard nonlinear multigrid method are a local damping of the restricted defect, a global upwind prolongation of the correction and a gIobal upwind restriction of the defect. Satisfactory multigrid convergence results are shown for the computation of a hypersonic launch and reentry flow around a blunt forebody with
canopy. For the test cases considered, it appears that the improved multigrid method performs
significantly better than a standard nonlinear multigrid method. For the test cases considered it
appears that the most significant improvement comes from the upwind prolongation, rather than from the upwind restriction and the defect damping.

M3 - Chapter

SN - 0-7923-1673-8

T3 - Fluid mechanics and its applications

SP - 203

EP - 231

BT - Computational methods in hypersonic aerodynamics

A2 - Murthy, T.K.S.

PB - Kluwer Academic Publishers

CY - Dordrecht

ER -