The Effect Of Mesh Quality On Solution Efficiiency

Proceedings, 6th International Meshing Roundtable, Sandia National Laboratories, pp.249, October 1997

MESHING
RESEARCH
CORNER

Lori A. Freitag
Argonne National Laboratory
freitag@mcs.anl.gov

Abstract
It is well known that mesh quality affects both efficiency and accuracy of CFD solutions. Meshes with distorted elements make solutions both more difficult to compute and less accurate. We recently proposed a technique for improving mesh quality as measured by element angle (dihedral angle in three dimensions) using a combination of optimization-based smoothing techniques and local reconnection schemes [1]. In this presentation, we quantify the cost and benefit of these techniques for several application problems.

Preliminary numerical experiments are reported here to demonstrate the effect of mesh quality on the convergence rate of the commonly-used GMPES solver with Jacobi preconditioning, for incompressible flow over a cylinder. As shown in the figure on the left, large maximum angles significantly affect the number of iterations required for convergence, particularly if the maximum angle is greater than 178'. We also note that as the problem size increases (as indicated by N) the convergence degradation is more severe, In the figure on the right, we plot the difference in the time required to reach convergence on a poor quality mesh and the total time to reach convergence on an improved mesh which includes the time for mesh smoothing for three different problem sizes. The amount of time required for mesh smoothing is approximately 3.8, 8, and 15.7 seconds for N = 800, 1600 and 3200, respectively. Clearly, as the problem size and the maximum angle in the mesh increase, the amount of time saved by smoothing the mesh also increases. The presentation also includes results for GMRES with ILU preconditioning and purely advective and advective-diffusive applications.

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