An Investigation of Directional-Coarsening and Line-Implicit Smoothing Applied to Agglomeration Multigrid

Abstract

The convergence rates of explicit agglomeration multigrid algorithms for turbulent flow problems are significantly worse than for inviscid flow problems. Two techniques for reducing numerical stiffness are investigated and compared. Directional coarsening, controlled by the parameter β, alters the agglomeration algorithm to generate coarse grids that reduce localized cell stretching. Line-implicit smoothing, controlled by the parameter α, adds implicit terms to the preconditioner along one-dimensional lines constructed on the mesh. Optimal values of β and α are presented for structured and hybrid unstructured meshes. A factor of two improvement in asymptotic convergence rates has been demonstrated. Substantial improvements in CPU time can be obtained for a five-order residual reduction.

High-order implicit residual smoothing time scheme for direct and large eddy simulations of compressible flows

“…A possible alternative is to use line-detection techniques in conjunction with a structured formulation of the IRS operators (see, e.g. [44,45]). This approach, that has the advantage of leading to inversion of banded matrices, will be explored in the future.…”

Fast unsteady flow computations with a Jacobian-free Newton–Krylov algorithm

“…In the literature a few techniques are proposed to alleviate the stiffness induced by the large aspect ratio cells, e.g. semi-coarsening [7,8] and line implicit smoothing [7][8][9]. A combination of the two enabled Lassaline and Zingg [7] a speed up of a factor 3.5 for two-dimensional, subsonic, turbulent computations performed on structured c-grids.…”

“…semi-coarsening [7,8] and line implicit smoothing [7][8][9]. A combination of the two enabled Lassaline and Zingg [7] a speed up of a factor 3.5 for two-dimensional, subsonic, turbulent computations performed on structured c-grids. However, semi-coarsening is not practical in three dimensions whereas line implicit smoothing is difficult to apply on unstructured grids.…”

An aspect ratio agglomeration multigrid for unstructured grids

“…Mavriplis has addressed a combination of implicit line‐relaxation solver coupled with directional coarsening multigrid, resulting in an improved viscous convergence rate for Reynolds averaged Navier–Stokes equations on highly stretched unstructured grids. Many references demonstrate the better features for directional‐coarsening grid generator and implicit line‐relaxation strategy. The method in present is also inspired by those techniques.…”

“…Mavriplis [20] has addressed a combination of implicit line-relaxation solver coupled with directional coarsening multigrid, resulting in an improved viscous convergence rate for Reynolds averaged Navier-Stokes equations on highly stretched unstructured grids. Many references [19][20][21] demonstrate the better features for directional-coarsening grid generator and implicit line-relaxation strategy. The method in present is also inspired by those techniques.In this manuscript, we have preferred aspect ratio as an agglomeration weight and modified the standard advancing front agglomeration algorithm to fuse isotropic cells around a vertex, combining with advance high-stretched areas along cells' contraction direction.…”