On the development of an agglomeration multigrid solver for turbulent flows

Abstract

The paper describes the implementation details and validation results for an agglomeration multigrid procedure developed in the context of hybrid, unstructured grid solutions of aerodynamic flows. The governing equations are discretized using an unstructured grid finite volume method, which is capable of handling hybrid unstructured grids. A centered scheme as well as a second order version of Liou’s AUSM+ upwind scheme are used for the spatial discretization. The time march uses an explicit 5-stage Runge-Kutta time-stepping scheme. Convergence acceleration to steady state is achieved through the implementation of an agglomeration multigrid procedure, which retains all the flexibility previously available in the unstructured grid code. The calculation capability created is validated considering 2-D laminar and turbulent viscous flows over a flat plate. Studies of the various parameters affecting the multigrid acceleration performance are undertaken with the objective of determining optimal numerical parameter combinations

An aspect ratio agglomeration multigrid for unstructured grids

“…Another aspect ratio is defined as surface to volume ratio , specifically, in 3D and in 2D, where l stands for the circumferential length of the control volume. In this situation, high aspect ratio stands for high‐stretched cell, low‐aspect ratio stands for high quality in grid shape.…”

“…This method is first introduced by Lallemand and Smith , circumvents this problem by using heuristics to fuse the control volumes for the cell or vertex as seed. For isotropic agglomeration, several improvements have been made to optimize the fused cell according to aspect ratio and coarsening ratio between different grid levels, which work on vertex‐centered dual grid data structure and using a greedy‐type frontal algorithm. When come to cell‐centered scheme, agglomerate across cells sharing a common vertex is considered to be more suitable in complexities of time and space.…”

Agglomeration-Based Geometric Multigrid Solvers for Compact Discontinuous Galerkin Discretizations on Unstructured Meshes

“…The technique is not widely used for continuous Galerkin finite element methods, because of the difficulties in defining continuous approximation spaces on the resulting polyhedral elements. However, the technique has been used successfully for finite volume methods [11,4,18], where it is easier to update the element-averages after coarsening. This is also true for high-order discontinuous Galerkin methods, since they are straight-forward to implement on meshes of arbitrarily shaped elements [7,6].…”

Strong Coupled Agglomeration Multigrid for Navier-Stokes Equations on Unstructured Grids

“…The third to generate coarse grids through agglomeration, which is first introduced by Lallemand [4] and Smith [5], circumvents this problem by using heuristics to fuse the control volumes for the cell or vertex. Several improvements [6][7][8][9] have been made to agglomeration grids in order to optimize the fused cells according to a surface to volume ratio and coarsening ratio between different grid levels. Other improvements [10,11] need additional knowledge about the cell types of the primary grid for the agglomerated volumes.…”