Two-dimensional implicit time dependent calculations for incompressible flows on adaptive unstructured meshes

Abstract

An implicit muItigrid-driven algorithm for two-dimensional incompressible laminar viscous flows is coupled with a mesh adaptation method to better capture the important features of the flow for time dependent problems. Time dependent calculations are performed implicitly by regarding each time step as a steady-state problem in pseudotime. The method of artificial compressibility is used to solve the flow equations. An adaptation method performs local mesh refinement using an incremental Delaunay algorithm and mesh coarsening by means of an edge collapse. The method is validated by comparison with experimental results of low Reynolds number flow over a shedding circular cylinder.

Mesh deformation and modification for time dependent problems

“…The mesh has adapted automatically to the change in domain shape and has become highly enriched in the vicinity of the crack tip in order to resolve the large strain energy values in that region. An example in which only static adaptation is used can be found in the work of Lin [13]. He presents a computation of incompressible, laminar ow over a cylinder for Reynolds numbers between 50 and 180.…”

A finite volume unstructured multigrid method for efficient computation of unsteady incompressible viscous flows

“…Following the approach presented [12] for data transfer within the domain and incorporating the new technique developed here for curved boundary, there are two classes of mesh-to-mesh transfer operators being implemented in the present study, which are restriction operators and prolongation operators.…”

“…While physical time integration can usually be obtained with a three-point second-order implicit scheme, time stepping in pseudo time can be explicit [10][11][12] or implicit [8,13,14]. Liu et al [11] have developed a multigrid method using the dual time stepping scheme on structured grids for the computation of unsteady incompressible viscous ows while Lin [12] has attempted the unstructured multigrid method for calculating unsteady inviscid ows. In this study, we aim to extend the high-order characteristics-based ÿnite-volume scheme for unstructured grids in Reference [15] to simulate unsteady incompressible viscous ows by introducing an unstructured multigrid method.…”

Two‐dimensional implicit time‐dependent calculations on adaptive unstructured meshes with time evolving boundaries

“…Various convergence acceleration techniques can be used to speed up the convergence to steady state in pseudo-time. The three used in this work are multigrid, local time stepping, and residual averaging (details are provided in References [8,43]). A more detailed account of the numerical discretization can be found in References [39,40].…”

“…Chorin [10] proposed the method of artiÿcial compressibility for steady state problems, which was later modiÿed to treat time-dependent problems [11][12][13]. This artiÿcial compressibility approach has also been used successfully with Jameson's implicit multigrid-driven dual time stepping method [4,5,8].…”