A MULTIGRID-ACCELERATED THREE-DIMENSIONAL TRANSIENT- FLOW CODE AND ITS APPLICATION TO A NEW TEST PROBLEM

作者：Kumar D Santhosh^*; Dass Anoop K; Dewan Anupam

来源：Journal of Hydrodynamics, 2010, 22(6): 838-846.

DOI：10.1016/S1001-6058(09)60124-4

• incompressible flows
• three-dimensional cavity flow
• fractional-step method
• multigrid method
• Taylor-Gotler-Like (TGL) vortices
• grid transformation

A multigrid-assisted solver for the three-dimensional time-dependent incompressible Navier-Stokes equations on graded Cartesian meshes is developed. The spatial accuracy is third-order for the convective terms and fourth-order for the viscous terms, and a fractional-step strategy ensures second-order time accuracy. To achieve good time-wise efficiency a multigrid technique is used to solve the highly time-consuming pressure-Poisson equation that requires to be solved at every time step. The speed-up achieved by multigrid is shown in tabular form. The performance and accuracy of the code are first ascertained by computing the flow in a single-sided lid-driven cubic cavity with good grid-economy and comparing the results available in the literature. The code, thus validated, is then applied to a new test problem we propose and various transient and asymptotically obtained steady-state results are presented. Given the care taken to establish the credibility of the code and the good spatio-temporal accuracy of the discretization, these results are accurate and may be used for ascertaining the performance of any computational algorithm applied to this test problem.

• 出版日期2010-12