Computation of Time-Accurate Laminar Flows Using Dual Time Stepping and Local Preconditioning with Multigrid

Authors: MURAT UYGUN, KADİR KIRKKÖPRÜ

Abstract: A cell-centered finite volume method with explicit dual time-stepping and a low Mach number preconditioning technique is successfully applied to 2-dimensional Navier-Stokes equations for the numerical solution of time-dependent flows ranging from near incompressible limit to high subsonic Mach numbers. Preconditioning techniques have been widely used in order to remove the disparity between acoustic and convective speeds that degrades the convergence rate noticeably at low subsonic Mach numbers. In dual time stepping, a modified steady problem is solved by advancing in pseudo time at each physical time step. A multistage explicit Runge-Kutta time-stepping scheme is used for marching in pseudo time. Convergence is accelerated by means of local time stepping, residual smoothing, and multigrid. The accuracy of the time-accurate Navier-Stokes solver is verified by comparing predictions of the Strouhal numbers for the Karman vortex streets of the cylinder and of the blunt flat plate with the experimental data.

Keywords: Dual time stepping, Local preconditioning, Laminar flow, Multigrid

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