NUMERICAL SOLUTION OF 2-D EULER EQUATIONS WITH MULTIGRID

Abstract

A multigrid scheme is applied to accelerate the convergence of numerical solution of two dimensional Euler equations to steady state. Cell-centered finite volume method with central differencing scheme is used for discretization. Explicit multistage time-stepping algorithm is used to advance the solution in time. Acceleration techniques including local time stepping and implicit residual smoothing are used as well. Attention is directed towards the accuracy, convergence, and computational performance of the V-cycle and W-cycle multigrid strategies together with piece-wise constant and bilinear interpolations on two grid and three grid levels. Subsonic and transonic inviscid flows past NACA 0012 airfoil are computed as test cases.

Keywords

• Euler Equations
• Central Differencing Scheme
• Explicit Time-stepping
• Multigrid Acceleration