Deterministic High Order Vortex Methods for the 2D Navier–Stokes Equation with Rezoning

✍ Scribed by Henrik O. Nordmark

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 453 KB
• Volume: 129
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1996.0232

✦ Synopsis

In this paper, we extend the use of automatic rezoning to viscous flow in two dimensions. In a previous paper, we tested this technique on inviscid flow, with very good results. To simulate viscosity, we follow Fishelov's idea of explicitly taking the Laplacian of the cutoff function, but unlike Fishelov we use a moving grid. This eliminates the need to approximate the gradient of the vorticity, but rezoning needs to be used to keep the discretization error low. We first test the method on a radially symmetric problem where the exact vorticity is known for all time. Using both an eighth order cutoff function and an infinite order cutoff function, we obtain low errors and high rates of convergence. Then, we calculate the evolution of two circular vortex patches and of a square vorticity patch. The exact solution for the last two problems is not known. In all test problems we use a viscosity coefficient of 0.0005.