language: en

High-Order Accurate Schemes for Incompressible Viscous Flow

John C. Strikwerday
Computer Sciences Department University of Wisconsin-Madison

Abstract We present new finite difference schemes for the incompressible Navier-Stokes equations. The schemes are based on two spatial differencing methods, one is fourth-order accurate and the other is sixth-order accurate. The temporal differencing is based on backward differencing formulas. The schemes use non-staggered grids and satisfy regularity estimates, guaranteeing smoothness of the solutions. The schemes are computationally efficient. Computational results demonstrating the accuracy are presented.

Keywords: incompressible Navier-Stokes, finite difference schemes, GMRES. AMS(MOS) classifications: 65M05, 65N05, 76D05

1. Introduction.