Stable and Spectrally Accurate Schemes for the Navier–Stokes Equations

Abstract

In this paper, we present an accurate, efficient and stable numerical method for the incompressible Navier-Stokes equations (NSEs). The method is based on (1) an equivalent pressure Poisson equation formulation of the NSE with proper pressure boundary conditions, which facilitates the design of high-order and stable numerical methods, and (2) the Krylov deferred correction (KDC) accelerated method of lines transpose ($\mbox{MoL}^{\it T}$), which is very stable, efficient, and of arbitrary order in time. Numerical tests with known exact solutions in three dimensions show that the new method is spectrally accurate in time, and a numerical order of convergence 9 was observed. Two-dimensional computational results of flow past a cylinder and flow in a bifurcated tube are also reported.