Compact Finite-Differencing and Filtering Procedure Applied to the Incompressible Navier-Stokes Equations

摘要

A high-order discretization and filtering procedure is applied to the solution of the incompressible Navier-Stokes equations in a vorticity/stream-function formulation, which is implemented in curvilinear coordinates. Compact finite differencing is coupled with the use of a low-pass filtering operator to augment the stability of the scheme for high-Reynolds-number flows and/or low-resolution meshes. Advancement in time is done through either first- or second-order, backward Euler time integrations, which are supplemented with Newton-like subiterations. Temporal and spatial formal orders of accuracy are examined through exact solutions of the governing equations, where the theoretical orders of accuracy are achieved for up to sixth-order spatial and second-order temporal discretizations. The technique is also demonstrated on both steady and unsteady incompressible flow canonical problems, including the lid-driven cavity and unsteady flow over a cylinder. The advantage of the high-order scheme coupled with the filter becomes apparent from more accurate solutions being achievable on much coarser meshes.