A compact finite differences exact projection method for theudNavier–Stokes equations on a staggered grid with fourth-orderudspatial precision

摘要

An exact projection method for the numerical solution of the incompressible Navier–Stokes equations isuddevised. In all spatial discretizations, fourth-order compact finite differences are used, including domainudboundaries and the Poisson equation that arises from the projection method. The integration in time isudcarried out by a second-order Adams–Bashforth scheme. The discrete incompressibility constraint isudimposed exactly (up to machine precision) by a simple and efficient discretization of the Poisson equation.udSpatial and temporal accuracies, for both velocity and pressure, are verified through the use of analyticaludand manufactured solutions. The results show that the method converges with fourth-orderudaccuracy in space and second-order accuracy in time, for both velocity and pressure. Additionally, twoudpopular benchmark problems, the flow over a backward facing step and the lid-driven cavity flow, areudused to demonstrate the robustness and correctness of the code.