A high-order finite volume method solving viscous incompressible flows using general pressure equation

Abstract

A high-order accurate finite volume method on Cartesian meshes has been developed to solve viscous incompressible flows using the general pressure equation (GPE). The GPE is a pressure evolution equation that replaces the divergence-free constraint equation when computing incompressible flows. The high-order spatial accuracy of the current method is deduced from the high-order flow reconstruction model using the conserved volume integrals, and the high-order accurate computations of the flux integrals. The Roe’s flux difference scheme was adapted to compute the inviscid fluxes. The grid convergence tests using the solution of Taylor-Green decaying vortices showed that the current method is spatially fifth order accurate for both velocity and pressure. The problem of doubly periodic shear layers and the lid-driven cavity flow were computed to demonstrate the capability of the current method in transient and steady state computations.