Navier-stokes Numerical Solutions For Flows With A Pressure Discontinuity

摘要

A numerical solution for the 2D Navier-Stokes Equations is given for viscous incompressible flow in the presence of high pressure gradient variations. Governing equations are expressed in a general curvilinear coordinates using primitive variables (p,u,v). The method is based on the artificial compressibility approach so that a simultaneous resolution of the N-S equations can be elaborated to calculate pressure and velocity fields. The implicit convective terms are first-order differenced using the Steger & Warming decomposition, whereas for the explicit one, a third order or fifth order Roe flux-difference splitting method is applied to eliminate pressure fluctuations. The system of equations is solved with an approximate 9 points LU factorization. Results mentioned in this paper include some well-known steady-state cases: 1) a driven-cavity flow for the Reynolds numbers Re= 10 000, 2) the case of a flow across an axisymmetric sudden constriction of an aspect ratio of 2.88.