Pressure marching schemes that work

Abstract

SUMMARYNumerical solutions for two-dimensional or axisymmetric viscous fluid flow problems are usually based on the stream function/vorticity formulation. Frequently, however, the pressure distribution is of prime interest. Difficulties have been reported in the literature with the use of obvious pressure marching schemes. Consequently, several investigators have preferred to use an iterative method which involves solving a Poisson equation with Neumann boundary conditions. In this paper, the fundamental cause of failure of the marching schemes is investigated. The authors introduce the concept of compatible pressure and vorticity schemes and show that lack of compatibility has been the principal reason for the poor results obtained using marching schemes. Compatible pressure marching methods are developed and shown to give good results. Comparisons are made between the Poisson equation method and the compatible marching method. To make the comparisons meaningful, special test cases with analytical solutions have been used.

Long wave interaction with a partially immersed body. Part I: Mathematical models

“…As a result, we have a natural splitting of our problem. To determine the velocity function u , we have a system of non-homogeneous * If one needs to reconstruct the depth-integrated pressure ℘ , it can be achieving using a marching pressure scheme [83].…”

Numerical modelling of the steady fluid flows in the framework of a shallow-water model

“…This method was considered in [6] for the case of rectangular grids. It is known as the marching method of calculating the pressure in viscous incompressible fluid flows [9].…”