Reevaluation of the Vertex Collocated Mesh for Primitive Variable Computation of Incompressible Fluid Flows by Enforcing Continuity-Based Boundary Conditions

Abstract

Complementing a previous comparative study of the accuracy of the fundamental mesh structures for primitive variable computations of incompressible fluid flows, this article considers some alternative approaches to the closure of the pressure equations in the boundary nodes of the vertex collocated mesh. In the previous study, these boundary pressures were determined directly by a discretized Poisson equation; in the present article the pressure equations at these nodes are derived from specific continuity equations, obtained by mass balance on the half-cells and by unilateral parabolic approximation of the velocity component normal to the wall. The first approach reduces the accuracy of the vertex collocated mesh to first-order, while the second approach remains second-order-accurate, except in the traditional cavity problem, and provides better results than the Poisson equation approach for rough and moderate refinements. However, in comparison with the other types of mesh, the vertex collocated mesh remains the least accurate for refined meshes.

Acknowledgments

The authors wish to express their gratitude to the Brazilian National Council for Scientific and Technological Development (CNPq) for its support of the present work in the form of a postdoctoral grant (process number 150804/2010-5).