Discretized pressure Poisson algorithm for steady incompressible flow on two-dimensional triangular unstructured grids

Abstract

Abstract Many numerical algorithms have developed for Computational Fluid Dynamics (CFD). Previously, we provided a discretized pressure Poisson algorithm for steady incompressible flow on structured grids. Though this algorithm is very simple, there are still some problems for this algorithm to be implemented on unstructured grids. In order to solve incompressible flow problems on unstructured grids simply and easily, this paper developed some strategies to implement discretized pressure Poisson algorithm for steady incompressible flow on unstructured grids. Firstly, this paper discretized the convective term and diffusion term of momentum equations easily by the quantities of nodes and nearby points. Combined with the incenter-based Finite Volume Method (FVM), discretization of governing equations on triangular unstructured grids could be more easily implemented. Secondly, for the application of discretized pressure Poisson algorithm, this paper provided a discretization strategy for the continuity equation on unstructured grids. Thus, the mass conservation could be easily satisfied during the iteration of velocity calculation, which bring great advantages for the velocity calculation on unstructured grids. Then, discretized pressure Poisson algorithm was successfully used to calculate the lid-driven cavity flow problem on unstructured grids; the whole process was very simple and the results were also reliable.