Calculation of the diffusive flow in complex domains by the finite volume method

Abstract

This paper describes a strategy to discretize the Poisson equation on unstructured meshes using the finite volume method based on the center of the cells. This approach is based on Date’s work[1] that uses an iterative technique known as deferred correction to obtain the right diffusive flow field in no orthogonal meshes. It was found that the method proposed by Date does not converge when the internal angles are less than 40°, then we proposes a new way to calculate the gradient in order to ensure the convergence. It shows a  convergence study that demonstrates  the high effectiveness of the proposed method. After  solving a  typical problem, based on  the solution of the  Poisson equation,  we compared  the results obtained with the analytical  solution, where there was a high correspondence of results without compromising  the computational time. Finally, we have demonstrate the  flexibility  of the approach implemented by performing  simulations on structured and unstructured   meshes, using elements  in the form of   quadrilaterals  and triangles in  2D, and curvilinear cubes  and tetrahedrons  in 3D.