An efficient edge based data structure implementation for a vertex based finite volume method

An efficient edge based data structure has been proposed for the implementation of vertex based finite volume formulation. In the present approach, the quad-edge and halfedge data structures are redesigned and simplified in order to fit requirements of the cell-vertex centered finite volume methods. The present data structure is not limited with triangles, arbitrary polygons are also supported in the mesh without putting any additional effort. An explicit second-order compressible Euler solver based on the present data structure has been implemented in order to demonstrate its efficiency compared to the classical edge-based implementation for a vertex based finite volume formulation. Nevertheless, a fully implicit version of the present numerical algorithm has also been implemented based on PETSc library in order to improve the robustness of the algorithm. As a benchmark problem, the calculations over an RAE2822 airfoil and a circular cylinder are performed in order to demonstrate its efficiency.