Optimizing computational high-order schemes in finite volume simulations using unstructured mesh and topological data structures

Abstract

Many numerical methods are based in mesh files to represent the computational domain. Also, an efficient storage and retrieval of mesh information can be achieved by data structures. Moreover, the development of topological operators is one of the important goals of the geometric modeling research field. While it loads mesh files more efficiently, it also allocates less main memory, provides persistence and allows consistent query operations. This paper proposes an improving of the computational scheme of high-order WENO schemes by coupling a standard cell centered, unstructured mesh, finite volume method with an topological data structure. The solver module uses the finite volume technique with a formulation that sets the property values to the control volume centroids. The two dimensional Euler equations are considered to represent the flow of interest. Beyond experiments using the improved approach, the computational cost of the data structure was measured by comparing with the traditional representation, and the results showed that our approach provides scalable loading and managing of meshes, having less memory occupation rate when comparing meshes with an increasing number of elements.