Topologic data structures applied on compressible flows simulations using finite volume and high-order methods

The storage and access of grid files by data structures and topologic operators is one of the most important goals of geometric modeling research field, which allows an efficient and stable implementation of adaptive refinement mechanisms, cells alignment and access to incidence and adjacency properties from grid elements, representing great concernment in the majority of applications from fluid mechanics. In the case of non-structured grids, the cellular decomposition if non-uniform and is better suited by a more sophisticated strategy - the topologic data structs. The topologic data structs index grid elements representing incidence and adjacency properties from grid elements, ensuring quick access to information. One of most common aspects from problems solved by computational fluid mechanic is the complexity of the domain geometry where the fluid ows. The usage of data structures to manipulate computational grids is of great importance because it performs efficiently queries on grid information and centers all operations to the grid on a unique module, allowing its extension and flexible usage on many problems. This work aims at exploring the coupling of a topologic data structure, the Mate Face, on a solver module, by controlling all grid access providing operators and iterators that perform complex neighbor queries at each grid element. The solver module solves the governing equations from fluid mechanics though the finite volume technique with a formulation that sets the property values to the control volume centroids, using high order methods - the ENO and WENO schemes, which have the purpose of efficiently capture the discontinuities appearing in problems governed by hyperbolic conservation laws. The two dimensional Euler equations are considered to represent the flows of interest. The coupling of the Mate Face data structure to the solver module was achieved by a creation of a library that acts as an interface layer between both modules, the Mate Face and the solver, which had been implemented using different programming languages. Therefore, all Mate Face class methods are available to the solver module though the interface library in the form of procedures. A study of dynamic grids was made by using spring methods for the moving grid under pitch movement case. The goal was to analyze the applicability of such method to aid non stationary simulations. Another contribution of this work was to show how the Mate Face can be extended in order to deal with non-supported types of elements, allowing it to aid numeric simulations using the spectral finite volume method. The spectral nite volume method is used to obtain high spatial resolution, also by setting the property values to the control volume centroids, but here the control volumes are partitioned into smaller volumes of different types, from triangles to hexagons. Then, an extension of the Mate Face was developed in order to hold the new generated grid by the partitioning specfied by the spectral finite volume method. The extension of Mate Face represents all partitioned elements locally for each original control volume. For all implementations and proposals from this work, experiments were performed to validate the usage of the Mate Face along with numeric methods. Finally, the data structure can aid the fluid flow simulation tools by managing the grid file and providing efficient query operators (AU)