On the Accuracy of the Finite Volume Method on Polygonal Grids with Adaptive Mesh Refinement and Coarsening PDF Download

Author: Joe Antoine Rached
Publisher:
ISBN:
Category :
Languages : en
Pages : 266

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Book Description
The aim of this thesis is divided into two parts. The first part consists of imp lementing and testing the accuracy of polygonal grids in the Finite Volume Metho d (FVM) context, a method usually used in Computational Fluid Mechanics (CFD). T he use of polygonal elements instead of triangular or quadrilateral elements lie s behind the nature of the FVM, which adapts to any Control Volume (CV) shape. P ure advection and real flow test cases were conducted for this end. Results show ed that more insight should be made in developing a tailored differencing scheme to be used on polygonal grids. The accuracy was acceptable but the solution tim e was not enhanced. The second part of this thesis is to implement Adaptive Mesh Refinement (AMR) us ing the hanging nodes method, a technique that resolves cells in regions where n eeded. Since the computational cost is directly related to the number of element s used in the numerical simulation, AMR is capable of automatically refining the grid where large gradients are present and hence the accuracy of the solution i s increased with less computational cost and time, compared to uniform refinemen t. Mesh refinement alone is not sufficient because previously refined grids migh t not be needed anymore, especially in transient problems. To this end, a new me sh coarsening method was developed in order to decrease the density of the grid in regions where large gradients are not present anymore. AMR and Coarsening (AM RC) are usually implemented in a tree-structure, using a children-parent sort of linkage. In the developed method, the tree structure is abandoned and AMRC is d one locally without the need to store the history of the refined element. In order to speed up the simulation on adapted grids, a good initial guess on th e refined grid is needed. To this end, the solution of the original grid is mapp ed on the initial grid, leading to less time and computational cost in reaching a converged solution. Pure advection and real flow problems for fluid flows at a ll speeds where conducted. The method proves accuracy especially in the compress ible flow regime.