Efficient Implementation of High-Order Accurate Numerical Methods on Unstructured Grids

This thesis focuses on the development of high-order finite volume methods and discontinuous Galerkin methods, and presents possible solutions to a number of important and common problems encountered in high-order methods, such as the shock-capturing strategy and curved boundary treatment, then applies these methods to solve compressible flows.

Nominated by Tsinghua university as an outstanding PhD thesis Novel ideas in constructing limiters for finite volume and discontinuous Galerkin methods Solves viscous compressible flows using unstructured high order finite volume methods Includes supplementary material: sn.pub/extras

Inhalt
Introduction.- High Order Finite Volume Method for the Compressible Flows.- Accuracy-Preserving Limiters for High Order Finite Volume Methods.- Mixed Element and Curved Boundary Treatment.- The Discontinuous Galerkin Method.- Conclusions and Prospects.