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.

The book covers intimately all the topics necessary for the development of a robust magnetohydrodynamic (MHD) code within the framework of the cell-centered finite volume method (FVM) and its applications in space weather study. First, it presents a brief review of existing MHD models in studying solar corona and the heliosphere. Then it introduces the cell-centered FVM in three-dimensional computational domain. Finally, the book presents some applications of FVM to the MHD codes on spherical coordinates in various research fields of space weather, focusing on the development of the 3D Solar-InterPlanetary space-time Conservation Element and Solution Element (SIP-CESE) MHD model and its applications to space weather studies in various aspects. The book is written for senior undergraduates, graduate students, lecturers, engineers and researchers in solar-terrestrial physics, space weather theory, modeling, and prediction, computational fluid dynamics, and MHD simulations. It helps readers to fully understand and implement a robust and versatile MHD code based on the cell-centered FVM.

This book consists of important contributions by world-renowned experts on adaptive high-order methods in computational fluid dynamics (CFD). It covers several widely used, and still intensively researched methods, including the discontinuous Galerkin, residual distribution, finite volume, differential quadrature, spectral volume, spectral difference, PNPM, and correction procedure via reconstruction methods. The main focus is applications in aerospace engineering, but the book should also be useful in many other engineering disciplines including mechanical, chemical and electrical engineering. Since many of these methods are still evolving, the book will be an excellent reference for researchers and graduate students to gain an understanding of the state of the art and remaining challenges in high-order CFD methods.

Handbook of Numerical Methods for Hyperbolic Problems explores the changes that have taken place in the past few decades regarding literature in the design, analysis and application of various numerical algorithms for solving hyperbolic equations. This volume provides concise summaries from experts in different types of algorithms, so that readers can find a variety of algorithms under different situations and readily understand their relative advantages and limitations. - Provides detailed, cutting-edge background explanations of existing algorithms and their analysis - Ideal for readers working on the theoretical aspects of algorithm development and its numerical analysis - Presents a method of different algorithms for specific applications and the relative advantages and limitations of different algorithms for engineers or readers involved in applications - Written by leading subject experts in each field who provide breadth and depth of content coverage

The development of high-order accurate numerical discretization techniques for irregular domains and meshes is often cited as one of the remaining chal lenges facing the field of computational fluid dynamics. In structural me chanics, the advantages of high-order finite element approximation are widely recognized. This is especially true when high-order element approximation is combined with element refinement (h-p refinement). In computational fluid dynamics, high-order discretization methods are infrequently used in the com putation of compressible fluid flow. The hyperbolic nature of the governing equations and the presence of solution discontinuities makes high-order ac curacy difficult to achieve. Consequently, second-order accurate methods are still predominately used in industrial applications even though evidence sug gests that high-order methods may offer a way to significantly improve the resolution and accuracy for these calculations. To address this important topic, a special course was jointly organized by the Applied Vehicle Technology Panel of NATO's Research and Technology Organization (RTO), the von Karman Institute for Fluid Dynamics, and the Numerical Aerospace Simulation Division at the NASA Ames Research Cen ter. The NATO RTO sponsored course entitled "Higher Order Discretization Methods in Computational Fluid Dynamics" was held September 14-18,1998 at the von Karman Institute for Fluid Dynamics in Belgium and September 21-25,1998 at the NASA Ames Research Center in the United States.

This book presents the select proceedings of the 48th National Conference on Fluid Mechanics and Fluid Power (FMFP 2021) held at BITS Pilani in December 2021. It covers the topics such as fluid mechanics, measurement techniques in fluid flows, computational fluid dynamics, instability, transition and turbulence, fluid‐structure interaction, multiphase flows, micro- and nanoscale transport, bio-fluid mechanics, aerodynamics, turbomachinery, propulsion and power. The book will be useful for researchers and professionals interested in the broad field of mechanics.

This book collects papers presented during the European Workshop on High Order Nonlinear Numerical Methods for Evolutionary PDEs (HONOM 2013) that was held at INRIA Bordeaux Sud-Ouest, Talence, France in March, 2013. The central topic is high order methods for compressible fluid dynamics. In the workshop, and in this proceedings, greater emphasis is placed on the numerical than the theoretical aspects of this scientific field. The range of topics is broad, extending through algorithm design, accuracy, large scale computing, complex geometries, discontinuous Galerkin, finite element methods, Lagrangian hydrodynamics, finite difference methods and applications and uncertainty quantification. These techniques find practical applications in such fields as fluid mechanics, magnetohydrodynamics, nonlinear solid mechanics, and others for which genuinely nonlinear methods are needed.

With considerations such as complex-dimensional geometries and nonlinearity, the computational solution of partial differential systems has become so involved that it is important to automate decisions that have been normally left to the individual. This book covers such decisions: 1) mesh generation with links to the software generating the domain geometry, 2) solution accuracy and reliability with mesh selection linked to solution generation. This book is suited for mathematicians, computer scientists and engineers and is intended to encourage interdisciplinary interaction between the diverse groups.