Numerical Methods for Unsteady Compressible Flow Problems

Numerical Methods for Unsteady Compressible Flow Problems is written to give both mathematicians and engineers an overview of the state of the art in the field, as well as of new developments. The focus is on methods for the compressible Navier-Stokes equations, the solutions of which can exhibit shocks, boundary layers and turbulence. The idea of the text is to explain the important ideas to the reader, while giving enough detail and pointers to literature to facilitate implementation of methods and application of concepts.

The book covers high order methods in space, such as Discontinuous Galerkin methods, and high order methods in time, in particular implicit ones. A large part of the text is reserved to discuss iterative methods for the arising large nonlinear and linear equation systems. Ample space is given to both state-of-the-art multigrid and preconditioned Newton-Krylov schemes.

• Applications to aerospace, high-speed vehicles, heat transfer, and more besides
• Suitable as a textbook for graduate-level courses in CFD, or as a reference for practitioners in the field

《非穩定可壓縮流數值方法》這本書旨在為數學家和工程師提供該領域的最新發展概述。重點是壓縮性納維爾-斯托克斯方程的方法，其解可以展示出震波、邊界層和湍流。本書的目的是向讀者解釋重要的概念，同時提供足夠的細節和文獻指引，以便實施方法和應用概念。

本書涵蓋了空間中的高階方法，如不連續伽辣金方法，以及時間中的高階方法，特別是隱式方法。文中的大部分內容用於討論解決大型非線性和線性方程系統的迭代方法。同時詳細介紹了最先進的多重網格和預條件牛頓-克里洛夫方案。

特點：
- 應用於航空航天、高速車輛、熱傳等領域
- 適合作為計算流體力學研究生課程的教材，或作為該領域從業人員的參考書籍

Philipp Birken is an associate professor for numerical analysis and scientific computing at the Centre for the Mathematical Sciences at Lund University, Sweden. He received his PhD in mathematics in 2005 from the University of Kassel, Germany, where he also received his habilitation in 2012. He was a PostDoc and a consulting assistant professor at the Institute for Computational & Mathematical Engineering at Stanford University, USA. His work is in numerical methods for compressible CFD and Fluid-Structure-Interaction.

Philipp Birken是瑞典隆德大學數值分析和科學計算中心的副教授。他於2005年在德國卡塞爾大學獲得數學博士學位，並於2012年在該校獲得博士後資格。他曾在美國斯坦福大學計算與數學工程研究所擔任博士後研究員和諮詢助理教授。他的研究領域包括可壓縮流體動力學和流體結構相互作用的數值方法。