Computational Algorithms for Shallow Water Equations
暫譯: 淺水方程的計算演算法

Toro, Eleuterio F.

Computational Algorithms for Shallow Water Equations
  • 出版商: Springer
  • 出版日期: 2025-08-02
  • 售價: $2,400
  • 貴賓價: 9.5 折 $2,280
  • 語言: 英文
  • 頁數: 408
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 303161397X
  • ISBN-13: 9783031613975
  • 相關分類: 工程數學 Engineering-mathematics

    • 海外代購書籍(需單獨結帳)

商品描述

This book is a thoroughly revised and enlarged version of "Shock-capturing methods for free-surface shallow flows", first published by Wiley and Sons, 2001. The book describes mathematically free-surface flows through partial differential equations and includes modern shock-capturing methods to solve them, with strong emphasis on finite volume upwind and centred methods. Such equations and methods are fundamental in simulating shallow water flows but also atmospheric flows, dispersion of dense gases and the dynamics of mixtures of materials.

The book is accompanied by numerical software in the form of sample computer programs as supplementary material. In this new edition, additional sections have been introduced to existing chapters. Also, new chapters have been included; one contains a review of the mathematics of hyperbolic partial differential equations, another introduces the numerical analysis of partial differential equations and another one deals with advanced very-high order numerical methods in the finite volume and discontinuous Galerkin frameworks. Furthermore, comprehensive modifications and corrections have been made throughout various sections of the text, and numerous figures depicting numerical results have been enhanced.

This book is primarily intended for environmental scientists, applied mathematicians and engineers in academia, research laboratories, industry and consultancy organisations. Senior undergraduate and postgraduate students involved with mathematical modelling and computational methods for environmental problems will benefit from studying this book. Lecturers could use most of the material for courses on numerical methods for wave propagation problems in hydraulics, oceanography, atmospherics and other geophysical fluid dynamics contexts.

商品描述(中文翻譯)

這本書是《自由表面淺流的震波捕捉方法》的全面修訂和擴充版本，首次由Wiley and Sons於2001年出版。該書通過偏微分方程數學地描述自由表面流動，並包括現代震波捕捉方法來解決這些方程，特別強調有限體積的上風和中心方法。這些方程和方法在模擬淺水流動、氣象流動、密度氣體的擴散以及材料混合物的動力學中都是基本的。

本書附有數值軟體，形式為示範計算機程式作為補充材料。在這個新版本中，對現有章節引入了額外的部分。此外，還新增了章節；其中一章包含了對雙曲型偏微分方程數學的回顧，另一章介紹了偏微分方程的數值分析，還有一章處理有限體積和不連續Galerkin框架中的高階數值方法。此外，文本的各個部分進行了全面的修改和更正，並增強了許多描繪數值結果的圖形。

本書主要針對環境科學家、應用數學家以及學術界、研究實驗室、工業和顧問機構的工程師。參與環境問題的數學建模和計算方法的高年級本科生和研究生將從學習本書中受益。講師可以使用大部分材料來教授水力學、海洋學、大氣學及其他地球物理流體動力學背景下的波傳播問題的數值方法課程。

作者簡介

Eleuterio F. Toro is currently Emeritus Professor of Mathematics at the University of Trento, Italy, and formerly Professor of Numerical Analysis (Professore Chiara Fama) at the same University. He holds an Honours B.Sc. in pure mathematics, an M.Sc. in functional analysis and differential equations, and a Ph.D. in computational mathematics. Since 1982, and prior to his appointment in Italy (2002), he held several academic positions in the UK, including a full professorship; he has also held many visiting appointments in various countries, such as Japan, Russia, China, and USA; he is Recipient of several honours and distinctions in various countries. His research has for many years focused on the construction of computational methods for solving time-dependent evolutionary partial differential equations, with emphasis on hyperbolic balance laws and applications to industrial, aerospace, environmental, and medical problems. He is Author/Editor of several books and Author of more than 300 publications.

作者簡介(中文翻譯)

埃盧特里奧·F·托羅（Eleuterio F. Toro）目前是義大利特倫托大學的名譽數學教授，曾擔任該大學的數值分析教授（Professore Chiara Fama）。他擁有純數學的榮譽理學士學位、函數分析與微分方程的碩士學位，以及計算數學的博士學位。自1982年以來，在他於義大利任職之前（2002年），他在英國擔任過多個學術職位，包括全職教授；他還在日本、俄羅斯、中國和美國等多個國家擔任過多個訪問職位；並在多個國家獲得了多項榮譽和獎項。他的研究多年來專注於構建解決時間相關的演化偏微分方程的計算方法，特別強調雙曲平衡法則及其在工業、航空航天、環境和醫療問題上的應用。他是多本書籍的作者/編輯，並且發表了超過300篇的學術論文。

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