Computational Algorithms for Shallow Water Equations

Toro, Eleuterio F.

Computational Algorithms for Shallow Water Equations
  • 出版商: Springer
  • 出版日期: 2024-08-02
  • 售價: $2,780
  • 貴賓價: 9.5 折 $2,641
  • 語言: 英文
  • 頁數: 400
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031613945
  • ISBN-13: 9783031613944
  • 相關分類: Algorithms-data-structures

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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《自由表面淺水流動的衝擊捕捉方法》的修訂和擴充版，首次由Wiley and Sons於2001年出版。該書描述了通過偏微分方程數學建模的自由表面流動，並介紹了現代的衝擊捕捉方法來解決這些問題，特別強調有限體積迎風和居中方法。這些方程和方法在模擬淺水流動、大氣流動、濃密氣體的傳播以及物質混合的動力學方面都是基礎。

該書附帶有數值軟件，以樣本計算機程序的形式作為補充材料。在這個新版本中，對現有章節進行了補充。此外，還新增了新的章節；其中一個章節回顧了双曲型偏微分方程的數學，另一個章節介紹了偏微分方程的數值分析，還有一個章節介紹了在有限體積和不連續Galerkin框架中的高階數值方法。此外，全書各個部分進行了全面的修改和校正，並增強了許多描繪數值結果的圖片。

這本書主要針對學術界、研究實驗室、工業界和咨詢機構中的環境科學家、應用數學家和工程師。從事數學建模和計算方法解決環境問題的高年級本科生和研究生將受益於學習這本書。講師可以將大部分材料用於水力學、海洋學、大氣學和其他地球物理流體動力學背景下的波動問題數值方法課程。

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)

Eleuterio F. Toro目前是意大利特倫托大學的名譽數學教授，曾任該大學的數值分析教授（Professore Chiara Fama）。他擁有純數學榮譽學士學位、泛函分析和微分方程碩士學位，以及計算數學博士學位。自1982年起，在意大利任職之前（2002年），他在英國擔任過多個學術職位，包括教授職位；他還在日本、俄羅斯、中國和美國等多個國家擔任過訪問學者職位；他在多個國家獲得了多項榮譽和殊榮。多年來，他的研究主要集中在構建用於解決時間依賴性演化偏微分方程的計算方法上，重點關注双曲平衡定律以及在工業、航空航天、環境和醫學問題中的應用。他是多本書的作者/編輯，並發表了300多篇論文。

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