Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods

ISBN-13: 9780128498941 / Angielski / Miękka / 2015 / 484 str.

Mazumder, Sandip

Opis

Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods focuses on two popular deterministic methods for solving partial differential equations (PDEs), namely finite difference and finite volume methods. The solution of PDEs can be very challenging, depending on the type of equation, the number of independent variables, the boundary, and initial conditions, and other factors. These two methods have been traditionally used to solve problems involving fluid flow. For practical reasons, the finite element method, used more often for solving problems in solid mechanics, and covered extensively in various other texts, has been excluded. The book is intended for beginning graduate students and early career professionals, although advanced undergraduate students may find it equally useful. The material is meant to serve as a prerequisite for students who might go on to take additional courses in computational mechanics, computational fluid dynamics, or computational electromagnetics. The notations, language, and technical jargon used in the book can be easily understood by scientists and engineers who may not have had graduate-level applied mathematics or computer science courses.

• Presents one of the few available resources that comprehensively describes and demonstrates the finite volume method for unstructured mesh used frequently by practicing code developers in industry
• Includes step-by-step algorithms and code snippets in each chapter that enables the reader to make the transition from equations on the page to working codes
• Includes 51 worked out examples that comprehensively demonstrate important mathematical steps, algorithms, and coding practices required to numerically solve PDEs, as well as how to interpret the results from both physical and mathematic perspectives

Recenzje

"All in all, this is a good book for the engineering students being patient enough to study this exciting and advanced subject of numerically solving PDEs. These students will be able to analyse their computational results, compare them for several methods and use to judge on them since not all what the computer prints or draws is useful information." --Zentralblatt MATH

"The book is rich in examples and numerical results. Each chapter contains exercises. The book could be a valuable text for engineering students." --Mathematical Reviews

Spis treści

1. Introduction to Numerical Methods for Solving Differential Equations2. The Finite Difference Method (FDM)3. Solution to System of Linear Algebraic Equations4. Stability and Convergence of Iterative Solvers5. Treatment of Time Derivative (Parabolic and Hyperbolic PDEs)6. The Finite Volume Method (FVM)7. Unstructured Finite Volume Method8. Miscellaneous Topics

AppendixA: Useful Relationships in Matrix AlgebraB: Useful Relationships in Vector CalculusC: Tensor Notations and Useful Relationships

O autorze

Sandip Mazumder received his PhD from the Pennsylvania State University, and is currently Professor at The Ohio State University. His research in radiation has primarily involved developing efficient methods for solving the radiative transfer equation and coupling it to other modes of heat transfer for practical applications. Dr. Mazumder was employed at CFD Research Corporation for 7 years prior to joining Ohio State in 2004. He is the recipient of the McCarthy teaching award and the Lumley research award from the Ohio State College of Engineering, among other awards, and is a fellow of the ASME.