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

## Sandip Mazumder Ph.D.

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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

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From the Back Cover:

Numerical Methods for Partial Differential Equations 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. 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.

Key Features:

• Provides a thorough understanding of how to develop computer programs for solving partial differential equations typically encountered in science and engineering from the ground up.
• Demonstrates the finite volume method for unstructured mesh, a method used frequently by practicing code developers in industry
• Includes extensive instruction on how to solve a system of linear algebraic equations by iterative methods

Sandip Mazumder

Department of Mechanical and Aerospace Engineering, The Ohio State University, Columbus, OH

Professor Mazumder received his Ph.D. in Mechanical Engineering from Penn State University. After graduation, he joined CFD Research Corporation, where he was one of the architects and early developers of the commercial computational fluid dynamics code CFD-ACE+. In 2004, he joined the Ohio State University, where he teaches both graduate and undergraduate courses in heat and mass transfer, thermodynamics, numerical methods, and computational fluid dynamics. He is the author of over fifty journal publications, which have been cited more than one thousand times according to the ISI citation index. Dr. Mazumder is the recipient of several research and teaching awards, and is a Fellow of the American Society of Mechanical Engineers.

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Sandip Mazumder received his Ph.D. in Mechanical Engineering from Penn State University. After graduation, he joined CFD Research Corporation, where he was one of the architects and early developers of the commercial computational fluid dynamics code CFD-ACE+. In 2004, he joined the Ohio State University, where he teaches both graduate and undergraduate courses in heat and mass transfer, thermodynamics, numerical methods, and computational fluid dynamics. He is the author of over fifty journal publications, which have been cited more than one thousand times according to the ISI citation index. Dr. Mazumder is the recipient of several research and teaching awards, and is a Fellow of the American Society of Mechanical Engineers since 2011.