Download for FREE in 4 easy steps...
You can also read this in Bookboon.com Premium
This book will be useful to scientists and engineers who want a simple introduction to the finite volume method.
300+ Business books exclusively in our Premium eReader
- No adverts
- Advanced features
- Personal library
Users who viewed this item also viewed
Introductory Finite Difference Methods for PDEs
Computational Fluid Dynamics
An introduction to partial differential equations
A First Course on Aerodynamics
Engineering Fluid Mechanics Solution Manual
Fundamental Engineering Optimization Methods
Fluid Mechanics and the Theory of Flight
Engineering Fluid Mechanics
About the book
This book will be useful to scientists and engineers who want a simple introduction to the finite volume method. A series of computer codes are given on the companion website along with worked solutions to exercises. This book is a companion text to 'Introductory Finite Difference Methods for PDEs'.
This material is taught in the BSc. Mathematics degree programme at the Manchester Metropolitan University, UK. The Finite Volume Method (FVM) is taught after the Finite Difference Method (FDM) where important concepts such as convergence, consistency and stability are presented. The FDM material is contained in the online textbook, ‘Introductory Finite Difference Methods for PDEs’ which is free to download from this website
It is recommended that the FDM text book is read before this book. This textbook is also freely downloadable from the above website.
The following chapters contain core material supported by pen and paper exercises together with computer-based exercises where appropriate. Supporting material, including worked solutions, and computer codes can be found at the companion website:
Codes, with which the student can experiment, are written using Matlab. In the spirit of Open Source, it is hoped to reproduce these codes using Scilab (a Matlab clone, downloadable for free from www.scilab.org).
The emphasis of this book is on a practical understanding of the basics of the FVM and a minimum of theory is given to underpin the method. Revision material is provided in appendices. It is recommended that anyone wishing to use the FVM to solve systems of equations for real world applications reads up on the underlying physics of the problem.
This book is intended for final year undergraduates who have knowledge of Calculus, vectors and introductory level computer programming.
1.2 Obtaining the Integral Form from the Differential Form
1.3 Finite Volume Meshes
1.4 Discretising the Semi-Integral Equation
2 Finite Volume Schemes
2.2 FVM on a Cartesian Mesh
2.3 Finite Volume Schemes in 1D and 3D
2.4 Time Step Calculation for a Finite Volume Scheme
2.5 Finite Volume FOU 2D Scheme
2.6 Boundary Conditions
2.7 Coding a Finite Volume Solver
3 Derivation of Equations
3.2 Conservation Laws
3.3 Control Volume Approach
3.4 Deriving the Integral Form of the 2D Linear Advection Equation
3.5 Deriving the Differential Form of the 2D Linear Advection Equation
4 Further Finite Volume Schemes
4.2 Linear Interpolation
4.3 Quadratic Interpolation
4.4 Converting from Finite Difference to Finite Volume
5 Systems of Equations
5.2 The Shallow Water Equations
5.3 General FVS for the SWE
5.4 FVS for the 2D SWE on a Structured Mesh
5.5 Heuristic Time Step for a 2D SWE FVS
The embed frame is free to use for private persons, universities and schools. It is not allowed to be used by any company for commercial purposes unless it is for media coverage. You may not modify, build upon, or block any portion or functionality of the embed frame, including but not limited to links back to the bookboon.com website.
The Embed frame may not be used as part of a commercial business offering. The embed frame is intended for private people who want to share eBooks on their website or blog, professors or teaching professionals who want to make an eBook available directly on their page, and media, journalists or bloggers who wants to discuss a given eBook
If you are in doubt about whether you can implement the embed frame, you are welcome to contact Thomas Buus Madsen on firstname.lastname@example.org and seek permission.