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This textbook explores both the theoretical foundation of the Finite Volume Method (FVM) and its applications in Computational Fluid Dynamics (CFD). Readers will discover a thorough explanation of the FVM numerics and algorithms used for the simulation of incompressible and compressible fluid flows, along with a detailed examination of the components needed for the development of a collocated unstructured pressure-based CFD solver. Two particular CFD codes are explored. The first is uFVM, a three-dimensional unstructured pressure-based finite volume academic CFD code, implemented within Matlab. The second is OpenFOAM®, an open source framework used in the development of a range of CFD programs for the simulation of industrial scale flow problems.

With over 220 figures, numerous examples and more than one hundred exercise on FVM numerics, programming, and applications, this textbook is suitable for use in an introductory course on the FVM, in an advanced course on numerics, and as a reference for CFD programmers and researchers.

The Finite Volume Method in Computational Fluid Dynamics: An Advanced Introduction with OpenFOAM® and Matlab

Foundation

1 Introduction

2 Review of Vector Calculus

3 Mathematical Description of Physical Phenomena

4 The Discretization Process

5 The Finite Volume Method

6 The Finite Volume Mesh

7 The Finite Volume Mesh in OpenFOAM® and uFVM

Discretization

8 Spatial Discretization: The Diffusion Term

9 Gradient Computation

10 Solving the System of Algebraic Equations

11 Discretization of the Convection Term

12 High Resolution Schemes

13 Temporal Discretization: The Transient Term

14 Discretization of the Source Term, Relaxation, and Other Details

Algorithms

15 Fluid Flow Computation: Incompressible Flows

16 Fluid Flow Computation: Compressible Flows

Applications

17 Turbulence Modeling

18 Boundary Conditions in OpenFOAM® and uFVM

19 An OpenFOAM® Turbulent Flow Application

20 Closing Remarks

Appendices

20 Closing Remarks

Appendices

20 Closing Remarks

Appendices