The Finite Volume Method in Computational Fluid Dynamics: An Advanced Introduction with OpenFOAM® and Matlab (Fluid Mechanics and Its Applications Book 113)

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. Front Matter....Pages i-xxiii Front Matter....Pages 1-1 Introduction....Pages 3-8 Review of Vector Calculus....Pages 9-42 Mathematical Description of Physical Phenomena....Pages 43-83 The Discretization Process....Pages 85-101 The Finite Volume Method....Pages 103-135 The Finite Volume Mesh....Pages 137-171 The Finite Volume Mesh in OpenFOAM® and uFVM....Pages 173-207 Front Matter....Pages 209-209 Spatial Discretization: The Diffusion Term....Pages 211-271 Gradient Computation....Pages 273-302 Solving the System of Algebraic Equations....Pages 303-364 Discretization of the Convection Term....Pages 365-427 High Resolution Schemes....Pages 429-488 Temporal Discretization: The Transient Term....Pages 489-533 Discretization of the Source Term, Relaxation, and Other Details....Pages 535-557 Front Matter....Pages 559-559 Fluid Flow Computation: Incompressible Flows....Pages 561-654 Fluid Flow Computation: Compressible Flows....Pages 655-690 Front Matter....Pages 691-691 Turbulence Modeling....Pages 693-744 Boundary Conditions in OpenFOAM® and uFVM....Pages 745-759 An OpenFOAM® Turbulent Flow Application....Pages 761-776 Closing Remarks....Pages 777-777 Back Matter....Pages 779-791