This video presents a thorough introduction about the finite volume method.
In this video, first, the governing equations of fluid flows, including the conservative and non-conservative forms, are discussed. After that, the finite volume method is presented in detail.
Video Outline:
0:00:00 - Finite Volume Method: A Thorough Introduction
0:00:21 - Governing equations of fluid flows
0:03:07 - Conservative form of the governing equations of fluid flow
0:04:11 - Generic form of transport equations
0:06:05 - Mathematical classification of governing equations
0:07:43 - Finite Volume method
0:08:32 - Basic methodology
0:09:09 - Control volumes (Cells)
0:10:50 - Steady-state convection-diffusion problem
0:11:55 - Steady-state one-dimensional pure diffusion problem
0:14:41 - Establishing a matrix equation
0:16:42 - Steady-state two-dimensional pure diffusion problem
0:20:47 - Discretization of the diffusive term over non-orthogonal unstructured grid
0:24:10 - Steady-state convection-diffusion problem
0:25:16 - Steady-state one-dimensional convection-diffusion equation
0:27:11 - Central differencing method
0:32:07 - Upwind scheme
0:34:12 - Properties of discretization schemes
0:34:46 - Consistency
0:34:57 - Conservativeness
0:36:00 - Boundedness
0:37:29 - Transportiveness
0:39:08 - Stability
0:39:20 - Order of accuracy
0:41:52 - Economy
0:42:04 - Evaluation of the central differencing and upwind schemes for convection-diffusion problems
0:45:35 - Steady-state two-dimensional convection-diffusion equation
0:47:18 - Solving a steady-state two-dimensional convection-diffusion problem
0:49:39 - False diffusion and numerical dispersion in numerical solutions
0:53:20 - Advanced schemes for convection discretization
0:53:48 - Power-law scheme
0:56:47 - Hybrid scheme
0:58:39 - Schemes with higher order of accuracy
0:59:41 - Second-order upwind scheme
1:01:10 - Third-order upwind scheme (QUICK)
1:03:51 - Discretization of the convective term over non-orthogonal unstructured grid
1:05:02 - Flux-limiter schemes
1:06:38 - Van Leer scheme
1:07:39 - UMIST scheme
1:08:22 - High Resolution schemes
To elaborate this lecture, the following references are utilized:
[1] Versteeg, Henk Kaarle, and Weeratunge Malalasekera. An introduction to computational fluid dynamics: the finite volume method. Pearson education, 2007.
[2] Kolditz, Olaf, and Margot Gerritsen. "Computational Methods in Environmental Fluid Mechanics." Physics Today 56.5 (2003): 60-62.
[3] Darwish, Marwan, and Fadl Moukalled. The finite volume method in computational fluid dynamics: an advanced introduction with OpenFOAM® and Matlab®. Springer, 2016.
[4] Ferziger, Joel H., and Milovan PeriC. "Computational methods for fluid dynamics." (2002): 2002-430.