[CFD | ENG] Algorithms for the solution of the Navier-Stokes equations. Part II: The PISO algoritmh скачать в хорошем качестве

[CFD | ENG] Algorithms for the solution of the Navier-Stokes equations. Part II: The PISO algoritmh

In this video, we will be focusing on describing one of the most used algorithms in CFD to solve the Navier-Stokes equations for transient incompressible flows: the PISO (Pressure-Implicit with Split Operator) algorithm. This algorithm is used in the most popular open-source software OpenFOAM, which uses the finite volume method (FVM) to solve the conservation equations. For this reason, in order to explain the PISO algorithm, we will start this video by giving a brief introduction to the FVM, where we will discretise the convective, diffusive and source terms of the Navier-Stokes equations. Then, we will introduce two temporal discretisation techniques used in the FVM: the explicit Euler and the implicit Euler schemes. Once we have reviewed these topics, we will have to carry out an initial computation of the velocity (called the "momentum predictor"), which will be used to decompose a given matrix that will help us to derive a Poisson equation for the pressure. The solution of this equation will be used to correct the velocity field. However, the problem of this last step is that the new velocity no longer satisfies the continuity equation, and this is where the PISO algorithm becomes relevant, which consists of a series of pressure calculations and velocity corrections. Lastly, we will discuss some of the advantages of the PISO algorithm and the main differences in comparison with the SIMPLE (Semi-Implicit Method for Pressure Linked Equations). Video "Algorithms for the solution of the Navier-Stokes equations. Part I: Projection Methods":    • [CFD | ENG]  Algorithms for the solution o...   Video "Introduction to the finite volume method in CFD":    • [CFD | ENG] Introduction to the finite vol...   Timestamps 00:00 Introduction and overview of the presentation 01:17 The Navier-Stokes equations for transient incompressible flows 07:05 Important points to consider to solve the incompressible Navier-Stokes equations 09:04 Brief description of the finite volume method 12:34 Source term discretisation 13:38 Diffusive term discretisation 16:51 Convective term discretisation 19:08 Discretised form of the Navier-Stokes equations 20:52 Temporal discretisation: explicit Euler 25:05 Temporal discretisation: implicit Euler 28:28 Descomposition AU = apU-H 30:31 Matrices ap and H 32:55 Derivation of the Poisson equation for the pressure 34:26 Introduction to the PISO algorithm 38:12 Summary of the PISO algorithm 42:42 Final points and references Links of interest The OpenFOAM system: https://openfoam.org/ The foam-extend system: https://sourceforge.net/projects/foam... Dr. Jasak's doctoral thesis that describes with great detail the finite volume method used in both the OpenFOAM and foam-extend systems can be read here: https://www.researchgate.net/publicat... Personal webpage where you can read more about my research related to fluid dynamics and other popular-science articles: https://hugocastillocom.wordpress.com