[CFD | ENG] Introduction to the finite difference method in CFD скачать в хорошем качестве

[CFD | ENG] Introduction to the finite difference method in CFD

In this video, we will give an introduction to the finite difference method for the solution of conservation equations used in Computational Fluid Dynamics (CFD) We will start by reviewing some basic concepts, such as derivatives, discretisation techniques and Taylor series. We will also give a brief introduction to different finite difference schemes, such as forward, backward and central differences. Some examples of computation of derivatives of basic functions using the previously mentioned methods will be provided. Lastly, we will show how we use the finite difference method in CFD for the solution of two basic flow problems: simple shear flow and shear flow with pressure gradient, where our goal is to obtain an approximate solution of the velocity profile for a Newtonian fluid. Our numerical solution will then be compared with analytical equations obtained in our previous videos. Timestamps 00:00 Introduction and overview of the presentation 01:48 Definition of the concept of finite differences 05:37 Forward difference 07:58 Backward difference 09:06 Central difference 09:49 Taylor series for the computation of 1st-order derivatives 18:18Approximation of higher order derivatives using Taylor series 20:32 Examples of computation of derivatives using finite differences 26:30 Description of the flow geometries for simple shear flow and shear flow with pressure gradient 30:14 Mesh creation for finite differences 32:24 Discretisation of the equations using finite differences 35:35 Linear system of equations and assembling of the matrix system Au=b 40:45 Approximate solution for the velocity profile in simple shear flow 43:13 Approximate solution for the velocity profile in shear flow with pressure gradient This video is part of the course called "Introduction to CFD" which I am offering for free in the channel. The presentation called "Shear flow with pressure gradient for a Newtonian fluid. Analytical solution", which is the previous video, can be found here:    • [CFD | ENG] Shear flow with pressure gradi...   The video where we obtain an analytical solution for the velocity profile in simple shear flow is here:    • [CFD | ENG] Simple shear flow for a Newton...   The next video called "Introduction to the finite volume method in CFD"" is found here:    • [CFD | ENG] Introduction to the finite vol...   I encourage you to watch all the videos of the course. Enjoy the content. Links of interest Personal webpage where you can read more about my research related to fluid dynamics and other popular-science articles: https://hugocastillocom.wordpress.com