[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

I encourage you to watch all the videos of the course. Enjoy the content.

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