# DISCRETISATION TECHNIQUES

Techniques for approximating the partial differential or integral equations. There is always loss of information during discretisation and this is the major part of CFD.

Big Three
Finite Difference

Finite Volume

Finite Element

Other Techniques
Spectral Methods, Boundary Element Methods BEM, Particle Methods

# Two aspects of discretisation

Geometry: Grid, Mesh, Particles
Model: all mathematical operators(d/dx) to arithmetic operators on grid points

## Grid generation: Popular Techniques

The derivative transformations
Matrices and Jacobians
Grid Generation (for finite difference calculations)
Mesh Generation (for finite volume calculations)
Unstructured meshes, Cartesian meshes

# Techniques

Lax-Wendroff Technique: This is an explicit, finite difference menthod. applicable to time and space marching solutions, especially hyperbolic equations

Maccormack’s Technique: applicable to time and space marching solutions, especially hyperbolic equations

Crank-Nicolson Technique: applicable to time and space marching solutions, especially parabolic equations

Relaxation Technique: applicable to elliptic equations

Alternating-Direction-Implicit(ADI) Technique: applicable to time and space-marching solutions, hyperbolic and parabolic equations

The pressure correction technique: application to elliptic, parabolic and hyperbolic equations

Udemy

Intro to FEA

For every physical phenomenon there are governing equations that can be converted to codes(approximations).
The core idea is transforming simple PDEs into simple difference equations.

FVM, FDM, FEM are representations of governing equations(approximations)

What does Ansys do?

• Internally, codes are written for governing equations.
• Geometry is divided into elements(meshing)
• Governing equations are then solved for parameters(pressure, stress, deformation) at each centre/node.
• These are then sent for post-processing(plotting velocity-pressure, stress-deformation distributions)

What is Workbench?

It’s a platform of solvers.

# Meshing: Ansys meshing tool

## FEA

Global settings: Sizing of the whole domain, setting problem physics
meshing methods: prisms, hexagonal, mesh assembly
local settings

finer mesh -> better efficiency but greater computation time

Mesh Convergence/ mesh independent solution

we refine the mesh till the variation in numerical results becomes under acceptable range(5%).

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