# Day 4

Welcome back to Day 4. Today we will go even further into the depths and find, where the rubber meets the road (at least mathematically). We will have a special focus on discretization. Why is this important? Did you ever try to solve the fluid dynamic equations for an arbitrary industrial application by hand? Well... In most cases it is a better idea to break down the partial differential/integral equations into "simple" operations (+,-,*,/) and solve them for "small" volumens (yes, the cells in your mesh). This is called discretization. Today you will gain the knowledge, how this works.

Go back to "3 weeks" series.

## Contents

# Crash introduction to the FVM

In these slides you will find an in depth summary of the theory of CFD and also OpenFOAM. A brief list of the topics covered:

- finite volume method
- CFL number
- linear solvers
- solution methods
- unsteady and steady simulation
- residuals
- boundary and initial conditions

# Detailed Numerics

This tutorial provides additional insights about numerics in OpenFOAM, comprising:

- 1. Differencing schemes - representation of individual derivatives
- 2. Matrix inversion - iterative solution of individual equations
- 3. Algorithms - SIMPLE, PISO, Pimple (etc)

In OpenFOAM the methods for all these operations need to be specified: 1. is in fvSchemes and 2, 3 in fvSolution.

# Discretization

Discretization and the influence of different schemes on the simulation results are the major topics covered in this tutorial, which covers:

- spatial discretization
- face interpolation
- changing schemes in OpenFOAM
- divergence schemes
- influence of discretization on the simulation results of a passive scalar
- postprocessing

The pdf version can be found here

# Discretization strategies

In this tutorial you will find strategies on how to improve your simulation results by optimizing the utilized discretization settings. The focus is on

- gradient scheme
- gradient limiter
- convection discretization
- face interpolation
- diffusion discretization

# End of Day 4

Thank you for finishing the fourth day. We really-really hope, that you did not skip this day. It is a dry topic, but it is essential for understanding how to run high-quality simulations. Bare with us. Tomorrow on Day 5 we have some fun simulations for you.

Until then take a break!