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
Discretization
To kick things off, follow this tutorial on discretization and the influence of different schemes on the simulation results. The pdf version can be found here. Here the focus is on:
- spatial discretization
- face interpolation
- changing schemes in OpenFOAM
- divergence schemes
- influence of discretization on the simulation results of a passive scalar
- postprocessing
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
Numerical scheme analyzing
The numerical discretization is treated by choosing different numerical schemes in OpenFOAM. Each numerical scheme behaves different which is demonstrated in a simple convection flow. Here, you will see the influence of the mesh type, hexaeder and tetraeder, the orientation of the mesh and the mesh density on the accuracy of the solution and if the scheme produces physical or also non-physical values. The following schemes will be covered
- upwind
- linear
- linearUpwind
- limitedLinear
- limitedLimitedLinear
- vanLeer
- limitedVanLeer
- cubic
- limitedCubic
- SFCD
- QUICK
- UMIST
Crash introduction to the FVM
To conclude this day, 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
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!
