Exercise

Introduction

The simulation setup of the incompressible flow over a backward-facing step had unresolved issues, namely:

end time of 1 second might be too short,
influence of the mesh resolution was not investigated,
spatial and temporal accuracy was only of first order.

In order to resolve these issues, additional simulations should be performed.

Tasks

1. Increase End Time

Change the endTime in the controlDict in the system directory from 1 to 2 seconds and rerun the simulation.

Questions

Are there any changes in the flow field beyond 1 second flow time?
How do the residuals change for a longer simulation time?

2. Increase Mesh Resolution

Create a copy of the backward-step case directory for a second simulation with a refined mesh:

cp -r backward-step backward-step-refined
cd backward-step-refined

Reduce the maximum cell size (maxCellSize) from \(2.5 \times 10^{-3} \, \text{m}\) to \(1.25 \times 10^{-3}\,\text{m}\) in the meshDict in the system directory. Make sure that the time step size deltaT in the controlDict is also reduced accordingly from \(6.25 \, \times 10^{-4}\,\text{s}\) to \(3.125 \, \times 10^{-4}\,\text{s}\) to maintain a Courant number of below 1. Regenerate the mesh with cartesian2DMesh and rerun the simulation.

Questions

Do you notice any major changes in the flow behavior due to the increased mesh resolution?
How did the total computational time change between the coarse and the medium-sized mesh?

3. Higher Order Discretization

Create a copy of the previously created medium-sized mesh setup. In fvSchemes in the system folder, change the temporal discretization from first order Euler to second order backward and the discretization of the convective term in the momentum equation from first order Gauss upwind to second order Gauss linear. Rerun the simulation.

Questions

Do you notice any major changes in the flow behavior due to second order discretization?
How did the total computational time and the residuals change between first and second order discretization?