pysphApproximator

Tool to test SPH approximation convergence

The UI of the application is simple and self explanatory.

It uses only the QuinticSpline kernel.

The user can select an SPH approximation present in the list or provide an approximation. The approximation should be coded using the PySPH framework. The code should have two function.

get_equations(dest, sources, derv=0, dim=1):
    ...

and

get_props():
    ...

The get_equation function return a list of SPH Equations. and get_props returns a list of properties required in the particle array. Users can use Edit code option to edit their code. In case you edit a custom code, it creates a copy of your passed code to a local copy and that is updated while editing.

The rest is pretty simple now.

• Scaling parameter: The scaling factor for the kernel to use. As is is seen that the increasing this value reduces the accuracy.
• Problem dimension: Whether to run in 1D, 2D, or 3D.
• Mesh kind: The kind of particle distribution. The No is a cartesian mesh, perturb denotes the randomly perturbed mesh, and pack is the packed particle distribution.
• Fraction: It sets the fraction of the particle spacing to set as maximum perturbation. So, 0.1 means 10% perturbation.
• Operator: The discretization we are comparing approximated the function, gradient, Laplacian or the divergence.
• Is periodic: Should we consider periodicity or not?
• Norm: The error norm to use for evaluation.

The program simulates the for [50, 100, 200, 250, 400, 500] resolution in a [1X1] domain.

Once we have a solution, the plot button activates. We can choose to plot by clicking on plot.

The render button will plot the particle distribution in the mayavi viewer.

Notice! we have a reset button at the left bottom corner.

So the nice thing about this program is that, we can run it on different combination e.g changing approximation, periodicity of domain. All the results are saved and plot will compare them as shown below

So the plot shows that the second order approximation is first order if the domain is not periodic.

Now, one can use reset button to clear all the previous run cases to begin a new comparison. However, using the remove button specific runs can be removed.

All this runs on PySPH, So the speed is incredible.