# Learning the ropes

In the tutorials, we will introduce the PySPH framework in the context of the examples provided. Read this if you are a casual user and want to use the framework as is. If you want to add new functions and capabilities to PySPH, you should read The PySPH framework. If you are new to PySPH however, we highly recommend that you go through this document and the next tutorial (A more detailed tutorial).

Recall that PySPH is a framework for parallel SPH-like simulations in Python. The idea therefore, is to provide a user friendly mechanism to set-up problems while leaving the internal details to the framework. All examples follow the following steps:

The tutorials address each of the steps in this flowchart for problems with increasing complexity.

The first example we consider is a “patch” test for SPH formulations for incompressible fluids in elliptical_drop.py. This problem simulates the evolution of a 2D circular patch of fluid under the influence of an initial velocity field given by:

u &= -100 x \\ v &= 100 y

The kinematical constraint of incompressibility causes the initially circular patch of fluid to deform into an ellipse such that the volume (area) is conserved. An expression can be derived for this deformation which makes it an ideal test to verify codes.

## Imports

Taking a look at the example (see elliptical_drop.py), the first several lines are imports of various modules:

    import os
    from numpy import array, ones_like, mgrid, sqrt
    import numpy as np

    from pysph.base.utils import get_particle_array
    from pysph.base.kernels import Gaussian

    from pysph.solver.application import Application
    from pysph.sph.integrator import EPECIntegrator
    from pysph.sph.scheme import WCSPHScheme

Note

This is common for most examples and it is worth noting the pattern of the PySPH imports. Fundamental SPH constructs like the kernel and particle containers are imported from the `base` subpackage. The framework related objects like the solver and integrator are imported from the `solver` subpackage. Finally, we import from the `sph` subpackage, the physics related part for this problem.

## Functions for loading/generating the particles

The code begins with a few functions related to obtaining the exact solution for the given problem which is used for comparing the computed solution.

A single new class called `EllipticalDrop` which derives from `pysph.solver.application.Application` is defined. There are several methods implemented on this class:

> - `initialize`: lets users specify any parameters of interest relevant to the simulation.
> - `create_scheme`: lets the user specify the `pysph.sph.scheme.Scheme` to use to solve the problem. Several standard schemes are already available and can be readily used.
> - `create_particles`: this method is where one creates the particles to be simulated.
> - `post_process`: optionally post-process the results generated.

Of these, `create_particles` and `create_scheme` are mandatory for without them SPH would be impossible. The rest (and other methods) are optional. To see a complete listing of possible methods that one can subclass see `pysph.solver.application.Application`.

The `create_particles` method looks like:

    class EllipticalDrop(Application):
        # ...
        def create_particles(self):
            """Create the circular patch of fluid."""
            dx = self.dx
            hdx = self.hdx
            co = self.co
            ro = self.ro
            name = 'fluid'
            x, y = mgrid[-1.05:1.05+1e-4:dx, -1.05:1.05+1e-4:dx]
            x = x.ravel()
            y = y.ravel()

            m = ones_like(x)*dx*dx
            h = ones_like(x)*hdx*dx
            rho = ones_like(x) * ro

            p = ones_like(x) * 1./7.0 * co**2
            cs = ones_like(x) * co

            u = -100*x
            v = 100*y

            # remove particles outside the circle
            indices = []
            for i in range(len(x)):
                if sqrt(x[i]*x[i] + y[i]*y[i]) - 1 > 1e-10:
                    indices.append(i)

            pa = get_particle_array(x=x, y=y, m=m, rho=rho, h=h, p=p, u=u, v=v,
                                    cs=cs, name=name)
            pa.remove_particles(indices)

            print("Elliptical drop :: %d particles"%(pa.get_number_of_particles()))
            self.scheme.setup_properties([pa])

            return [pa]

The method is used to initialize the particles in Python. In PySPH, we use a `ParticleArray` object as a container for particles of a given species. You can think of a particle species as any homogenous entity in a simulation. For example, in a two-phase air water flow, a species could be used to represent each phase. A `ParticleArray` can be conveniently created from the command line using NumPy arrays. For example

    >>> from pysph.base.utils import get_particle_array
    >>> x, y = numpy.mgrid[0:1:0.01, 0:1:0.01]
    >>> x = x.ravel(); y = y.ravel()
    >>> pa = sph.get_particle_array(x=x, y=y)

would create a `ParticleArray`, representing a uniform distribution of particles on a Cartesian lattice in 2D using the helper function `get_particle_array()` in the base subpackage. The `get_particle_array_wcsph()` is a special version of this suited to weakly-compressible formulations.

Note

ParticleArrays in PySPH use flattened or one-dimensional arrays.

The `ParticleArray` is highly convenient, supporting methods for insertions, deletions and concatenations. In the `create_particles` function, we use this convenience to remove a list of particles that fall outside a circular region:

    pa.remove_particles(indices)

where, a list of indices is provided. One could also provide the indices in the form of a `LongArray` which, as the name suggests, is an array of 64 bit integers.

Note

Any one-dimensional (NumPy) array is valid input for PySPH. You can generate this from an external program for solid modelling and load it.

Note

PySPH works with multiple ParticleArrays. This is why we actually return a list in the last line of the get_circular_patch function above.

The `create_particles` always returns a list of particle arrays even if there is only one. The method `self.scheme.setup_properties` automatically adds any properties needed for the particular scheme being used.

## Setting up the PySPH framework

As we move on, we encounter instantiations of the PySPH framework objects. In this example, the `pysph.sph.scheme.WCSPH` scheme is created in the `create_scheme` method. The `WCSPHScheme` internally creates other basic objects needed for the SPH simulation. In this case, the scheme instance is passed a list of fluid particle array names and an empty list of solid particle array names. In this case there are no solid boundaries. The class is also passed a variety of values relevant to the scheme and simulation. The kernel to be used is created and passed to the `configure_solver` method of the scheme. The `pysph.sph.integrator.EPECIntegrator` is used to integrate the particle properties. Various solver related parametes are also setup.

    def create_scheme(self):
        s = WCSPHScheme(
            ['fluid'], [], dim=2, rho0=self.ro, c0=self.co,
            h0=self.dx*self.hdx, hdx=self.hdx, gamma=7.0, alpha=0.1, beta=0.0
        )
        kernel = Gaussian(dim=2)
        dt = 5e-6; tf = 0.0076
        s.configure_solver(
            kernel=kernel, integrator_cls=EPECIntegrator, dt=dt, tf=tf,
            adaptive_timestep=True, cfl=0.3, n_damp=50,
            output_at_times=[0.0008, 0.0038]
        )
        return s

As can be seen, various options are configured for the solver, including initial damping etc. The scheme is responsible for:

> - setting up the actual equations that describe the interactions between particles (see SPH equations),
> - setting up the kernel (SPH Kernels) and integrator (Integrator module) to use for the simulation.
> - setting up the Solver (Module solver), which marshalls the entire simulation.

For a more detailed introduction to these aspects of PySPH please read, the A more detailed tutorial tutorial which provides greater detail on these. However, by simply creating the `WCSPHScheme` and creating the particles, one can simulate the problem.

The astute reader may notice that the `EllipticalDrop` example is subclassing the `Application`. This makes it easy to pass command line arguments to the solver. It is also important for the seamless parallel execution of the same example. To appreciate the role of the `Application` consider for a moment how might we write a parallel version of the same example. At some point, we would need some MPI imports and the particles should be created in a distributed fashion. All this (and more) is handled through the abstraction of the `Application` which hides all this detail from the user.

## Running the example

In the last two lines of the example, we instantiate the `EllipticalDrop` class and run it:

    if __name__ == '__main__':
        app = EllipticalDrop()
        app.run()

There is an additional `post_process` call in the code which is entirely optional and will generate some data for comparison with the exact solution.

The `Application` takes care of creating the particles, creating the solver, handling command line arguments etc. Many parameters can be configured via the command line, and these will override any parameters setup in the respective `create_*` methods. For example one may do the following to find out the various options:

    $ pysph run elliptical_drop -h

If we run the example without any arguments it will run until a final time of 0.0075 seconds. We can change this example to 0.005 by the following:

    $ pysph run elliptical_drop --tf=0.005

When this is run, PySPH will generate Cython code from the equations and integrators that have been provided, compiles that code and runs the simulation. This provides a great deal of convenience for the user without sacrificing performance. The generated code is available in `~/.pysph/source`. If the code/equations have not changed, then the code will not be recompiled. This is all handled automatically without user intervention. By default, output files will be generated in the directory `elliptical_drop_output`.

If we wish to utilize multiple cores we could do:

    $ pysph run elliptical_drop --openmp

If we wish to run the code in parallel (and have compiled PySPH with Zoltan and mpi4py) we can do:

    $ mpirun -np 4 pysph run elliptical_drop

This will automatically parallelize the run using 4 processors. In this example doing this will only slow it down as the number of particles is extremely small.

## Visualizing and post-processing

You can view the data generated by the simulation (after the simulation is complete or during the simulation) by running the `pysph view` command. To view the simulated data you may do:

    $ pysph view elliptical_drop_output

If you have Mayavi installed this should show a UI that looks like:

On the user interface, the right side shows the visualized data. On top of it there are several toolbar icons. The left most is the Mayavi logo and clicking on it will present the full Mayavi user interface that can be used to configure any additional details of the visualization.

On the bottom left of the main visualization UI there is a button which has the text “Launch Python Shell”. If one clicks on this, one obtains a full Python interpreter with a few useful objects available. These are:

    >>> dir()
    ['__builtins__', '__doc__', '__name__', 'interpolator', 'mlab',
     'particle_arrays', 'scene', 'self', 'viewer']
    >>> len(particle_arrays)
    1
    >>> particle_arrays[0].name
    'fluid'

The `particle_arrays` object is a list of ParticleArrays. The `interpolator` is an instance of `pysph.tools.interpolator.Interpolator` that is used by the viewer. The other objects can be used to script the user interface if desired.

### Loading output data files

The simulation data is dumped out either in `*.hdf5` files (if one has h5py installed) or `*.npz` files otherwise. You may use the `pysph.solver.utils.load()` function to access the raw data

    from pysph.solver.utils import load
    data = load('elliptical_drop_100.hdf5')
    # if one has only npz files the syntax is the same.
    data = load('elliptical_drop_100.npz')

When opening the saved file with `load`, a dictionary object is returned. The particle arrays and other information can be obtained from this dictionary:

    particle_arrays = data['arrays']
    solver_data = data['solver_data']

`particle_arrays` is a dictionary of all the PySPH particle arrays. You may obtain the PySPH particle array, `fluid`, like so:

    fluid = particle_arrays['fluid']
    p = fluid.p

`p` is a numpy array containing the pressure values. All the saved particle array properties can thus be obtained and used for any post-processing task. The `solver_data` provides information about the iteration count, timestep and the current time.

A good example that demonstrates the use of these is available in the `post_process` method of the `elliptical_drop.py` example.

### Interpolating properties

Data from the solver can also be interpolated using the `pysph.tools.interpolator.Interpolator` class. Here is the simplest example of interpolating data from the results of a simulation onto a fixed grid that is automatically computed from the known particle arrays:

    from pysph.solver.utils import load
    data = load('elliptical_drop_output/elliptical_drop_100.npz')
    from pysph.tools.interpolator import Interpolator
    parrays = data['arrays']
    interp = Interpolator(parrays.values(), num_points=10000)
    p = interp.interpolate('p')

`p` is now a numpy array of size 10000 elements shaped such that it interpolates all the data in the particle arrays loaded. `interp.x` and `interp.y` are numpy arrays of the chosen `x` and `y` coordinates corresponding to `p`. To visualize this we may simply do:

    from matplotlib import pyplot as plt
    plt.contourf(interp.x, interp.y, p)

It is easy to interpolate any other property too. If one wishes to explicitly set the domain on which the interpolation is required one may do:

    xmin, xmax, ymin, ymax, zmin, zmax = 0., 1., -1., 1., 0, 1
    interp.set_domain((xmin, xmax, ymin, ymax, zmin, zmax), (40, 50, 1))
    p = interp.interpolate('p')

This will create a meshgrid in the specified region with the specified number of points.

One could also explicitly set the points on which one wishes to interpolate the data as:

    interp.set_interpolation_points(x, y, z)

Where `x, y, z` are numpy arrays of the coordinates of the points on which the interpolation is desired. This can also be done with the constructor as:

    interp = Interpolator(parrays.values(), x=x, y=y, z=z)

For more details on the class and the available methods, see `pysph.tools.interpolator.Interpolator`.

In addition to this there are other useful pre and post-processing utilities described in Miscellaneous Tools for PySPH.

## Doing more

The `Application` has several more methods that can be used in additional contexts, for example one may override the following additional methods:

> - `add_user_options`: this is used to create additional user-defined command line arguments. The command line options are available in `self.options` and can be used in the other methods.
> - `consume_user_options`: this is called after the command line arguments are parsed, and can be optionally used to setup any variables that have been added by the user in `add_user_options`. Note that the method is called before the particles and solver etc. are created.
> - `create_domain`: this is used when a periodic domain is needed.
> - `create_inlet_outlet`: Override this to return any inlet an outlet objects. See the `pysph.sph.simple_inlet_outlet` module.

There are many others, please see the `Application` class to see these.

There are several examples that ship with PySPH, explore these to get a better idea of what is possible.