Contents
The basic idea of a pyclaw simulation is to construct a :class:`~pyclaw.solution.Solution` object, hand it to a :class:`~pyclaw.solver.Solver` object, and request a solution at a new time. The solver will take whatever steps are necessary to evolve the solution to the requested time.
The bulk of the work in order to run a simulation then is the creation and setup of the appropriate :class:`~pyclaw.grid.Grid`, :class:`~pyclaw.state.State`, :class:`~pyclaw.solution.Solution`, and :class:`~pyclaw.solver.Solver` objects needed to evolve the solution to the requested time.
A Pyclaw :class:`~pyclaw.solution.Solution` is a container for a collection of :class:`~pyclaw.grid.Grid` and :class:`~pyclaw.state.State` objects in order to support adaptive mesh refinement and multi-block simulations. The :class:`~pyclaw.solution.Solution` object keeps track of a list of :class:`~pyclaw.state.State` objects and controls the overall input and output of the entire collection of :class:`~pyclaw.state.State` objects. Each :class:`~pyclaw.state.State` object inhabits a ~pyclaw.grid.Grid, composed of :class:`~pyclaw.grid.Dimension` objects that define the extents of the :class:`~pyclaw.grid.Grid`. Multiple states can inhabit the same grid, but each :class:`~pyclaw.state.State` inhabits a single grid.
The process needed to create a :class:`~pyclaw.solution.Solution` object then follows from the bottom up.
>>> from pyclaw import Solution, State, Grid, Dimension
>>> x = Dimension('x', -1.0, 1.0, 200)
>>> y = Dimension('y', 0.0, 1.0, 100)
This code creates two dimensions, a dimension x on the interval
[-1.0, 1.0] with 200 grid points and a dimension y on the interval
[0.0, 1.0] with 100 grid points.
Note
Many of the attributes of a :class:`~pyclaw.grid.Dimension` object are set automatically so make sure that the values you want are set by default. Please refer to the :class:`~pyclaw.grid.Dimension` classes definition for what the default values are.
Next we have to create a :class:`~pyclaw.grid.Grid` object that will contain our :class:`~pyclaw.grid.Dimension` objects.
>>> grid = Grid([x,y]) >>> state = State(grid) >>> state.meqn = 2
Here we create a grid with the dimensions we created earlier to make a single 2D :class:`~pyclaw.grid.Grid` object. Then we create a ~pyclaw.state.State that inhabits this Grid. Finally, we set the number of equations the State will represent to 2. As before, many of the attributes of the :class:`~pyclaw.grid.Grid` and State objects are set automatically.
We now need to set the initial condition q and possibly aux to the correct
values.
>>> import numpy as np >>> sigma = 0.2 >>> omega = np.pi >>> state.q[:,0] = np.cos(omega * grid.x.center) >>> state.q[:,1] = np.exp(-grid.x.center**2 / sigma**2)
We now have initialized the first entry of q to a cosine function evaluated at the cell centers and the second entry of q to a gaussian, again evaluated at the grid cell centers.
Many Riemann solvers also require information about the problem we are going
to run which happen to be grid properties such as the impedence Z and
speed of sound c for linear acoustics. We can set these values in the
aux_global dictionary in one of two ways. The first way is to set them
directly as in:
>>> state.aux_global['c'] = 1.0 >>> state.aux_global[`Z`] = 0.25
If you're using a Fortran Riemann solver, these values will automatically get copied to the corresponding variables in the cparam common block of the Riemann solver. This is done in solver.setup(), which calls grid.set_cparam().
Last we have to put our :class:`~pyclaw.state.State` object into a :class:`~pyclaw.solution.Solution` object to complete the process. In this case, since we are not using adaptive mesh refinement or a multi-block algorithm, we do not have multiple grids.
>>> sol = Solution(state)
We now have a solution ready to be evolved in a :class:`~pyclaw.solver.Solver` object.
A Pyclaw :class:`~pyclaw.solver.Solver` can represent many different types of solvers; here we will use a 1D, classic Clawpack type of solver. This solver is defined in the :mod:`~pyclaw.clawpack` module.
First we import the particular solver we want and create it with the default configuration.
>>> from pyclaw.clawpack import ClawSolver1D >>> solver = ClawSolver1D() >>> solver.mthbc_lower[0] = pyclaw.BC.periodic >>> solver.mthbc_upper[0] = pyclaw.BC.periodic
Next we need to tell the solver which Riemann solver to use from the :doc:`Riemann solver package </pyclaw/evolve/rp>` . We can always check what Riemann solvers are available to use via the :meth:`~pyclaw.ClawSolver1D.list_riemann_solvers` method. Once we have picked one out, we let the solver pick it out for us via:
>>> solver.set_riemann_solver('acoustics')
In this case we have decided to use the linear acoustics Riemann solver. You can also set your own solver by importing the module that contains it and setting it directly to the :attr:`~pyclaw.clawpack.ClawSolver1D.rp` attribute to the particular function.
>>> import my_rp_module >>> solver.rp = my_rp_module.my_acoustics_rp
Last we finish up by specifying solver options, if we want to override the defaults. For instance, we might want to specify a particular limiter:
>>> solver.limiters = pyclaw.limiters.vanleer
If we wanted to control the simulation we could at this point by issuing the following commands:
>>> solver.evolve_to_time(sol,1.0)
This would evolve our solution sol to t = 1.0 but we are then
responsible for all output and other setup considerations.
The :class:`~pyclaw.controller.Controller` coordinates the output and setup of a run with the same parameters as the classic Clawpack. In order to have it control a run, we need only to create the controller, assign it a solver and initial condition, and call the :meth:`~pyclaw.controller.Controller.run` method.
>>> from pyclaw.controller import Controller >>> claw = Controller() >>> claw.solver = solver >>> claw.solutions['n'] = sol
Here we have imported and created the :class:`~pyclaw.controller.Controller` class, assigned the :class:`~pyclaw.solver.Solver` and :class:`~pyclaw.solution.Solution`.
These next commands setup the type of output the controller will output. The parameters are similar to the ones found in the classic clawpack claw.data format.
>>> claw.outstyle = 1 >>> claw.nout = 10 >>> claw.tfinal = 1.0
When we are ready to run the simulation, we can call the :meth:`~pyclaw.controller.Controller.run` method. It will then run the simulation and output the appropriate time points. If the :attr:`~pyclaw.controller.Controller.keep_copy` is set to True the controller will keep a copy of each solution output in memory in the frames array. For instance, you can then immediately plot the solutions output into the frames array.
To restart a simulation, simply initialize a Solution object using an output frame from a previous run; for example, to restart from frame 3:
>>> claw.solution = pyclaw.Solution(3,format='petsc')
Note
It is necessary to specify the output format ('petsc' or 'ascii').