Using PyClaw’s solvers: Classic and SharpClaw

At present, PyClaw includes two types of solvers:

  • Classic: the original Clawpack algorithms, in 1/2/3D
  • SharpClaw: higher-order wave propagation using WENO reconstruction and Runge-Kutta integration, in 1/2D

Solver initialization takes one argument: a Riemann solver, usually from the Riemann repository. Typically, all that is needed to select a different solver is to specify it in the problem script, e.g.

>>> from clawpack import pyclaw
>>> from clawpack import riemann
>>> solver = pyclaw.ClawSolver2D(riemann.acoustics_2D)

for the 2D acoustics equations and the Classic Clawpack solver or

>>> solver = pyclaw.SharpClawSolver2D(riemann.acoustics_2D)

for the SharpClaw solver. Most of the applications distributed with PyClaw are set up to use either solver, depending on the value of the command line option solver_type, which should be set to classic or sharpclaw.

Typically, for a given grid resolution, the SharpClaw solvers are more accurate but also more computationally expensive. For typical problems involving shocks, the Classic solvers are recommended. For problems involving high-frequency waves, turbulence, or smooth solutions, the SharpClaw solvers may give more accurate solutions at less cost. This is an active area of research and you may wish to experiment with both solvers.

Future plans include incorporation of finite-difference and discontinuous Galerkin solvers.

Key differences between the Classic and SharpClaw solvers are:

  • The source term routine for the Classic solver should return the integral of the source term over a step, while the source term routine for SharpClaw should return the instantaneous value of the source term.
  • The solvers have different options. For a list of options and possible values, see the documentation of the ClawSolver and SharpClawSolver classes.

SharpClaw Solvers

The SharpClaw solvers are a collection of solvers that contain the functionality of the Fortran code SharpClaw, developed in David Ketcheson’s thesis. The 1D SharpClaw solver contains a pure Python implementation as well as a wrapped Fortran version. The 2D solver is in progress but not available yet. The SharpClaw solvers provide an interface similar to that of the classic Clawpack solvers, but with a few different options. The superclass solvers are not meant to be used separately but are there to provide common routines for all the Clawpack solvers. Please refer to each of the inherited classes for more info about the methods and attributes they provide each class. .. The inheritance structure is:

Example:This is a simple example of how to instantiate and evolve a solution to a later time \(\text{t_end}\) using the 1D acoustics Riemann solver. 
>>> from clawpack import pyclaw
>>> solver = pyclaw.SharpClawSolver1D()           # Instantiate a default, 1d solver

>>> solver.evolve_to_time(solution,t_end)  # Evolve the solution to t_end

pyclaw.sharpclaw

System Message: WARNING/2 (/var/folders/_s/dx0xgftn3_x04rdx0_w5nq7w0000gn/T/tmplBPRI1sphinxcontrib_versioning/8b07e169f86998872fc1cf3755d1b7f4a8c40a33/doc/pyclaw/solvers.rst, line 96)

autodoc: failed to import class u’SharpClawSolver’ from module u’pyclaw.sharpclaw.solver’; the following exception was raised: Traceback (most recent call last): File “/usr/local/lib/python2.7/site-packages/sphinx/ext/autodoc.py”, line 551, in import_object __import__(self.modname) ImportError: No module named pyclaw.sharpclaw.solver

Pyclaw Classic Clawpack Solvers

The pyclaw classic clawpack solvers are a collection of solvers that represent the functionality of the older versions of clawpack. It comes in two forms, a pure python version and a python wrapping of the fortran libraries. All of the solvers available provide the same basic interface and provide the same options as the old versions of clawpack. The superclass solvers are not meant to be used separately but there to provide common routines for all the Clawpack solvers. Please refer to each of the inherited classes for more info about the methods and attributes they provide each class. .. The inheritance structure is:

Example:This is a simple example of how to instantiate and evolve a solution to a later time \(\text{t_end}\) using the linearized 1d acoustics Riemann solver 
>>> from clawpack import pyclaw
>>> solver = pyclaw.ClawSolver1D()                   # Instantiate a default, 1d solver
>>> solver.limiters = pyclaw.limiters.tvd.vanleer  # Use the van Leer limiter
>>> solver.dt = 0.0001                               # Set the initial time step
>>> solver.max_steps = 500                           # Set the maximum number of time steps

>>> solver.evolve_to_time(solution,t_end)  # Evolve the solution to t_end

pyclaw.classic.solver

class clawpack.pyclaw.classic.solver.ClawSolver(riemann_solver=None, claw_package=None)

Generic classic Clawpack solver

All Clawpack solvers inherit from this base class.

mthlim

Limiter(s) to be used. Specified either as one value or a list. If one value, the specified limiter is used for all wave families. If a list, the specified values indicate which limiter to apply to each wave family. Take a look at pyclaw.limiters.tvd for an enumeration. Default = limiters.tvd.minmod

order

Order of the solver, either 1 for first order (i.e., Godunov’s method) or 2 for second order (Lax-Wendroff-LeVeque). Default = 2

source_split

Which source splitting method to use: 1 for first order Godunov splitting and 2 for second order Strang splitting. Default = 1

fwave

Whether to split the flux jump (rather than the jump in Q) into waves; requires that the Riemann solver performs the splitting. Default = False

step_source

Handle for function that evaluates the source term. The required signature for this function is:

def step_source(solver,state,dt)

kernel_language

Specifies whether to use wrapped Fortran routines (‘Fortran’) or pure Python (‘Python’). Default = 'Fortran'.

verbosity

The level of detail of logged messages from the Fortran solver. Default = 0.

setup(solution)

Perform essential solver setup. This routine must be called before solver.step() may be called.

step(solution, take_one_step, tstart, tend)

Evolve solution one time step

The elements of the algorithm for taking one step are:

  1. Pick a step size as specified by the base solver attribute get_dt()
  2. A half step on the source term step_source() if Strang splitting is being used (source_split = 2)
  3. A step on the homogeneous problem \(q_t + f(q)_x = 0\) is taken
  4. A second half step or a full step is taken on the source term step_source() depending on whether Strang splitting was used (source_split = 2) or Godunov splitting (source_split = 1)

This routine is called from the method evolve_to_time defined in the pyclaw.solver.Solver superclass.

Input:
  • solution - (Solution) solution to be evolved
Output:
  • (bool) - True if full step succeeded, False otherwise
step_hyperbolic(solution)

Take one homogeneous step on the solution.

This is a dummy routine and must be overridden.

Change to Custom BC Function Signatures

To allow better access to aux array data in the boundary condition functions both the qbc and auxbc arrays are now passed to the custom boundary condition functions. The new signature is

def my_custom_BC(state, dim, t, qbc, auxbc, num_ghost):
...

and should be adopted as soon as possible. The old signature

def my_custom_BC(state, dim, t, bc_array, num_ghost):
...

can still be used but a warning will be issued and the old signature will not be supported when version 6.0 is released. This addition is available in versions > 5.2.0.