Integrator related modules¶
Basic code for the templated integrators.
Currently we only support twostep integrators.
These classes are used to generate the code for the actual integrators from the sph_eval module.

class
pysph.sph.integrator.
EPECIntegrator
(**kw)[source]¶ Bases:
pysph.sph.integrator.Integrator
Predictor corrector integrators can have two modes of operation.
In the EvaluatePredictEvaluateCorrect (EPEC) mode, the system is advanced using:
\[ \begin{align}\begin{aligned}F(y^n) > Evaluate\\y^{n+\frac{1}{2}} = y^n + F(y^n) > Predict\\F(y^{n+\frac{1}{2}}) > Evaluate\\y^{n+1} = y^n + \Delta t F(y^{n+\frac{1}{2}}) > Correct\end{aligned}\end{align} \]Notes:
The Evaluate stage of the integrator forces a function evaluation. Therefore, the PEC mode is much faster but relies on old accelertions for the Prediction stage.
In the EPEC mode, the final corrector can be modified to:
\[y^{n+1} = y^n + \frac{\Delta t}{2}\left( F(y^n) + F(y^{n+\frac{1}{2}}) \right)\]This would require additional storage for the accelerations.
Pass fluid names and suitable IntegratorStep instances.
For example:
>>> integrator = Integrator(fluid=WCSPHStep(), solid=WCSPHStep())
where “fluid” and “solid” are the names of the particle arrays.

one_timestep
(t, dt)[source]¶ User written function that actually does one timestep.
This function is used in the highperformance Cython implementation. The assumptions one may make are the following:
t and dt are passed.
the following methods are available:
 self.initialize()
 self.stage1(), self.stage2() etc. depending on the number of stages available.
 self.compute_accelerations(index=0, update_nnps=True)
 self.do_post_stage(stage_dt, stage_count_from_1)
 self.update_domain()
Please see any of the concrete implementations of the Integrator class to study. By default the Integrator implements a predictevaluatecorrect method, the same as PECIntegrator.


class
pysph.sph.integrator.
EulerIntegrator
(**kw)[source]¶ Bases:
pysph.sph.integrator.Integrator
Pass fluid names and suitable IntegratorStep instances.
For example:
>>> integrator = Integrator(fluid=WCSPHStep(), solid=WCSPHStep())
where “fluid” and “solid” are the names of the particle arrays.

one_timestep
(t, dt)[source]¶ User written function that actually does one timestep.
This function is used in the highperformance Cython implementation. The assumptions one may make are the following:
t and dt are passed.
the following methods are available:
 self.initialize()
 self.stage1(), self.stage2() etc. depending on the number of stages available.
 self.compute_accelerations(index=0, update_nnps=True)
 self.do_post_stage(stage_dt, stage_count_from_1)
 self.update_domain()
Please see any of the concrete implementations of the Integrator class to study. By default the Integrator implements a predictevaluatecorrect method, the same as PECIntegrator.


class
pysph.sph.integrator.
Integrator
(**kw)[source]¶ Bases:
object
Generic class for multistep integrators in PySPH for a system of ODES of the form \(\frac{dy}{dt} = F(y)\).
Pass fluid names and suitable IntegratorStep instances.
For example:
>>> integrator = Integrator(fluid=WCSPHStep(), solid=WCSPHStep())
where “fluid” and “solid” are the names of the particle arrays.

compute_time_step
(dt, cfl)[source]¶ If there are any adaptive timestep constraints, the appropriate timestep is returned, else None is returned.

initial_acceleration
(**kwargs)¶ Compute the initial accelerations if needed before the iterations start.
The default implementation only does this for the first acceleration evaluator. So if you have multiple evaluators, you must override this method in a subclass.

one_timestep
(t, dt)[source]¶ User written function that actually does one timestep.
This function is used in the highperformance Cython implementation. The assumptions one may make are the following:
t and dt are passed.
the following methods are available:
 self.initialize()
 self.stage1(), self.stage2() etc. depending on the number of stages available.
 self.compute_accelerations(index=0, update_nnps=True)
 self.do_post_stage(stage_dt, stage_count_from_1)
 self.update_domain()
Please see any of the concrete implementations of the Integrator class to study. By default the Integrator implements a predictevaluatecorrect method, the same as PECIntegrator.

set_acceleration_evals
(a_evals)[source]¶ Set the acceleration evaluators.
This must be done before the integrator is used.
If you are using the SPHCompiler, it automatically calls this method.

set_compiled_object
(c_integrator)[source]¶ Set the highperformance compiled object to call internally.

set_post_stage_callback
(callback)[source]¶ This callback is called when the particles are moved, i.e one stage of the integration is done.
This callback is passed the current time value, the timestep and the stage.
The current time value is t + stage_dt, for example this would be 0.5*dt for a two stage predictor corrector integrator.

step
(time, dt)[source]¶ This function is called by the solver.
To implement the integration step please override the
one_timestep
method.

update_domain
(**kwargs)¶ Update the domain of the simulation.
This is to be called when particles move so the ghost particles (periodicity, mirror boundary conditions) can be reset. Further, this also recalculates the appropriate cell size based on the particle kernel radius, h. This should be called explicitly when desired but usually this is done when the particles are moved or the h is changed.
The integrator should explicitly call this when needed in the one_timestep method.


class
pysph.sph.integrator.
LeapFrogIntegrator
(**kw)[source]¶ Bases:
pysph.sph.integrator.PECIntegrator
A leapfrog integrator.
Pass fluid names and suitable IntegratorStep instances.
For example:
>>> integrator = Integrator(fluid=WCSPHStep(), solid=WCSPHStep())
where “fluid” and “solid” are the names of the particle arrays.

one_timestep
(t, dt)[source]¶ User written function that actually does one timestep.
This function is used in the highperformance Cython implementation. The assumptions one may make are the following:
t and dt are passed.
the following methods are available:
 self.initialize()
 self.stage1(), self.stage2() etc. depending on the number of stages available.
 self.compute_accelerations(index=0, update_nnps=True)
 self.do_post_stage(stage_dt, stage_count_from_1)
 self.update_domain()
Please see any of the concrete implementations of the Integrator class to study. By default the Integrator implements a predictevaluatecorrect method, the same as PECIntegrator.


class
pysph.sph.integrator.
PECIntegrator
(**kw)[source]¶ Bases:
pysph.sph.integrator.Integrator
In the PredictEvaluateCorrect (PEC) mode, the system is advanced using:
\[ \begin{align}\begin{aligned}y^{n+\frac{1}{2}} = y^n + \frac{\Delta t}{2}F(y^{n\frac{1}{2}}) > Predict\\F(y^{n+\frac{1}{2}}) > Evaluate\\y^{n + 1} = y^n + \Delta t F(y^{n+\frac{1}{2}})\end{aligned}\end{align} \]Pass fluid names and suitable IntegratorStep instances.
For example:
>>> integrator = Integrator(fluid=WCSPHStep(), solid=WCSPHStep())
where “fluid” and “solid” are the names of the particle arrays.

one_timestep
(t, dt)[source]¶ User written function that actually does one timestep.
This function is used in the highperformance Cython implementation. The assumptions one may make are the following:
t and dt are passed.
the following methods are available:
 self.initialize()
 self.stage1(), self.stage2() etc. depending on the number of stages available.
 self.compute_accelerations(index=0, update_nnps=True)
 self.do_post_stage(stage_dt, stage_count_from_1)
 self.update_domain()
Please see any of the concrete implementations of the Integrator class to study. By default the Integrator implements a predictevaluatecorrect method, the same as PECIntegrator.


class
pysph.sph.integrator.
PEFRLIntegrator
(**kw)[source]¶ Bases:
pysph.sph.integrator.Integrator
A PositionExtended ForestRuthLike integrator [Omeylan2002]
References
[Omeylan2002] I.M. Omelyan, I.M. Mryglod and R. Folk, “Optimized ForestRuth and Suzukilike algorithms for integration of motion in manybody systems”, Computer Physics Communications 146, 188 (2002) http://arxiv.org/abs/condmat/0110585 Pass fluid names and suitable IntegratorStep instances.
For example:
>>> integrator = Integrator(fluid=WCSPHStep(), solid=WCSPHStep())
where “fluid” and “solid” are the names of the particle arrays.

one_timestep
(t, dt)[source]¶ User written function that actually does one timestep.
This function is used in the highperformance Cython implementation. The assumptions one may make are the following:
t and dt are passed.
the following methods are available:
 self.initialize()
 self.stage1(), self.stage2() etc. depending on the number of stages available.
 self.compute_accelerations(index=0, update_nnps=True)
 self.do_post_stage(stage_dt, stage_count_from_1)
 self.update_domain()
Please see any of the concrete implementations of the Integrator class to study. By default the Integrator implements a predictevaluatecorrect method, the same as PECIntegrator.


class
pysph.sph.integrator.
TVDRK3Integrator
(**kw)[source]¶ Bases:
pysph.sph.integrator.Integrator
In the TVDRK3 integrator, the system is advanced using:
\[ \begin{align}\begin{aligned}y^{n + \frac{1}{3}} = y^n + \Delta t F( y^n )\\y^{n + \frac{2}{3}} = \frac{3}{4}y^n + \frac{1}{4}(y^{n + \frac{1}{3}} + \Delta t F(y^{n + \frac{1}{3}}))\\y^{n + 1} = \frac{1}{3}y^n + \frac{2}{3}(y^{n + \frac{2}{3}} + \Delta t F(y^{n + \frac{2}{3}}))\end{aligned}\end{align} \]Pass fluid names and suitable IntegratorStep instances.
For example:
>>> integrator = Integrator(fluid=WCSPHStep(), solid=WCSPHStep())
where “fluid” and “solid” are the names of the particle arrays.

one_timestep
(t, dt)[source]¶ User written function that actually does one timestep.
This function is used in the highperformance Cython implementation. The assumptions one may make are the following:
t and dt are passed.
the following methods are available:
 self.initialize()
 self.stage1(), self.stage2() etc. depending on the number of stages available.
 self.compute_accelerations(index=0, update_nnps=True)
 self.do_post_stage(stage_dt, stage_count_from_1)
 self.update_domain()
Please see any of the concrete implementations of the Integrator class to study. By default the Integrator implements a predictevaluatecorrect method, the same as PECIntegrator.

Integrator steps for different schemes.
Implement as many stages as needed.

class
pysph.sph.integrator_step.
ADKEStep
[source]¶ Bases:
pysph.sph.integrator_step.IntegratorStep
Predictor Corrector integrator for Gasdynamics ADKE

initialize
(d_idx, d_x0, d_y0, d_z0, d_x, d_y, d_z, d_u0, d_v0, d_w0, d_u, d_v, d_w, d_e, d_e0, d_rho, d_rho0)[source]¶


class
pysph.sph.integrator_step.
AdamiVerletStep
[source]¶ Bases:
pysph.sph.integrator_step.IntegratorStep
Verlet time integration described in A generalized wall boundary condition for smoothed particle hydrodynamics 2012, JCP, 231, pp 7057–7075
This integrator can operate in either PEC mode or in EPEC mode as described in the paper.

class
pysph.sph.integrator_step.
EulerStep
[source]¶ Bases:
pysph.sph.integrator_step.IntegratorStep
Fast but inaccurate integrator. Use this for testing

class
pysph.sph.integrator_step.
GasDFluidStep
[source]¶ Bases:
pysph.sph.integrator_step.IntegratorStep
Predictor Corrector integrator for Gasdynamics

initialize
(d_idx, d_x0, d_y0, d_z0, d_x, d_y, d_z, d_h, d_u0, d_v0, d_w0, d_u, d_v, d_w, d_e, d_e0, d_h0, d_converged, d_omega, d_rho, d_rho0, d_alpha1, d_alpha2, d_alpha10, d_alpha20)[source]¶


class
pysph.sph.integrator_step.
InletOutletStep
[source]¶ Bases:
pysph.sph.integrator_step.IntegratorStep
A trivial integrator for the inlet/outlet particles

class
pysph.sph.integrator_step.
IntegratorStep
[source]¶ Bases:
object
Subclass this and implement the methods
initialize
,stage1
etc. Use the same conventions as the equations.

class
pysph.sph.integrator_step.
LeapFrogStep
[source]¶ Bases:
pysph.sph.integrator_step.IntegratorStep
Using this stepper with XSPH as implemented in pysph.base.basic_equations.XSPHCorrection is not directly possible and requires a nicer implementation where the correction alone is added to
ax, ay, az
.

class
pysph.sph.integrator_step.
OneStageRigidBodyStep
[source]¶ Bases:
pysph.sph.integrator_step.IntegratorStep
Simple one stage rigidbody motion

class
pysph.sph.integrator_step.
PEFRLStep
[source]¶ Bases:
pysph.sph.integrator_step.IntegratorStep
Using this stepper with XSPH as implemented in pysph.base.basic_equations.XSPHCorrection is not directly possible and requires a nicer implementation where the correction alone is added to
ax, ay, az
.
stage2
(d_idx, d_x, d_y, d_z, d_u, d_au, d_v, d_av, d_w, d_aw, d_ax, d_ay, d_az, d_rho, d_arho, d_e, d_ae, dt=0.0)[source]¶

stage3
(d_idx, d_x, d_y, d_z, d_u, d_au, d_v, d_av, d_w, d_aw, d_ax, d_ay, d_az, d_rho, d_arho, d_e, d_ae, dt=0.0)[source]¶


class
pysph.sph.integrator_step.
SolidMechStep
[source]¶ Bases:
pysph.sph.integrator_step.IntegratorStep
Predictor corrector Integrator for solid mechanics problems

initialize
(d_idx, d_x0, d_y0, d_z0, d_x, d_y, d_z, d_u0, d_v0, d_w0, d_u, d_v, d_w, d_rho0, d_rho, d_s00, d_s01, d_s02, d_s11, d_s12, d_s22, d_s000, d_s010, d_s020, d_s110, d_s120, d_s220, d_e0, d_e)[source]¶

stage1
(d_idx, d_x0, d_y0, d_z0, d_x, d_y, d_z, d_u0, d_v0, d_w0, d_u, d_v, d_w, d_rho0, d_rho, d_au, d_av, d_aw, d_ax, d_ay, d_az, d_arho, d_e, d_e0, d_ae, d_s00, d_s01, d_s02, d_s11, d_s12, d_s22, d_s000, d_s010, d_s020, d_s110, d_s120, d_s220, d_as00, d_as01, d_as02, d_as11, d_as12, d_as22, dt)[source]¶

stage2
(d_idx, d_x0, d_y0, d_z0, d_x, d_y, d_z, d_u0, d_v0, d_w0, d_u, d_v, d_w, d_rho0, d_rho, d_au, d_av, d_aw, d_ax, d_ay, d_az, d_arho, d_e, d_ae, d_e0, d_s00, d_s01, d_s02, d_s11, d_s12, d_s22, d_s000, d_s010, d_s020, d_s110, d_s120, d_s220, d_as00, d_as01, d_as02, d_as11, d_as12, d_as22, dt)[source]¶


class
pysph.sph.integrator_step.
TransportVelocityStep
[source]¶ Bases:
pysph.sph.integrator_step.IntegratorStep
Integrator defined in ‘A transport velocity formulation for smoothed particle hydrodynamics’, 2013, JCP, 241, pp 292–307
For a predictorcorrector style of integrator, this integrator should operate only in PEC mode.

class
pysph.sph.integrator_step.
TwoStageRigidBodyStep
[source]¶ Bases:
pysph.sph.integrator_step.IntegratorStep
Simple rigidbody motion
At each stage of the integrator, the prescribed velocity and accelerations are incremented by dt/2.
Note that the time centered velocity is used for updating the particle positions. This ensures exact motion for a constant acceleration.

class
pysph.sph.integrator_step.
VelocityVerletSymplecticWCSPHStep
[source]¶ Bases:
pysph.sph.integrator_step.IntegratorStep
Another symplectic second order integrator described in the review paper by Monaghan:
J. Monaghan, “Smoothed Particle Hydrodynamics”, Reports on Progress in Physics, 2005, 68, pp 1703–1759 [JM05]
kick–drift–kick form of the verlet integrator

class
pysph.sph.integrator_step.
VerletSymplecticWCSPHStep
[source]¶ Bases:
pysph.sph.integrator_step.IntegratorStep
Symplectic second order integrator described in the review paper by Monaghan:
J. Monaghan, “Smoothed Particle Hydrodynamics”, Reports on Progress in Physics, 2005, 68, pp 1703–1759 [JM05]
Notes:
This integrator should run in PEC mode since in the first stage, the positions are updated using the current velocity. The accelerations are then computed to advance to the full time step values.
This version of the integrator does not update the density. That is, the summation density is used instead of the continuity equation.

class
pysph.sph.integrator_step.
WCSPHStep
[source]¶ Bases:
pysph.sph.integrator_step.IntegratorStep
Standard Predictor Corrector integrator for the WCSPH formulation
Use this integrator for WCSPH formulations. In the predictor step, the particles are advanced to t + dt/2. The particles are then advanced with the new force computed at this position.
This integrator can be used in PEC or EPEC mode.
The same integrator can be used for other problems. Like for example solid mechanics (see SolidMechStep)

initialize
(d_idx, d_x0, d_y0, d_z0, d_x, d_y, d_z, d_u0, d_v0, d_w0, d_u, d_v, d_w, d_rho0, d_rho)[source]¶


class
pysph.sph.integrator_step.
WCSPHTVDRK3Step
[source]¶ Bases:
pysph.sph.integrator_step.IntegratorStep
TVD RK3 stepper for WCSPH
This integrator requires \(2\) stages for the storage of the acceleration variables.

initialize
(d_idx, d_x0, d_y0, d_z0, d_x, d_y, d_z, d_u0, d_v0, d_w0, d_u, d_v, d_w, d_rho0, d_rho)[source]¶

stage1
(d_idx, d_x0, d_y0, d_z0, d_x, d_y, d_z, d_u0, d_v0, d_w0, d_u, d_v, d_w, d_rho0, d_rho, d_au, d_av, d_aw, d_ax, d_ay, d_az, d_arho, dt)[source]¶


class
pysph.sph.gas_dynamics.magma2.
TVDRK2Integrator
(**kw)[source]¶ Bases:
pysph.sph.integrator.Integrator
Total variation diminishing (TVD) secondorder Runge–Kutta (RK2) integrator. Prescribed equations in [Rosswog2020b] are,
\[ \begin{align}\begin{aligned}y^{*} = y^n + \Delta t f(y^{n}) > Predict\\y^{n+1} = 0.5 (y^n + y^{*} + \Delta t f(y^{*})) > Correct\end{aligned}\end{align} \]This is not suitable to be used with periodic boundaries. Say, if a particle crosses the left boundary at the prediction step, update_domain() will introduce that particle at the right boundary. Afterwards, the correction step essentially averages the positions and the particle ends up near the midpoint. To do away with this issue, the equation for the correction step is changed to,
\[y^{n+1} = y^{*} + 0.5 * \Delta t (f(y^{*})  f(y^{n}))\]Pass fluid names and suitable IntegratorStep instances.
For example:
>>> integrator = Integrator(fluid=WCSPHStep(), solid=WCSPHStep())
where “fluid” and “solid” are the names of the particle arrays.

class
pysph.sph.gas_dynamics.magma2.
TVDRK2IntegratorWithRecycling
(**kw)[source]¶ Bases:
pysph.sph.integrator.Integrator
Total variation diminishing (TVD) secondorder Runge–Kutta (RK2) integrator with recycling of derivatives. The system is advanced using:
\[ \begin{align}\begin{aligned}y^{*,n} = y^n + \Delta t f(y^{*,n1})\\y^{n+1} = 0.5 (y^n + y^{*} + \Delta t f(y^{*,n}))\end{aligned}\end{align} \]This is not suitable to be used with periodic boundaries. Say, if a particle crosses the left boundary at the prediction step, update_domain() will introduce that particle at the right boundary. Afterwards, the correction step essentially averages the positions and the particle ends up near the midpoint. To do away with this issue, the equation for correction step is changed to,
\[y^{n+1} = y^{*} + 0.5 * \Delta t (f(y^{*,n})  f(y^{*,n1}))\]Pass fluid names and suitable IntegratorStep instances.
For example:
>>> integrator = Integrator(fluid=WCSPHStep(), solid=WCSPHStep())
where “fluid” and “solid” are the names of the particle arrays.

class
pysph.sph.gas_dynamics.magma2.
TVDRK2Step
[source]¶ Bases:
pysph.sph.integrator_step.IntegratorStep
Total variation diminishing (TVD) secondorder Runge–Kutta (RK2) integrator step.