SSPRK22

class pathsim.solvers.ssprk22.SSPRK22(*solver_args, **solver_kwargs)

Bases: ExplicitRungeKutta

Two-stage, 2nd order Strong Stability Preserving (SSP) Runge-Kutta method.

Also known as Heun’s method. SSP methods preserve monotonicity and total variation diminishing (TVD) properties of the spatial discretisation under a timestep restriction scaled by the SSP coefficient.

Characteristics

• Order: 2

• Stages: 2

• Explicit, fixed timestep

• SSP coefficient \(\mathcal{C} = 1\)

Note

Relevant when a block diagram wraps a method-of-lines discretisation of a hyperbolic PDE (e.g. shallow water, compressible Euler) inside an ODE block and the spatial operator is TVD under forward Euler. For typical ODE-based block diagrams without such structure, RK4 or RKDP54 are more appropriate choices.

References

[1]

Shu, C.-W., & Osher, S. (1988). “Efficient implementation of essentially non-oscillatory shock-capturing schemes”. Journal of Computational Physics, 77(2), 439-471. :doi:`10.1016/0021-9991(88)90177-5`

[2]

Gottlieb, S., Shu, C.-W., & Tadmor, E. (2001). “Strong stability-preserving high-order time discretization methods”. SIAM Review, 43(1), 89-112. :doi:`10.1137/S003614450036757X`

interpolate(r, dt)

Interpolate solution after successful timestep as a ratio in the interval [t, t+dt].

This is especially relevant for Runge-Kutta solvers that have a higher order interpolant. Otherwise this is just linear interpolation using the buffered state.

Parameters:

• r (float) – ration for interpolation within timestep

• dt (float) – integration timestep

Returns:

x – interpolated state

Return type:

numeric, array[numeric]