SSPRK33

class pathsim.solvers.ssprk33.SSPRK33(*solver_args, **solver_kwargs)

Bases: ExplicitRungeKutta

Three-stage, 3rd order Strong Stability Preserving (SSP) explicit Runge-Kutta method.

Offers higher accuracy than SSPRK22 while maintaining the SSP property. This is the optimal 3-stage 3rd order SSP method. A popular choice for problems where TVD properties are important or when a simple, stable 3rd order explicit method is needed.

Characteristics:

• Order: 3

• Stages: 3

• Explicit (SSP)

• Fixed timestep only

• SSP coefficient: \(C = 1\)

• Optimal 3-stage SSP method

• Good stability properties for an explicit 3rd order method

When to Use

• Hyperbolic conservation laws: Standard choice for higher-order TVD schemes

• Higher accuracy than SSPRK22: When 3rd order accuracy is needed with SSP

• WENO schemes: Common pairing with weighted essentially non-oscillatory methods

• Compressible flow: Euler and Navier-Stokes equations with shocks

Recommended as the standard SSP method for most applications requiring 3rd order accuracy. For enhanced stability, consider SSPRK34 (4 stages).

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.

[2]

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

[3]

Gottlieb, S., Ketcheson, D. I., & Shu, C. W. (2011). “Strong Stability Preserving Runge-Kutta and Multistep Time Discretizations”. World Scientific.

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]