petsc-3.7.1 2016-05-15
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# TSSSP

Explicit strong stability preserving ODE solver Most hyperbolic conservation laws have exact solutions that are total variation diminishing (TVD) or total variation Many brbounded (TVB) although these solutions often contain discontinuities. Spatial discretizations such as Godunov's Many brscheme and high-resolution finite volume methods (TVD limiters, ENO/WENO) are designed to preserve these properties, Many brbut they are usually formulated using a forward Euler time discretization or by coupling the space and time Many brdiscretization as in the classical Lax-Wendroff scheme. When the space and time discretization is coupled, it is very Many brdifficult to produce schemes with high temporal accuracy while preserving TVD properties. An alternative is the Many brsemidiscrete formulation where we choose a spatial discretization that is TVD with forward Euler and then choose a Many brtime discretization that preserves the TVD property. Such integrators are called strong stability preserving (SSP). Many br

Let c_eff be the minimum number of function evaluations required to step as far as one step of forward Euler while Many brstill being SSP. Some theoretical bounds Many br

1. There are no explicit methods with c_eff > 1. Many br

2. There are no explicit methods beyond order 4 (for nonlinear problems) and c_eff > 0. Many br

3. There are no implicit methods with order greater than 1 and c_eff > 2. Many br

This integrator provides Runge-Kutta methods of order 2, 3, and 4 with maximal values of c_eff. More stages allows Many brfor larger values of c_eff which improves efficiency. These implementations are low-memory and only use 2 or 3 work Many brvectors regardless of the total number of stages, so e.g. 25-stage 3rd order methods may be an excellent choice. Many br

Methods can be chosen with -ts_ssp_type {rks2,rks3,rk104} Many br

rks2: Second order methods with any number s>1 of stages. c_eff = (s-1)/s Many br

rks3: Third order methods with s=n^2 stages, n>1. c_eff = (s-n)/s Many br

rk104: A 10-stage fourth order method. c_eff = 0.6 Many br

Many br

### References

| 1. | - Ketcheson, Highly efficient strong stability preserving Runge Kutta methods with low storage implementations, SISC, 2008. Many br
| 2. | - Gottlieb, Ketcheson, and Shu, High order strong stability preserving time discretizations, J Scientific Computing, 2009. Many br

### See Also

TSCreate(), TS, TSSetType()

Level:beginner
Location:src/ts/impls/explicit/ssp/ssp.c
Index of all TS routines
Table of Contents for all manual pages
Index of all manual pages

### Examples

src/ts/examples/tutorials/ex9.c.html
src/ts/examples/tutorials/ex11.c.html
src/ts/examples/tutorials/ex31.c.html