A New Class of Optimal High-Order Strong-Stability-Preserving Time Discretization Methods

By Raymond J. Spiteri, Steven J. Ruuth. SIAM Journal on Numerical Analysis, 2002

820 citations recorded by the source corpus.

Subfields: Computational Mechanics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/7c9d0fb4987741d7c28f0075f89d3d9b42d416f1

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Citations in the corpus

A Toolbox of Level Set Methods (2005, neutral): “In particular, code to accompany [16] provides for additional explicit Runge-Kutta integrators from [32] and a new motion by mean curvature approximation from [21].”
A multiphase model for compressible granular–gaseous flows: formulation and initial tests (2016, methodology): “The solutions were advanced in time using a third-order Runge–Kutta (Spiteri & Ruuth 2003) algorithm with a Courant–Friedrichs– Lewy (CFL) number of 0.5, based on the maximum wave speed, λmax = max(|ug| + cg, |us| + cs).”
The black hole accretion code (2016, neutral): “Several temporal update schemes are available: simple predictor-corrector, thirdorder Runge-Kutta (RK) RK3 [91] and the strong-stability preserving s-step, pthorder RK schemes SSPRK(s,p) schemes: SSPRK(4,3), SSPRK(5,4) due to [92].”
High Order Strong Stability Preserving Time Discretizations (2009, neutral): “This class of methods was further studied in [29] [30] [74] [77] [81] [82] [27] [41] [75] [39] [72] [80] [45] [47] [60].”
Strong stability of singly-diagonally-implicit Runge--Kutta methods (2008, background): “Moreover, for p = 3,4 and various s 5, values for es,p were found that are not much smaller than s − p + 1, see the above papers and [34,35,28].”
The influence of initial conditions on turbulent mixing due to Richtmyer–Meshkov instability† (2010, methodology): “Finally, a second-order accurate three-stage Runge–Kutta time-stepping method is employed (Spiteri & Ruuth 2002).”
Finite-volume WENO schemes for three-dimensional conservation laws (2004, methodology): “Our experience suggests that for most cases the accuracy of the third order Runge-Kutta method (10) is comparable with that of the forth order Runge-Kutta method of [ 21 ] whereas the third order method has a lower computational cost and requires less memory as well.”
Beyond ideal MHD: towards a more realistic modelling of relativistic astrophysical plasmas (2008, methodology): “A numerical scheme that maintains strong stability at the discrete level is called Strong Stability Preserving (SSP) (see Spiteri & Ruuth (2002) for a detailed description of optimalSSP schemes and their properties).”
NCAR Release of CAM‐SE in CESM2.0: A Reformulation of the Spectral Element Dynamical Core in Dry‐Mass Vertical Coordinates With Comprehensive Treatment of Condensates and Energy (2018, methodology): “The SE tracer advection algorithm uses a three-stage RK strong stability preserving time-stepping method, ensuring that the time step will preserve any shape-preserving properties preserved by the underlying spatial discretization (Spiteri & Ruuth, 2002).”
The Flexible, Extensible and Efficient Toolbox of Level Set Methods (2008, background): “Adopting the - parameterization from [36], but extending to time-dependent L requires de nition of the substep sample times for i = 0; : : : ; s as t(i) = tn + t i 1 X k=0 cik; where cik = ik + i 1 X j=k+1 ijcjk; (the cik can be computed recursively [38]).”
A unifying lifting collocation penalty formulation including the discontinuous Galerkin, spectral volume/difference methods for conservation laws on mixed grids (2009, methodology): “The time integration schemes used are the TVD or SSP Runge–Kutta schemes of 3rd or 4th order accuracy [16,38].”