The application of Runge-Kutta schemes designed to enjoy a large region of absolute stability can significantly increase the efficiency of numerical methods for PDEs based on a method of lines approach. In this work we investigate the improvement in the efficiency of the time integration of relaxation schemes for degenerate diffusion problems, using SSP Runge-Kutta schemes and computing the maximal CFL coeffcients. This technique can be extended to other PDEs, linear and nonlinear, provided the space operator has eigenvalues with a non-zero real part.
Increasing efficiency through optimal RK time integration of diffusion equations / F. Cavalli, G. Naldi, G. Puppo, M. Semplice - In: Hyperbolic problems : theory, numerics and applications / [a cura di] D. Serre, S. Benzoni-Gavage. - Berlin : Springer-Verlag, 2008. - ISBN 9783540757115. - pp. 955-962 (( Intervento presentato al 11. convegno 11 International Conference on Hyperbolic Problems : Theory, Numerics, Applications tenutosi a Lyon nel 2006 [10.1007/978-3-540-75712-2].
Increasing efficiency through optimal RK time integration of diffusion equations
F. CavalliPrimo
;G. NaldiSecondo
;M. SempliceUltimo
2008
Abstract
The application of Runge-Kutta schemes designed to enjoy a large region of absolute stability can significantly increase the efficiency of numerical methods for PDEs based on a method of lines approach. In this work we investigate the improvement in the efficiency of the time integration of relaxation schemes for degenerate diffusion problems, using SSP Runge-Kutta schemes and computing the maximal CFL coeffcients. This technique can be extended to other PDEs, linear and nonlinear, provided the space operator has eigenvalues with a non-zero real part.
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