SPECTRAL VANISHING VISCOSITY METHOD FOR NONLINEAR CONSERVATION LAWS
SPECTRAL VANISHING VISCOSITY METHOD FOR NONLINEAR CONSERVATION LAWS
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Date
2001
Authors
GUO, BEN-YU
MA, HE-PING
TADMOR, EITAN
Advisor
Citation
B.-Y. Guo, H.-P. Ma & E. Tadmor (2001). Spectral vanishing viscosity method for nonlinear conservation laws. SIAM Journal on Numerical Analysis 39 (2001), 1254-1268.
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Abstract
We propose a new spectral viscosity(SV) scheme for the accurate solution of nonlinear
conservation laws. It is proved that the SV solution converges to the unique entropysolution
under appropriate reasonable conditions. The proposed SV scheme is implemented directlyon high
modes of the computed solution. This should be compared with the original nonperiodic SV scheme
introduced byMada y, Ould Kaber, and Tadmor in [SIAM J. Numer. Anal., 30 (1993), 321–342],
where SV is activated on the derivative of the SV solution. The new proposed SV method could
be viewed as a correction of the former, and it offers an improvement which is confirmed byour
numerical experiments. A postprocessing method is implemented to greatlyenhance the accuracyof
the computed SV solution. The numerical results show the efficiencyof the new method.