SPECTRAL VANISHING VISCOSITY METHOD FOR NONLINEAR CONSERVATION LAWS

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.