A Legendre Pseudospectral Viscosity Method

entropy flux F is related to U and to the flux f by F 9 5 U 9f 9. The (weak) solution of (1.1)–(1.4) is then unique. We use the Legendre spectral viscosity method to solve nonlinear conservation laws. This method essentially consists in adding a In this paper, we are interested in computing the entropic spectral viscosity to the equations for the high wavenumbers of solution of Eq. (1.1), i.e., the unique weak solution satisthe numerical solution. This viscosity is sufficient to stabilize the fying the entropy inequality (1.4) for all convex entropy numerical scheme while small enough to retain spectral accuracy. U. This will be obtained by using spectral methods. Several tests are considered including the 1D and 2D Euler equations Spectral methods consist in finding the first Fourier-like of gas dynamics. Q 1996 Academic Press, Inc. coefficients of the solution of partial differential equations (pure spectral method) or the values of this solution at