Chebyshev--Legendre Spectral Viscosity Method for Nonlinear Conservation Laws

Chebyshev–legendre Spectral Viscosity Method for Nonlinear Conservation Laws∗

In this paper, a Chebyshev–Legendre spectral viscosity (CLSV) method is developed for nonlinear conservation laws with initial and boundary conditions. The boundary conditions are dealt with by a penalty method. The viscosity is put only on the high modes, so accuracy may be recovered by postprocessing the CLSV approximation. It is proved that the bounded solution of the CLSV method converges t...

Chebyshev–legendre Super Spectral Viscosity Method for Nonlinear Conservation Laws∗

In this paper, a super spectral viscosity method using the Chebyshev differential operator of high order Ds = ( √ 1− x2∂x) is developed for nonlinear conservation laws. The boundary conditions are treated by a penalty method. Compared with the second-order spectral viscosity method, the super one is much weaker while still guaranteeing the convergence of the bounded solution of the Chebyshev–Ga...

Spectral Vanishing Viscosity Method For Nonlinear Conservation Laws

Entropy viscosity method for nonlinear conservation laws

A new class of high-order numerical methods for approximating nonlinear conservation laws is described (entropy viscosity method). The novelty is that a nonlinear viscosity based on the local size of an entropy production is added to the numerical discretization at hand. This new approach does not use any flux or slope limiters, applies to equations or systems supplemented with one or more entr...

Spectral Viscosity Method with Generalized Hermite Functions and Its Spectral Filter for Nonlinear Conservation Laws

In this paper, we propose a new spectral viscosity method for the solution of nonlinear scalar conservation laws in the whole line. The proposed method is based on the generalized Hermite functions. It is shown rigorously that this scheme converges to the unique entropy solution by using compensated compactness arguments. The numerical experiments of the inviscid Burger’s equation support our r...