Spectral viscosity method with generalized Hermite functions for nonlinear conservation laws
Provides a theoretical convergence guarantee for spectral methods on unbounded domains, relevant for computational fluid dynamics and PDE solvers.
Proposed spectral viscosity methods using generalized Hermite functions for nonlinear conservation laws on the whole line, proving convergence to the entropy solution via compensated compactness, with numerical validation on Burgers' equation.
In this paper, we propose new spectral viscosity methods based on the generalized Hermite functions for the solution of nonlinear scalar conservation laws in the whole line. It is shown rigorously that these schemes converge to the unique entropy solution by using compensated compactness arguments, under some conditions. The numerical experiments of the inviscid Burger's equation support our result, and it verifies the reasonableness of the conditions.