A comparative study of advanced shock-capturing schemes applied to Burgers' equation

A systematic evaluation is conducted of all extant numerical schemes for nonlinear scalar transport problems, and several advanced shock-capturing schemes are used to solve the nonlinear Burgers' equation in order to characterize their ability to resolve the sharp discontinuity, expansion zone, and propagation and collision features of shocks. For discontinuous functions, the Warming-Beam scheme generates preshock wiggles, while the Lax-Wendroff scheme generates postshock ones. Such limiters as the MUSCL or the superbee are more compressive than minimod or monotonic limiters. The performance of such TVD schemes as the upwind, the symmetric, and the Roe-Sweby, resemble each other.