The solution of nonstrictly hyperbolic conservation laws may be hard to compute
SIAM Journal on Scientific Computing
Suppression of oscillations in Godunov's method for a resonant non-strictly hyperbolic system
SIAM Journal on Numerical Analysis
SIAM Journal on Applied Mathematics
The discontinuous finite element method for red-and-green light models for the traffic flow
Mathematics and Computers in Simulation
A class of approximate Riemann solvers and their relation to relaxation schemes
Journal of Computational Physics
SIAM Journal on Scientific Computing
Journal of Computational and Applied Mathematics
δ-mapping algorithm coupled with WENO reconstruction for nonlinear elasticity in heterogeneous media
Applied Numerical Mathematics
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Following the previous paper, this one continues to study numerical approximations to the space-dependent flux functions in hyperbolic conservation laws. The investigation is based on the wave propagation behavior, Riemann problem, steady flows, hyperbolic properties, cell entropy inequalities, along with such well known numerical fluxes as the Godunov, Local Lax-Friedrichs and Engquist-Osher. All these give rise to correct description for the consistency and monotonicity of numerical fluxes, which ensure properly confined numerical solutions. Numerical examples show that the accordingly designed fluxes resolve discontinuities and smooth solutions very precisely.