Solution of the Cauchy problem for a conservation law with a discontinuous flux function
SIAM Journal on Mathematical Analysis
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 Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
The discontinuous finite element method for red-and-green light models for the traffic flow
Mathematics and Computers in Simulation
Hyperbolic conservation laws with space-dependent fluxes: II. general study of numerical fluxes
Journal of Computational and Applied Mathematics
Journal of Computational Physics
δ-mapping algorithm coupled with WENO reconstruction for nonlinear elasticity in heterogeneous media
Applied Numerical Mathematics
Hyperbolic conservation laws with space-dependent fluxes: II. General study of numerical fluxes
Journal of Computational and Applied Mathematics
Riemann solver for a kinematic wave traffic model with discontinuous flux
Journal of Computational Physics
Hi-index | 7.30 |
In the paper, a kind of one-dimensional scalar hyperbolic conservation laws with flux functions dependent on space variable is discussed and analyzed. A better understanding about the behavior of wave propagation of the kind problems is presented. Especially, some sufficient and necessary conditions that ensure the unique physically relevant solution to the Riemann problem are proposed. Because the numerical flux obtained from the Riemann's solver is theoretically correct and exact to the problem, it must also be of high resolution in its nature. For comparison, some convincing numerical examples from traffic flow problems are given at the end of the paper.