Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Non-oscillatory central differencing for hyperbolic conservation laws
Journal of Computational Physics
On Godunov-type methods near low densities
Journal of Computational Physics
The effects of numerical viscosities. I: slowly moving shocks
Journal of Computational Physics
A well-balanced scheme for the numerical processing of source terms in hyperbolic equations
SIAM Journal on Numerical Analysis
Analysis and Approximation of Conservation Laws with Source Terms
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Journal of Computational Physics
Mathematics and Computers in Simulation
Flux difference splitting and the balancing of source terms and flux gradients
Journal of Computational Physics
The surface gradient method for the treatment of source terms in the shallow-water equations
Journal of Computational Physics
A well-balanced gas-kinetic scheme for the shallow-water equations with source terms
Journal of Computational Physics
Semidiscrete Central-Upwind Schemes for Hyperbolic Conservation Laws and Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
Equilibrium schemes for scalar conservation laws with stiff sources
Mathematics of Computation
A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Numerical approximation for a Baer-Nunziato model of two-phase flows
Applied Numerical Mathematics
Journal of Computational Physics
Hi-index | 31.45 |
We propose a simple well-balanced method named the slope selecting method which is efficient in both steady state capturing and preserving for hyperbolic system with geometrical source terms having concentrations. Physical problems under consideration include the shallow water equations with discontinuous topography, and the quasi-one-dimensional nozzle flows with discontinuous cross-sectional area. This method is an extension from the interface type method developed in [S. Jin, X. Wen, An efficient method for computing hyperbolic systems with geometrical source terms having concentrations, J. Comput. Math. 22 (2004) 230-249]. The slope selecting method keeps two merits of the previous method. It can be applied when the homogeneous system solver is available and has efficient steady state capturing property. Compared with the previous method, the slope selecting method has two improvements. One is this method also has satisfactory steady state preserving property. The other is this method can be applied to any conservative scheme for the homogeneous system. Numerical examples provide strong evidence on the effectiveness of this slope selecting method for various unsteady, steady and quasi-steady state solutions calculations as well as the flexibility of this method of being applicable to any conservative scheme for the homogeneous system.