Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Uniformly high-order accurate nonoscillatory schemes
SIAM Journal on Numerical Analysis
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
A well-balanced scheme for the numerical processing of source terms in hyperbolic equations
SIAM Journal on Numerical Analysis
Rankine-Hugonoit-Riemann solver considering source terms and multidimensional effects
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
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
Journal of Computational Physics
Upwind Schemes with Exact Conservation Property for One-Dimensional Open Channel Flow Equations
SIAM Journal on Scientific Computing
Journal of Computational Physics
Journal of Computational Physics
Journal of Scientific Computing
Fourth-order balanced source term treatment in central WENO schemes for shallow water equations
Journal of Computational Physics
Computers & Mathematics with Applications
Binary weighted essentially non-oscillatory (BWENO) approximation
Journal of Computational and Applied Mathematics
High order well-balanced CDG-FE methods for shallow water waves by a Green-Naghdi model
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.48 |
In this paper we construct numerical schemes of high order of accuracy for hyperbolic balance law systems with spatially variable flux function and a source term of the geometrical type. We start with the original finite difference characteristicwise weighted essentially nonoscillatory (WENO) schemes and then we create new schemes by modifying the flux formulations (locally Lax-Friedrichs and Roe with entropy fix) in order to account for the spatially variable flux, and by decomposing the source term in order to obtain balance between numerical approximations of the flux gradient and of the source term. We apply so extended WENO schemes to the one-dimensional open channel flow equations and to the one-dimensional elastic wave equations. In particular, we prove that in these applications the new schemes are exactly consistent with steady-state solutions from an appropriately chosen subset. Experimentally obtained orders of accuracy of the extended and original WENO schemes are almost identical on a convergence test. Other presented test problems illustrate the improvement of the proposed schemes relative to the original WENO schemes combined with the pointwise source term evaluation. As expected, the increase in the formal order of accuracy of applied WENO reconstructions in all the tests causes visible increase in the high resolution properties of the schemes.