Efficient construction and utilisation of approximate riemann solutions
Proc. of the sixth int'l. symposium on Computing methods in applied sciences and engineering, VI
Numerical computation of internal & external flows: fundamentals of numerical discretization
Numerical computation of internal & external flows: fundamentals of numerical discretization
An approach to interface synthesis
ISSS '95 Proceedings of the 8th international symposium on System synthesis
Approximate Riemann solvers, parameter vectors, and difference schemes
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
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
Construction of second-order TVD schemes for nonhomogeneous hyperbolic conservation laws
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Scientific Computing
Remarks on the Consistency of Upwind Source at Interface Schemes on Nonuniform Grids
Journal of Scientific Computing
Hybrid Well-balanced WENO Schemes with Different Indicators for Shallow Water Equations
Journal of Scientific Computing
Hi-index | 31.46 |
An algebraic technique is presented for balancing flux gradients and source terms when applying Roe's approximate Riemann solver in finite volume schemes. The numerical imbalance is eradicated by reformulating the governing matrix hyperbolic system of conservation laws in terms of deviations away from an unforced but separately specified equilibrium state. Thus, balancing is achieved by the incorporation of this extra physical information and bypasses conventional numerical treatments of the imbalance. The technique is first applied to the shallow water equations. Simulations of benchmark flows including wind-induced flow in a two-dimensional basin, transcritical flow in a one-dimensional channel and wave propagation over a two-dimensional hump are in close agreement with analytical solutions and predictions by alternative numerical schemes. The technique is then applied to a more complicated coupled pair of equation sets, the hyperbolic period-and depth-averaged ray-type wave conservation and modified shallow water equations that describe wave current interaction in the nearshore zone at the coast. Reasonable agreement is obtained with laboratory measurements of wave diffraction behind a submerged elliptical shoal [Coastal Engrg. 6 (1982) 255] and of wave-induced nearshore currents at a half-sinusoidal beach [Wave-induced nearshore currents, Ph.D. Thesis, Liverpool University, UK, 1981].