On Godunov-type methods for gas dynamics
SIAM Journal on Numerical Analysis
On Godunov-type methods near low densities
Journal of Computational Physics
A well-balanced scheme for the numerical processing of source terms in hyperbolic equations
SIAM Journal on Numerical Analysis
On postshock oscillations due to shock capturing schemes in unsteady flows
Journal of Computational Physics
Wave propagation algorithms for multidimensional hyperbolic systems
Journal of Computational Physics
Approximate Riemann solvers, parameter vectors, and difference schemes
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Computations of slowly moving shocks
Journal of Computational Physics
Analysis and Approximation of Conservation Laws with Source Terms
SIAM Journal on Numerical Analysis
Journal of Computational Physics
A class of approximate Riemann solvers and their relation to relaxation schemes
Journal of Computational Physics
SIAM Journal on Scientific Computing
Journal of Computational Physics
A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows
SIAM Journal on Scientific Computing
Augmented Riemann solver for urethra flow modeling
Mathematics and Computers in Simulation
Journal of Computational Physics
Journal of Computational Physics
Shallow Water Flows in Channels
Journal of Scientific Computing
A Well-Balanced Path-Integral f-Wave Method for Hyperbolic Problems with Source Terms
Journal of Scientific Computing
C3: A finite volume-finite difference hybrid model for tsunami propagation and runup
Computers & Geosciences
Improved Riemann solvers for complex transport in two-dimensional unsteady shallow flow
Journal of Computational Physics
Journal of Computational Physics
A Riemann solver for unsteady computation of 2D shallow flows with variable density
Journal of Computational Physics
A large time step 1D upwind explicit scheme (CFL1): Application to shallow water equations
Journal of Computational Physics
Original Article: High order well-balanced scheme for river flow modeling
Mathematics and Computers in Simulation
A kinetic flux-vector splitting method for single-phase and two-phase shallow flows
Computers & Mathematics with Applications
Hi-index | 31.48 |
We present a class of augmented approximate Riemann solvers for the shallow water equations in the presence of a variable bottom surface. These belong to the class of simple approximate solvers that use a set of propagating jump discontinuities, or waves, to approximate the true Riemann solution. Typically, a simple solver for a system of m conservation laws uses m such discontinuities. We present a four wave solver for use with the the shallow water equations-a system of two equations in one dimension. The solver is based on a decomposition of an augmented solution vector-the depth, momentum as well as momentum flux and bottom surface. By decomposing these four variables into four waves the solver is endowed with several desirable properties simultaneously. This solver is well-balanced: it maintains a large class of steady states by the use of a properly defined steady state wave-a stationary jump discontinuity in the Riemann solution that acts as a source term. The form of this wave is introduced and described in detail. The solver also maintains depth non-negativity and extends naturally to Riemann problems with an initial dry state. These are important properties for applications with steady states and inundation, such as tsunami and flood modeling. Implementing the solver with LeVeque's wave propagation algorithm [R.J. LeVeque, Wave propagation algorithms for multi-dimensional hyperbolic systems, J. Comput. Phys. 131 (1997) 327-335] is also described. Several numerical simulations are shown, including a test problem for tsunami modeling.