10,344 research outputs found
Modeling overland flow and soil erosion on nonuniform hillslopes: a finite volume scheme.
This paper presents a finite volume scheme for coupling the St. Venant equations with the multi-
particle size class Hairsine-Rose soil erosion model. A well-balanced MUSCL-Hancock scheme is
proposed to minimize spurious waves in the solution arising from an imbalance between the flux
gradient and the source terms in the momentum equation. Additional criteria for numerical stability
when dealing with very shallow flows and wet-dry fronts are highlighted. Numerical tests show that
the scheme performs well in terms of accuracy and robustness for both the water and sediment
transport equations. The proposed scheme facilitates the application of the Hairsine-Rose model to
complex scenarios of soil erosion with concurrent interacting erosion processes over a non-uniform
topography
A Godunov-type method for the shallow water equations with discontinuous topography in the resonant regime
We investigate the Riemann problem for the shallow water equations with
variable and (possibly) discontinuous topography and provide a complete
description of the properties of its solutions: existence; uniqueness in the
non-resonant regime; multiple solutions in the resonant regime. This analysis
leads us to a numerical algorithm that provides one with a Riemann solver.
Next, we introduce a Godunov-type scheme based on this Riemann solver, which is
well-balanced and of quasi-conservative form. Finally, we present numerical
experiments which demonstrate the convergence of the proposed scheme even in
the resonance regime, except in the limiting situation when Riemann data
precisely belong to the resonance hypersurface.Comment: 39 page
Well-balanced fifth-order finite difference Hermite WENO scheme for the shallow water equations
In this paper, we propose a well-balanced fifth-order finite difference
Hermite WENO (HWENO) scheme for the shallow water equations with non-flat
bottom topography in pre-balanced form. For achieving the well-balance
property, we adopt the similar idea of WENO-XS scheme [Xing and Shu, J. Comput.
Phys., 208 (2005), 206-227.] to balance the flux gradients and the source
terms. The fluxes in the original equation are reconstructed by the nonlinear
HWENO reconstructions while other fluxes in the derivative equations are
approximated by the high-degree polynomials directly. And an HWENO limiter is
applied for the derivatives of equilibrium variables in time discretization
step to control spurious oscillations which maintains the well-balance
property. Instead of using a five-point stencil in the same fifth-order WENO-XS
scheme, the proposed HWENO scheme only needs a compact three-point stencil in
the reconstruction. Various benchmark examples in one and two dimensions are
presented to show the HWENO scheme is fifth-order accuracy, preserves
steady-state solution, has better resolution, is more accurate and efficient,
and is essentially non-oscillatory.Comment: 24 pages, 11 figure
Bound-preserving and entropy-stable algebraic flux correction schemes for the shallow water equations with topography
A well-designed numerical method for the shallow water equations (SWE) should
ensure well-balancedness, nonnegativity of water heights, and entropy
stability. For a continuous finite element discretization of a nonlinear
hyperbolic system without source terms, positivity preservation and entropy
stability can be enforced using the framework of algebraic flux correction
(AFC). In this work, we develop a well-balanced AFC scheme for the SWE system
including a topography source term. Our method preserves the lake at rest
equilibrium up to machine precision. The low-order version represents a
generalization of existing finite volume approaches to the finite element
setting. The high-order extension is equipped with a property-preserving flux
limiter. Nonnegativity of water heights is guaranteed under a standard CFL
condition. Moreover, the flux-corrected space discretization satisfies a
semi-discrete entropy inequality. New algorithms are proposed for realistic
simulation of wetting and drying processes. Numerical examples for well-known
benchmarks are presented to evaluate the performance of the scheme
A finite volume shock-capturing solver of the fully coupled shallow water-sediment equations
This paper describes a numerical solver of well-balanced, 2D depth-averaged shallow water-sediment
equations. The equations permit variable variable horizontal fluid density and are designed to model watersediment
flow over a mobile bed. A Godunov-type, HLLC finite volume scheme is used to solve the fully
coupled system of hyperbolic conservation laws which describe flow hydrodynamics, suspended sediment
transport, bedload transport and bed morphological change. Dependent variables are specially selected to
handle the presence of the variable density property in the mathematical formulation. The model is verified
against analytical and semi-analytical solutions for bedload transport and suspended sediment transport,
respectively. The well-balanced property of the equations is verified for a variable-density dam break flow
over discontinuous bathymetry. Simulations of an idealised dam-break flow over an erodible bed are in
excellent agreement with previously published results ([1]), validating the ability of the model to capture
the complex interaction between rapidly varying flow and an erodible bed and validating the eigenstructure
of the system of variable-density governing equations. Flow hydrodynamics and final bed topography of a
laboratory-based 2D partial dam breach over a mobile bed are satisfactorily reproduced by the numerical
model. Comparison of the final bed topographies, computed for two distinct sediment transport methods,
highlights the sensitivity of shallow water-sediment models to the choice of closure relationships
- …