Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 231, Issue 4, Pages 1963-2001Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2011.11.014
Keywords
Weak solutions; Well-balanced approach; Roe methods; Mud/debris flow; Stability region; Wet/dry front; Shallow water systems; Turbulent stress; Dispersive stress; Coulomb stress; Yield stress; Viscous stress; Stopping conditions
Funding
- Spanish Ministry of Science and Technology [CGL201128590]
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In this work, the source term discretization in hyperbolic conservation laws with source terms is considered using an approximate augmented Riemann solver. The technique is applied to the shallow water equations with bed slope and friction terms with the focus on the friction discretization. The augmented Roe approximate Riemann solver provides a family of weak solutions for the shallow water equations, that are the basis of the upwind treatment of the source term. This has proved successful to explain and to avoid the appearance of instabilities and negative values of the thickness of the water layer in cases of variable bottom topography. Here, this strategy is extended to capture the peculiarities that may arise when defining more ambitious scenarios, that may include relevant stresses in cases of mud/debris flow. The conclusions of this analysis lead to the definition of an accurate and robust first order finite volume scheme, able to handle correctly transient problems considering frictional stresses in both clean water and debris flow, including in this last case a correct modelling of stopping conditions. (C) 2011 Elsevier Inc. All rights reserved.
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