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A Riemann solver for unsteady computation of 2D shallow flows with variable density

AuthorsMurillo, J.; Latorre Garcés, Borja ; García-Navarro, Pilar
KeywordsMulti-component transport
Variable density
Upwind method
Weak solutions
Well-balanced approach
Roe solver
Reactive terms
Riemann problem
Source terms
Issue DateMay-2012
CitationMurillo J, Latorre B, García-Navarro P. A Riemann solver for unsteady computation of 2D shallow flows with variable density. Journal of Computational Physics 231: 4775-4807 (2012)
AbstractA novel 2D numerical model for vertically homogeneous shallow flows with variable horizontal density is presented. Density varies according to the volumetric concentration of different components or species that can represent suspended material or dissolved solutes. The system of equations is formed by the 2D equations for mass and momentum of the mixture, supplemented by equations for the mass or volume fraction of the mixture constituents. A new formulation of the Roe-type scheme including density variation is defined to solve the system on two-dimensional meshes. By using an augmented Riemann solver, the numerical scheme is defined properly including the presence of source terms involving reaction. The numerical scheme is validated using analytical steady-state solutions of variable-density flows and exact solutions for the particular case of initial value Riemann problems with variable bed level and reaction terms. Also, a 2D case that includes interaction with obstacles illustrates the stability and robustness of the numerical scheme in presence of non-uniform bed topography and wetting/drying fronts. The obtained results point out that the new method is able to predict faithfully the overall behavior of the solution and of any type of waves.
Description13 Pags., 29 Figs.
Publisher version (URL)http://dx.doi.org/10.1016/j.jcp.2012.03.016
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