Shock-Capturing Methods for Free-Surface Shallow Flows

By Eleuterio F. Toro. 2001

1,357 citations recorded by the source corpus.

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Citations in the corpus

Assimilation of spatially distributed water levels into a shallow-water flood model. Part I: Mathematical method and test case (2009, methodology): “The solver uses the rotational invariant property of the equations, then it uses a local 1D HLLC Riemman solver [26] with a consistent intermediate wave speed, [6].”
A simple and efficient unstructured finite volume scheme for solving the shallow water equations in overland flow applications (2015, methodology): “…have been applied to the equations written as in (1) [Begnudelli et al., 2008; Berthon et al., 2011; Canestrelli et al., 2009; Cea and V azquez-Cend on, 2012; Chertock et al., 2010; LeVeque, 2002; Liang, 2010; Martinez-Gavara and Donat, 2011; Sanders et al., 2008; Toro, 2001; Wang et al., 2011].”
Efficient computation of surf zone waves using the nonlinear shallow water equations with non-hydrostatic pressure (2008, methodology): “Traditionally, the shock-capturing schemes applied to shallow water flows at collocated grids are based on the Godunovtype approach, where a discontinuity in the unknown variables (water depth and discharge) is assumed at the cell edges and a Riemann solver is employed to compute the variable flux a”
Simulation of dam‐ and dyke‐break hydrodynamics on dynamically adaptive quadtree grids (2004, methodology): “Toro [4] gives a comprehensive review of recent developments in Godunov-type nite volume solvers for dam-break hydrodynamics.”
Modelling debris flows down general channels (2005, methodology): “…literature (see, e.g., Harten, 1983; Harten et al., 1986; Yee, 1987; Nessyahu and Tadmor, 1990; LeVeque, 1990; Kr̈oner, 1997; Jiang and Tadmor, 1998; Toro, 2001) and its application to avalanches is, e.g., given by Tai et al. (2002), Pudasaini (2003), Pudasaini and Hutter (2003a), Wang et al.…”
One-dimensional explicit finite-volume model for sediment transport (2008, methodology): “Many of these methods have been verified and successfully applied in the simulation of transient flows, especially dam-break flow, over fixed beds (Toro, 1997, 2001).”
On Universal Osher-Type Schemes for General Nonlinear Hyperbolic Conservation Laws (2011, background): “For the compressible Euler equations for ideal gases see [43] for full details, for the shallow water equations see [42].”
On the well-balance property of Roe?s method for nonconservative hyperbolic systems (2004, background): “It is known that, in the presence of source terms, standard methods can fail in approximating steady or nearly steady flows (see [25, 30, 33], .”
A depth-integrated model for weakly dispersive, turbulent, and rotational fluid flows (2009, methodology): “By using the constructed interface values, the numerical fluxes are computed by HLLC approximate Riemann solvers (Toro, 2002) on a cartesian grid.”
Solution of the generalized Riemann problem for advection–reaction equations (2002, background): “…the conventional piecewise constant data Riemann problem GRP0, the exact solution of which is available for a number of well-known systems of homogeneous (no source terms) conservation laws, such as the Euler equations of gas dynamics and the nonlinear shallow-water equations (Toro 1999, 2001).”