Some recent finite volume schemes for one and two layers shallow water equations with variable density

PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Finite volume methods applied to problems in fluid mechanics (76M12) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)

Cites Work

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A finite volume method for scalar conservation laws with stochastic time-space dependent flux functions
Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry
Numerical simulation of two-layer shallow water flows through channels with irregular geometry.
A finite volume method for numerical simulation of shallow water models with porosity
The modified Rusanov scheme for solving the ultra-relativistic Euler equations
A predictor-corrector scheme for simulation of two-phase granular flows over a moved bed with a variable topography
High-order numerical solutions to the shallow-water equations on the rotated cubed-sphere grid
Embedded domain reduced basis models for the shallow water hyperbolic equations with the shifted boundary method
A new approach for designing moving-water equilibria preserving schemes for the shallow water equations
A sign matrix based scheme for non-homogeneous PDE's with an analysis of the convergence stagnation phenomenon
High order well-balanced asymptotic preserving finite difference WENO schemes for the shallow water equations in all Froude numbers
A Generalized Rusanov method for Saint-Venant Equations with Variable Horizontal Density
An entropy satisfying scheme for two-layer shallow water equations with uncoupled treatment
1-D numerical modelling of shallow flows with variable horizontal density
Maximal two-layer exchange over a sill and through the combination of a sill and contraction with barotropic flow
Alternating bar instabilities in unsteady channel flows over erodible beds
Finite volume scheme for numerical simulation of the sediment transport model
Finite-volume schemes for shallow-water equations

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