In this paper a new set of Boussinesq wave equations with improved linear dispersion properties is proposed for extending its application to deeper water without having its mathematical form changed. The improvements are due to the combination of a generalized set of Boussinesq wave equations expressed in terms of any velocity, with additional dispersive terms obtained by invoking the linear sh...

Aim of this study is to present robust numerical methods for shallow water equations permitting to correctly predict long water-wave phenomena. A semi-intrusive and polynomialchaos based method are coupled with a residual based distribution scheme by considering several sources of uncertainties in the simulation of a long wave runup on a conical island. Stochastic results are assessed by compar...

A discontinuous Galerkin shallow water model on the cubed sphere is developed, thereby extending the transport scheme developed by Nair et al. The continuous flux form nonlinear shallow water equations in curvilinear coordinates are employed. The spatial discretization employs a modal basis set consisting of Legendre polynomials. Fluxes along the element boundaries (internal interfaces) are app...

Wall-jet flow is an important flow field in hydraulic engineering, and its applications include flow from the bottom outlet of dams and sluice gates. In this paper, the plane turbulent wall jet in shallow tailwater is simulated by solving the Reynolds Averaged Navier-Stokes equations using the standard  turbulence closure model. This study aims to explore the ability of a time splitting method ...

We derive here various equivalent mathematical formulations of the water waves problem (and some extensions to the two-fluids problem). We then propose a dimensionless version of these equations that is well adapted to the qualitative description of the solutions. The way we nondimensionalize the water waves equations relies on a rough analysis of their linearization around the rest state and s...

In this study, a framework for simulating the flow field and heat transfer processes in small shallow inland water bodies has been developed. As the dynamics and thermal structure of these water bodies are crucial in studying the quality of stored water , and in assessing the heat fluxes from their surfaces as well, the heat transfer and temperature simulations were modeled. The proposed model ...

Quasi-bubble nite element approximations to the shallow water equations are investigated focusing on implementations of the surface elevation boundary condition. We rst demonstrate by numerical results that the conventional implementation of the boundary condition degrades the accuracy of the velocity solution. It is also shown that the degraded velocity leads to a critical instability if the a...

The Shallow Water Equations (SWE) are a set of nonlinear hyperbolic equations, describing long waves relative to the water depth. Physical phenomena such as tidal waves in rivers and seas, breaking of waves on shallow beaches and even harbour oscillations can be modelled successfully with the SWE. The 3D SWE (1.1){(1.3) given below for Cartesian (;) coordinates are based on the hydrostatic assu...

We derive a second-order semi-discrete central-upwind scheme for oneand two-dimensional systems of two-layer shallow water equations. We prove that the presented scheme is wellbalanced in the sense that stationary steady-state solutions are exactly preserved by the scheme, and positivity preserving, that is, the depth of each fluid layer is guaranteed to be nonnegative. We also propose a new te...

A computational algorithm based on the multiquadric, which is a continuously diierentiable radial basis function, is devised to solve the shallow-water equations. The numerical solutions are evaluated at scattered collocation points and the spatial partial derivatives are formed directly from partial derivatives of the radial basis function, not by any diierence scheme. The method does not requ...