Recently, a Hamiltonian regularised shallow water (Saint-Venant) system has been introduced by Clamond and Dutykh (2018). This is Galilean invariant, linearly non-dispersive conserves formally an H1-like energy. In this paper, we extend regularisation in two directions. First, consider the more general barotropic Euler system, equations being very special case. Second, introduce class regularis...

We address three related problems in the theory of elasticity, formulated framework double forms: Saint-Venant compatibility condition, existence and uniqueness solutions for equations arising incompatible stress potentials. The scope this work is manifolds with boundary arbitrary dimension, having constant sectional curvature. central analytical machinery regular ellipticity a boundary-value p...

We present a multi-core, GPU-based framework for simulation and visualization of two-dimensional floods, based on the full implementation of Saint Venant equations. A validated CPU-based flood model was converted to NVIDIA’s CUDA architecture. The model was run on two different NVIDIA graphics cards, a GeForce 8400 GS and a Tesla T10. The model was tested using two case study applications. Impl...

This paper describes the Simulation Program for River Networks (SPRINT) that is proposed as a tool for studying Continental River Dynamics (CRD), the solution of physics-based equations for large-scale river networks. Existing coupled hydrologic/hydraulic models have been unable to solve the full Saint-Venant equations for river networks larger than O(10) elements, but continental scales requir...

Abstract The Saint-Venant equations are numerically solved to simulate free surface flows in one dimension. A Riemann solver is needed compute the numerical flux for capturing shocks and flow discontinuities occurring situations such as hydraulic jump, dam-break wave propagation, or bore propagation. that captures not yet reported be implemented within framework of a meshless method solving equ...

Using backstepping design, exponential stabilization of the linearized Saint-Venant–Exner (SVE) model of water dynamics in a sediment-filled canal with arbitrary values of canal bottom slope, friction, porosity, andwater–sediment interaction, is achieved. The linearized SVEmodel consists of two rightward convecting transport Partial Differential Equations (PDEs) and one leftward convecting tran...