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The classical dam break problem has become the de facto standard in validating the Nonlinear Shallow Water Equations (NSWE) solvers. Moreover, the NSWE are widely used for flooding simulations. While applied mathematics community is…
In this work, the exact reproduction of a moving-water steady flow via the numerical solution of the one-dimensional shallow water equations is studied. A new scheme based on a modified version of the HLLEM approximate Riemann solver…
We use numerical methods to study the behaviour of the Serre equations in the presence of steep gradients because there are no known analytical solutions for these problems. In keeping with the literature we study a class of initial…
When dealing with shallow water simulations, the velocity profile is often assumed to be constant along the vertical axis. However, since in many applications this is not the case, modeling errors can be significant. Hence, in this work, we…
This paper presents a simple numerical scheme for the two dimensional Shallow-Water Equations (SWEs). Inspired by the study of numerical approximation of the one dimensional SWEs Audusse et al. (2015), this paper extends the problem from 1D…
The shallow water equations (SWE) model a variety of geophysical flows. Flows in channels with rectangular cross sections may be modelled with a simplified one-dimensional SWE with varying width. Among other model parameters, information…
The capability to accurately predict flood flows via numerical simulations is a key component of contemporary flood risk management practice. However, modern flood models lack the capacity to accurately model flow interactions with linear…
An exact solution to the lock-exchange problem, which is a two-layer analogue of the classical dam-break problem, is obtained in the shallow-water (SW) approximation for two immiscible fluids with slightly different densities. The problem…
We propose a novel Skew Gradient Embedding (SGE) framework for systematically reformulating thermodynamically consistent partial differential equation (PDE) models-capturing both reversible and irreversible processes-as generalized gradient…
Numerous codes are being developed to solve Shallow Water equations. Because they are used in hydraulics and environmental studies, their capability to simulate properly flow dynamics is essential to guarantee infrastructure and human…
Reduced models for free-surface flows are required due to the high dimensionality of the underlying incompressible Navier-Stokes equations, which need to fully resolve the flow in vertical direction to compute the surface height. On the…
Shallow Water Moment Equations (SWME) are extensions to the well-known Shallow Water Equations (SWE) for the efficient modeling and numerical simulation of free-surface flows. While the SWE typically assume a depth-averaged vertical…
Finite-volume numerical method for study shallow water flows over an arbitrary bed profile in the presence of external force is proposed. This method uses the quasi-two-layer model of hydrodynamic flows over a stepwise boundary with…
This work focuses on the numerical approximation of the Shallow Water Equations (SWE) using a Lagrange-Projection type approach. We propose to extend to this context recent implicit-explicit schemes developed in the framework of…
The purpose of the present work is to expand substantially the type of control and estimation problems that can be addressed following the paradigm of Schr\"odinger bridges, by incorporating termination (killing) of stochastic flows.…
We propose a novel dispersive regularization framework for the numerical simulation of the one-dimensional shallow water equations (SWE). The classical hyperbolic system is regularized by a third-order dispersive term in the momentum…
A numerical method is proposed for solving the two layer shallow water equations with variable bathymetry in one dimension based on high-resolution f-wave-propagation finite volume methods. The method splits the jump in the fluxes and…
Shallow free surface flows are often characterized by both subdomains that require high modeling complexity and subdomains that can be sufficiently accurately modeled with low modeling complexity. Moreover, these subdomains may change in…
Numerous codes are being developed to solve Shallow Water equations. Because there are used in hydraulic and environmental studies, their capability to simulate properly flow dynamics is critical to guarantee infrastructure and human…
Simulation and control of the transient flow in natural gas networks involve solving partial differential equations (PDEs). This paper proposes a semi-analytical solutions (SAS) approach for fast and accurate simulation of the natural gas…