Related papers: Primitive variable regularization to derive novel …
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…
Models for shallow water flow often assume that the lateral velocity is constant over the water height. The recently derived shallow water moment equations are an extension of these standard shallow water equations. The extended models…
In this paper, we investigate steady states of shallow water moment equations including bottom topographies. We derive a new hyperbolic shallow water moment model based on linearized moment equations that allows for a simple assessment of…
The shallow water equations often assume a constant velocity profile along the vertical axis. However, this assumption does not hold in many practical applications. To better approximate the vertical velocity distribution, models such as…
Shallow flow models are used for a large number of applications including weather forecasting, open channel hydraulics and simulation-based natural hazard assessment. In these applications the shallowness of the process motivates…
In this paper we analyze the stability of equilibrium manifolds of hyperbolic shallow water moment equations. Shallow water moment equations describe shallow flows for complex velocity profiles which vary in vertical direction and the…
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…
In this paper, we investigate the two-dimensional extension of a recently introduced set of shallow water models based on a regularized moment expansion of the incompressible Navier-Stokes equations…
In this article we address some issues related to the initial value problems for a rotating shallow water hyperbolic system of equations and the diffusive regularization of this system. For initial data close to the solution at rest, we…
Shallow flows are governed by the Navier-Stokes equations. They are commonly modelled using the shallow water equations, a great simplification of the Navier-Stokes equations, which often yields inaccurate results. For that reason, a model…
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…
In this paper, we introduce a new approach for constructing robust well-balanced numerical methods for the one-dimensional Saint-Venant system with and without the Manning friction term. Following the idea presented in [R. Abgrall, Commun.…
The shallow-water system is a standard model for long waves in shallow water. The system is hyperbolic and, for a large class of initial data, solutions develop steep gradients leading to shock formation in finite time. Since such…
In the present study, we propose a modified version of the Nonlinear Shallow Water Equations (Saint-Venant or NSWE) for irrotational surface waves in the case when the bottom undergoes some significant variations in space and time. The…
Geophysical flow simulations using hyperbolic shallow water moment equations require an efficient discretization of a potentially large system of PDEs, the so-called moment system. This calls for tailored model order reduction techniques…
The Shallow Water Moment Equations (SWME) are an extension of the Shallow Water Equations (SWE) for improved modelling of free-surface flows. In contrast to the SWE, the SWME incorporate vertical velocity profile information. The SWME…
Originally introduced to describe a transition region in stars, the magnetic rotating shallow water (MRSW) model is now used in many solar physics and geophysical applications. Derived from the 3-D incompressible magnetohydrodynamic system,…
We derive a hyperbolic system of equations approximating the two-layer dispersive shallow water model for shear flows recently proposed by Gavrilyuk, Liapidevskii \& Chesnokov (J. Fluid Mech., vol. 808, 2016, pp. 441--468). The use of this…
In this study we investigate shallow turbidity density currents and underflows from mechanical point of view. We propose a simple hyperbolic model for such flows. On one hand, our model is based on very basic conservation principles. On the…
Shallow water moment equations are reduced-order models for free-surface flows that allow to represent vertical variations of the velocity profile at the expense of additional evolution equations for a number of additional variables, so…