Related papers: A finite area scheme for shallow granular flows on…

Models and simulations of the flow of thin films of fluids have many important applications in industrial and natural processes. We consider the motion of a thin layer of an incompressible, Newtonian fluid over an arbitrary solid,…

Consider the 3D flow of a viscous Newtonian fluid upon a curved 2D substrate when the fluid film is thin as occurs in many draining, coating and biological flows. We derive a comprehensive model of the dynamics of the film, the model being…

Consider the three-dimensional flow of a viscous Newtonian fluid upon an abitrarily curved substrate when the fluid film is thin as occurs in many draining, coating and biological flows. We derive a model of the dynamics of the film, the…

A formulation of the shallow water equations adapted to general complex terrains is proposed. Its derivation starts from the observation that the typical approach of depth integrating the Navier-Stokes equations along the direction of…

In this work we present a multilayer shallow model to approximate the Navier-Stokes equations with hydrostatic pressure and the $\mu(I)$-rheology. The main advantages of this approximation are (i) the low cost associated with the numerical…

We propose a two-dimensional flow model of a viscous fluid between two close moving surfaces. We show that its asymptotic behavior, when the distance between the two surfaces tends to zero, is the same as that of the the Navier-Stokes…

The flow of thin liquid films on inclined or vertical surfaces is one of immense importance, with applications spanning many types of process industries, due to the increased mass and heat transfer brought about by the presence of waves on…

We consider the two-dimensional (2D) flow in a flat free-slip surface that bounds a three-dimensional (3D) volume in which the flow is turbulent. The equations of motion for the two-dimensional flow in the surface are neither compressible…

In this work, we develop a modelling framework for granular flows based on the shallow water moment equations on inclined planes. Under the assumption of a polynomial expansion of the velocity field, the model extends the classical shallow…

Approximate streamsurfaces of a 3D velocity field have recently been constructed as isosurfaces of the closest first integral of the velocity field. Such approximate streamsurfaces enable effective and efficient visualization of vortical…

In many applications, it is important to reconstruct a fluid flow field, or some other high-dimensional state, from limited measurements and limited data. In this work, we propose a shallow neural network-based learning methodology for such…

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…

Energy distributions of high frequency linear wave fields are often modelled in terms of flow or transport equations with ray dynamics given by a Hamiltonian vector field in phase space. Applications arise in underwater and room acoustics,…

We propose a new reduced model for gravity-driven free-surface flows of shallow elastic fluids. It is obtained by an asymptotic expansion of the upper-convected Maxwell model for elastic fluids. The viscosity is assumed small (of order…

Similar to the notion of h-adaptivity, where the discretization resolution is adaptively changed, I propose the notion of model adaptivity, where the underlying model (the governing equations) is adaptively changed in space and time.…

Models that involve coupled dynamics in a mixed-dimensional geometry are of increasing interest in several applications. Here, we describe the development of a simulation model for flow in fractured porous media, where the fractures and…

It is shown how a complete set of hydrodynamic equations describing an unsteady three-dimensional viscous flow nearby a solid body, can be reduced to a closed system of surface equations using the method of dimension reduction of…

The integral method can be used to model accurately flows down an inclined plane. Such a method consists in projecting the full 3D equations on a lower dimensional representation. The vertical velocity profiles have their functional form…

To understand the process of pattern formation in a low-density granular flow, we propose a simple particle model. This model considers spherical particles moving over an inclined flat surface based on three forces: gravity as the driving…

We derive general depth-integrated model equations for overland flows featuring the evolution of suspended sediment that may be eroded from or deposited onto the underlying topography ('morphodynamics'). The resulting equations include…