Related papers: A two-layer approach for Coupling 1D/2D Shallow Wa…
One dimensional (1D) simulations of the flow and flooding of open channels are known to be inaccurate as the flow is multi-dimensional in nature, especially at the flooded regions. However, multi-dimensional simulations, even in two…
Our goal was to develop a robust algorithm for numerical simulation of one-dimensional shallow-water flow in a complex multiply-connected channel network with arbitrary geometry and variable topography. We apply a central-upwind scheme with…
To simulate the interaction of ocean waves with marine structures, coupling approaches between a potential flow model and a viscous model are investigated. The first model is a fully nonlinear potential flow (FNPF) model based on the…
In this paper, we propose to use the HLL finite volume scheme combined with implicit techniques for modelling the coupled surface and subsurface water flows. In our approach, we used the shallow water equations modelling surface water flow…
There is growing interest in developing mathematical models and appropriate numerical methods for problems involving networks formed by, essentially, one-dimensional (1D) domains joined by junctions. Examples include hyperbolic equations in…
A wide variety of interface capturing methods have been introduced for simulating two-phase flows throughout the years. However, there is a noticeable dearth of literature focusing on objective comparisons between these methods, especially…
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…
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…
Vertical equilibrium models have proven to be well suited for simulating fluid flow in subsurface porous media such as saline aquifers with caprocks. However, in most cases the dimensionally reduced model lacks the accuracy to capture the…
We present a new high-resolution, non-oscillatory semi-discrete central-upwind scheme for one-dimensional two-layer shallow-water flows with friction and entrainment along channels with arbitrary cross sections and bottom topography. These…
Computer simulation is an important tool for scientific progress, especially when lab experiments are either extremely costly and difficult or lack the required resolution. However, all of the simulation methods come with limitations. In…
We consider in this work the numerical resolution of a 2D shallow water system with a Coriolis effect and bottom friction stresses on unstructured meshes by a new Finite Volume Characteristics (FVC) scheme, which has been introduced in the…
We develop a framework for constructing mixed multiscale finite volume methods for elliptic equations with multiple scales arising from flows in porous media. Some of the methods developed using the framework are already known…
Analysing two-dimensional shallow water equations with idealised bottom topographies have many applications in the atmospheric and oceanic sciences; however, restrictive flow pattern assumptions have been made to achieve explicit solutions.…
This paper proposes a comparison of four popular interface capturing methods : the volume of fluid (VOF), the standard level set (SLS), the accurate conservative level set (ACLS) and the coupled level set and volume of fluid (CLSVOF). All…
We present an hybrid VOF/embedded boundary method allowing to model two-phase flows in presence of solids with arbitrary shapes. The method relies on the coupling of existing methods: a geometric Volume of fluid (VOF) method to tackle the…
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…
This paper presents a finite volume method for simulating two-phase flows using a level set approach coupled with volume of fluid method capable of simulating sharp fluid interfaces. The efficiency of the method is a result of the fact that…
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.…
In a companion study \cite{patterson2020computing2D}, we present a numerical method for simulating 2D viscous flow through an open compliant closed channel, drive by pressure gradient. We consider the highly viscous regime, where fluid…