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A low-Mach-number flow, in the laminar regime, has intrinsically two characteristic spatial scales for a given time scale, or two characteristic temporal scales for a given spatial scale, and these dual scales are very different due to the…
A comprehensive scheme for the spatial discretisation of continuity equation, momentum advection and normal and shear stresses at the fluid interfaces is presented for numerically simulating the incompressible two phase flows based on the…
A hydrogeological model for the spread of pollution in an aquifer is considered. The model consists in a convection-diffusion-reaction equation involving the dispersion tensor which depends nonlinearly of the fluid velocity. We introduce an…
In this study, we focus on the modelling of coupled systems of shallow water flows and solute transport with source terms due to variable topography and friction effect. Our aim is to propose efficient and accurate numerical techniques for…
This work theoretically analyzes the sound absorption properties of a chirped multi-layer porous material including transmission, in particular showing the broadband unidirectional absorption properties of the system. Using the combination…
In this paper we propose and analyse a new formulation and pointwise divergence-free mixed finite element methods for the numerical approximation of Darcy--Brinkman equations in vorticity--velocity--pressure form, coupled with a transport…
The study of flow in fractured porous media is a key ingredient for many geoscience applications, such as reservoir management and geothermal energy production. Modelling and simulation of these highly heterogeneous and geometrically…
We propose a model for increasing liquid saturation in a granular packing which can account for liquid redistribution at saturation levels beyond the well-studied capillary bridge regime. The model is capable of resolving and combining…
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…
The paper develops a hybrid method for solving a system of advection--diffusion equations in a bulk domain coupled to advection--diffusion equations on an embedded surface. A monotone nonlinear finite volume method for equations posed in…
Evaporating droplets and films are used in applications from different fields. Various methods of evaporative self-assembly are of particular interest. The paper describes a mathematical model of mass transfer in a droplet drying on a…
We propose two closely--related Lagrangian numerical methods for the simulation of physical processes involving advection, reaction and diffusion. The methods are intended to be used in settings where the flow is nearly incompressible and…
Insoluble surfactants adsorbed at liquid-liquid or gas-liquid interfaces alter interfacial tension, leading to variations in the normal stress jump and generating tangential Marangoni stresses that can dramatically affect the flow dynamics.…
We consider surface finite elements and a semi-implicit time stepping scheme to simulate fluid deformable surfaces. Such surfaces are modeled by incompressible surface Navier-Stokes equations with bending forces. Here, we consider closed…
Detailed understanding of the coupling between fluid flow and solid deformation in porous media is crucial for the development biomedical devices and novel energy technologies relating to a wide range of geological and biological processes.…
We use a concept of weak asymptotic solution for homogeneous as well as non-homogeneous fractional advection dispersion type equations. Using Legendre scaling functions as basis, a numerical method based on Galerkin approximation is…
We study low-speed flows of a highly compressible, single-phase fluid in the presence of gravity, for example in a regime appropriate for modeling recent space-shuttle experiments on fluids near the liquid-vapor critical point. In the…
Sampling a target probability distribution with an unknown normalization constant is a fundamental challenge in computational science and engineering. Recent work shows that algorithms derived by considering gradient flows in the space of…
We provide a numerical algorithm for the model characterizing anomalous diffusion in expanding media, which is derived in [F. Le Vot, E. Abad, and S. B. Yuste, Phys. Rev. E {\bf96} (2017) 032117]. The Sobolev regularity for the equation is…
We study the time-dependent flow behavior of gravity-driven free surface granular flows using the discrete element method and continuum modeling. Discrete element method (DEM) simulations of slightly polydisperse disks flowing over a…