Related papers: Accurate numerical simulation of moisture front in…
In this study, a novel semi-implicit second-order temporal scheme combined with the finite element method for space discretization is proposed to solve the coupled system of infiltration and solute transport in unsaturated porous media. The…
A fractional diffusion equation with advection term is rigorously derived from a kinetic transport model with a linear turning operator, featuring a fat-tailed equilibrium distribution and a small directional bias due to a given vector…
In this paper, we propose and analyze a numerically stable and convergent scheme for a convection-diffusion-reaction equation in the convection-dominated regime. Discontinuous Galerkin (DG) methods are considered since standard finite…
Convection heat transfer in porous media is a universal phenomenon in nature, and it is also frequently encountered in scientific and engineering fields. An in-depth understanding of the fundamental mechanism of convection heat transfer in…
The objective of this study is to better understand the influence of fractures on the possibility of free convection in porous media. To this aim, we introduce a mathematical model for density driven flow in the presence of fractures, and…
We present a numerical formulation for the solution of non-isothermal, compressible, Navier-Stokes equations with thermal fluctuations to describe mesoscale transport phenomena in multispecies fluid mixtures. The novelty of our numerical…
Results of direct numerical simulations (DNS) of porous-wall turbulent flows in open channels with conjugate heat transfer are reported in this work. For the conductive porous walls considered here, the change in heat transfer is not…
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…
We propose a nonlinear Discrete Duality Finite Volume scheme to approximate the solutions of drift diffusion equations. The scheme is built to preserve at the discrete level even on severely distorted meshes the energy / energy dissipation…
We construct, analyse and assess various schemes of second order of accuracy in space and time for model advection-diffusion-reaction differential equations. The constructed schemes are meant to be of practical use in solving industrial…
In this study, we investigate the Shallow Water Equations incorporating source terms accounting for Manning friction and a non-flat bottom topology. Our primary focus is on developing and validating numerical schemes that serve a dual…
We present an exact mathematical transformation which converts a wide class of advection-diffusion equations into a form allowing simple and direct spatial discretization in all dimensions, and thus the construction of accurate and more…
Fluid flow and convective heat transfer in rotor-stator configurations, which are of great importance in different engineering applications, are treated in details in this review. The review focuses on convective heat transfer in…
In this paper, an algorithm is presented to calculate the transition rates between adjacent mesoscopic subvolumes in the presence of flow and diffusion. These rates can be integrated in stochastic simulations of reaction-diffusion systems…
We study the homogenization of a steady diffusion equation in a highly heterogeneous medium made of two subregions separated by a periodic barrier through which the flow is proportional to the jump of the temperature by a layer conductance…
Spatial discretisation of geometrically complex computational domains often entails unstructured meshes of general topology for Computational Fluid Dynamics (CFD). Mesh skewness is then typically encountered causing severe deterioration of…
We consider an initial-boundary value problem motivated by a mathematical model of moisture transport in porous media. We establish the existence of strong solutions and provide an error estimate for the approximate solutions constructed by…
Atmospheric water vapour is an essential ingredient of weather and climate. Key features of its distribution can be represented by kinematic models which treat it as a passive scalar advected by a prescribed flow and reacting through…
This note introduces a simple metric for benchmarking shock-capturing schemes. This metric is especially focused on the shock-capturing overshoots, which may undermine the robustness of numerical simulations, as well as the reliability of…
We perform direct numerical simulations (DNS) of a turbulent channel flow over porous walls. In the fluid region the flow is governed by the incompressible Navier--Stokes (NS) equations, while in the porous layers the Volume-Averaged…