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The aim of this study is to compare numerical methods for the simulation of single-phase flow and transport in fractured media, described here by means of the Discrete Fracture Network (DFN) model. A Darcy problem is solved to compute the…
Implicit time-stepping for advection is applied locally in space and time where Courant numbers are large, but standard explicit time-stepping is used for the remaining solution which is typically the majority. This adaptively implicit…
Thermal flows characterized by high Prandtl number are numerically challenging as the transfer of momentum and heat occurs at different time scales. To account for very low thermal conductivity and obey the Courant-Friedrichs-Lewy…
In the present work, we propose an advection-diffusion equation with Hausdorff deformed derivatives to stud the turbulent diffusion of contaminants in the atmosphere. We compare the performance of our model to fit experimental data against…
Subsurface flows are commonly modeled by advection-diffusion equations. Insufficient measurements or uncertain material procurement may be accounted for by random coefficients. To represent, for example, transitions in heterogeneous media,…
We propose an efficient numerical strategy for simulating fluid flow through porous media with highly oscillatory characteristics. Specifically, we consider non-linear diffusion models. This scheme is based on the classical homogenization…
We have developed a new, very efficient numerical scheme to solve the CR diffusion convection equation that can be applied to the study of the nonlinear time evolution of CR modified shocks for arbitrary spatial diffusion properties. The…
In this paper we propose a numerical method to solve a 2D advection-diffusion equation, in the highly oscillatory regime. We use an efficient and robust integrator which leads to an accurate approximation of the solution without any time…
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…
Mineral precipitation and dissolution processes in a porous medium can alter the structure of the medium at the scale of pores. Such changes make numerical simulations a challenging task as the geometry of the pores changes in time in an…
This paper discusses the convective heat transfer enhancement of non-condensing slug flows by using phase separation for local liquid circulations through a porous-tube insert. Numerical simulations were carried out to study the air-water…
This article performs a unified convergence analysis of a variety of numerical methods for a model of the miscible displacement of one incompressible fluid by another through a porous medium. The unified analysis is enabled through the…
We investigate two common numerical techniques for integrating reversible moist processes in atmospheric flows in the context of solving the fully compressible Euler equations. The first is a one-step, coupled technique based on using…
The dispersion of solute in porous media shows a non-linear increase in the transition from diffusion to advection dominated dispersion as the flow velocity is raised. In the past, the behavior in this intermediate regime has been explained…
The objective for this work is to develop a data-driven proxy to high-fidelity numerical flow simulations using digital images. The proposed model can capture the flow field and permeability in a large verity of digital porous media based…
In this study, two initial boundary value problems for one dimensional advection-dispersion equation are solved by differential quadrature method based on sine cardinal functions. Pure advection problem modeling transport of conservative…
Long simulation times in climate sciences typically require coarse grids due to computational constraints. Nonetheless, unresolved subscale information significantly influences the prognostic variables and can not be neglected for reliable…
This article presents a new finite element method for convection-diffusion equations by enhancing the continuous finite element space with a flux space for flux approximations that preserve the important mass conservation locally on each…
Implicit schemes require important sub-iterations when dealing with highly nonlinear problems such as the combined heat and moisture transfer through porous building elements. The computational cost rises significantly when the…
Seismic imaging of the mantle has revealed large and small scale heterogeneities in the lower mantle; specifically structures known as large low shear velocity provinces (LLSVP) below Africa and the South Pacific. Most interpretations…