Related papers: A linear, mass-conserving, multi-time-step compact…
In this article we study the numerical approximation of incompressible miscible displacement problems with a linearised Crank-Nicolson time discretisation, combined with a mixed finite element and discontinuous Galerkin method. At the heart…
This paper presents a novel mass-conservative mixed multiscale method for solving flow equations in heterogeneous porous media. The media properties (the permeability) contain multiple scales and high contrast. The proposed method solves…
Accurate numerical simulations of interaction between fluid and solid play an important role in applications. The task is challenging in practical scenarios as the media are usually highly heterogeneous with very large contrast. To overcome…
In this work, fourth-order compact block-centered finite difference (CBCFD) schemes combined with the Crank-Nicolson discretization are constructed and analyzed for solving parabolic integro-differential type non-Fickian flows in…
A classical model for water-gas flows in porous media is considered. The degenerate coupled system of equations obtained by mass conservation is usually approximated by finite volume schemes in the oil reservoir simulations. The convergence…
We introduce a second-order numerical scheme for compressible atmospheric motions at small to planetary scales. The collocated finite volume method treats the advection of mass, momentum, and mass-weighted potential temperature in…
This paper is concerned with moving mesh finite difference solution of partial differential equations. It is known that mesh movement introduces an extra convection term and its numerical treatment has a significant impact on the stability…
The paper deals with homogenization of a model problem describing an immiscible compressible two-phase flow in random statistically homogeneous porous media. We derive the effective (macroscopic) problem and prove the convergence of…
The multiphase flow mechanism in miscible displacement through porous media is an important topic in various applications, such as petroleum engineering, low Reynolds number suspension flows, dusty gas dynamics, and fluidized beds. To…
Miscible multiphase flow in porous media is a key phenomenon in various industrial and natural processes, such as hydrogen storage and geological carbon sequestration. However, the parameters controlling the patterns of displacement and…
In this article, we have developed a higher order compact numerical method for variable coefficient parabolic problems with mixed derivatives. The finite difference scheme, presented here for two-dimensional domains, is based on fourth…
We present a novel asymptotic-preserving semi-implicit finite element method for weakly compressible and incompressible flows based on compatible finite element spaces. The momentum is sought in an $H(\mathrm{div})$-conforming space,…
An adaptive moving mesh finite difference method is presented to solve two types of equations with dynamic capillary pressure term in porous media. One is the non-equilibrium Richards Equation and the other is the modified Buckley-Leverett…
In order to prevent velocity, pressure, and temperature spikes at material discontinuities occurring when the interface-capturing schemes inconsistently simulate compressible multi-material flows(when the specific heats ratio is…
In this paper, uniformly unconditionally stable first and second order finite difference schemes are developed for kinetic transport equations in the diffusive scaling. We first derive an approximate evolution equation for the macroscopic…
Immiscible fluid displacement in porous media occurs in several natural and industrial processes. For example, during petroleum extraction from porous rock reservoirs, water is used to displace oil. In this paper, we investigate primary…
This paper is concerned with a space-time adaptive numerical method for instationary porous media flows with nonlinear interaction between porosity and pressure, with focus on problems with discontinuous initial porosities. A convergent…
In this paper, we propose a multicontinuum homogenization approach for nonlinear problems involving dynamically evolving multiscale media. The main idea of the proposed approach is that one of the fine-scale variables defines continua. It…
The non-modal linear stability of miscible viscous fingering in a two dimensional homogeneous porous medium has been investigated. The linearized perturbed equations for Darcy's law coupled with a convection-diffusion equation is…
In the present contribution, we construct a virtual element (VE) discretization for the problem of miscible displacement of one incompressible fluid by another, described by a time-dependent coupled system of nonlinear partial differential…