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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 prove an optimal error estimate for the flux variable for a stabilized unfitted Nitsche finite element method applied to an elliptic interface problem with discontinuous constant coefficients. Our result shows explicitly that this error…
High-speed boundary-layer transition is extremely sensitive to the free-stream disturbances which are often uncertain. This uncertainty compromises predictions of models and simulations. To enhance the fidelity of simulations, we directly…
The objective of this contribution is to develop a convergence analysis for SUPG-stabilized Virtual Element Methods in diffusion-convection problems that is robust also in the convection dominated regime. For the original method introduced…
In this work we are interested in dealing with single-phase flows in fractured porous media for underground processes. We focus our attention on domains where the presence of faults, with thickness several orders of magnitude smaller than…
Bubbly flows, as present in bubble column reactors, can be simulated using a variety of simulation techniques. In order to gain high resolution CFD methods are used to simulate a pseudo 2D bubble column using EL and EE techniques. The…
This work describes three diffuse-interface methods for the simulation of immiscible, compressible multiphase fluid flows and elastic-plastic deformation in solids. The first method is the localized-artificial-diffusivity approach of Cook…
We propose an alternative method for one-dimensional continuum diffusion models with spatially variable (heterogeneous) diffusivity. Our method, which extends recent work on stochastic diffusion, assumes the constant-coefficient homogenized…
The focus of the present study is the modified Buckley-Leverett (MBL) equation describing two-phase flow in porous media. The MBL equation differs from the classical Buckley-Leverett (BL) equation by including a balanced…
We consider the a posteriori error estimation for convection-diffusion-reaction equations in both diffusion-dominated and convection/reaction-dominated regimes. We present an explicit hybrid estimator, which, in each regime, is proved to be…
We use existing 3D Discrete Element simulations of simple shear flows of spheres to evaluate the radial distribution function at contact that enables kinetic theory to correctly predict the pressure and the shear stress, for different…
High Froude-number flows become self-aerated when the destabilizing effect of turbulence overcomes gravity and surface tension forces. Traditionally, the resulting air concentration profile has been explained using single-layer approaches…
In this work we present a mass conservative numerical scheme for two-phase flow in porous media. The model for flow consists on two fully coupled, non-linear equations: a degenerate parabolic equation and an elliptic equation. The proposed…
The analysis of the double-diffusion model and $\mathbf{H}(\mathrm{div})$-conforming method introduced in [B\"urger, M\'endez, Ruiz-Baier, SINUM (2019), 57:1318--1343] is extended to the time-dependent case. In addition, the efficiency and…
This paper is concerned with the optimized Schwarz waveform relaxation method and Ventcel transmission conditions for the linear advection-diffusion equation. A mixed formulation is considered in which the flux variable represents both…
This article presents a priori error estimates of the miscible displacement of one incompressible fluid by another through a porous medium characterized by a coupled system of nonlinear elliptic and parabolic equations. The study utilizes…
Shan-Chen model is a numerical scheme to simulate multiphase fluid flows using Lattice Boltzmann approach. The original Shan-Chen model suffers from inability to accurately predict behavior of air bubbles interacting in a non-aqueous fluid.…
Lack of conservation has been the biggest drawback in meshfree generalized finite difference methods (GFDMs). In this paper, we present a novel modification of classical meshfree GFDMs to include local balances which produce an approximate…
We investigate the modes of deformation of an initially spherical bubble immersed in a homogeneous and isotropic turbulent background flow. We perform direct numerical simulations of the two-phase incompressible Navier-Stokes equations,…
In this paper, we employ an finite volume method (FVM) based on the heterogenous multiscale method (HMM), for the multiscale convection-diffusion-reaction problem. The optimal order convergence rate in H^1-norm is given for periodic medias.