相关论文: Bernaise: A flexible framework for simulating two-…
We present a space-time continuous-Galerkin finite element method for solving incompressible Navier-Stokes equations. To ensure stability of the discrete variational problem, we apply ideas from the variational multi-scale method. The…
Fine-scale simulation of complex systems governed by multiscale partial differential equations (PDEs) is computationally expensive and various multiscale methods have been developed for addressing such problems. In addition, it is…
In this paper we present a technique for constructing robust solvers for stiff algebraic source terms, such as those typically used for modelling relaxation processes in hyperbolic systems of partial differential equations describing…
In this work, we present a parametric finite element approximation of two-phase Navier-Stokes flow with viscoelasticity. The free boundary problem is given by the viscoelastic Navier-Stokes equations in the two fluid phases, connected by…
The flow of incompressible fluids through porous media plays a crucial role in many technological applications such as enhanced oil recovery and geological carbon-dioxide sequestration. The flow within numerous natural and synthetic porous…
This paper focuses on the numerical simulation of geothermal systems in complex geological settings. The physical model is based on two-phase Darcy flows coupling the mass conservation of the water component with the energy conservation and…
In multiscale, multi-physics applications, there is an increasing need for coupling numerical solvers that are each applied to a different part of the problem. Here we consider the case of coupling a Lattice Boltzmann fluid model and a…
This paper presents a robust, adaptive numerical scheme for simulating high density ratio and high shear multiphase flows on locally refined Cartesian grids that adapt to the evolving interfaces and track regions of high vorticity. The…
We consider a thermodynamically consistent diffuse interface model describing two-phase flows of incompressible fluids in a non-isothermal setting. This model was recently introduced in a previous paper of ours, where we proved existence of…
We propose a two-scale finite element method designed for heterogeneous microstructures. Our approach exploits domain diffeomorphisms between the microscopic structures to gain computational efficiency. By using a conveniently constructed…
Numerous codes are being developed to solve Shallow Water equations. Because they are used in hydraulics and environmental studies, their capability to simulate properly flow dynamics is essential to guarantee infrastructure and human…
In this paper, we develop a framework for solving inverse deformation problems using the FEniCS Project finite element software. We validate our approach with experimental imaging data acquired from a soft silicone beam under gravity. In…
The lattice Boltzmann method, now widely used for a variety of applications, has also been extended to model multi-phase flows through different formulations. While already applied to many different configurations in the low Weber and…
The present document corresponds to the 4 th chapter of my thesis, the problem setting is not definitive, what matters most here are the mathematical results and the methodology of the existence proofs. In this work, we propose a framework…
We report on recent extensions and improvements to the Legolas code, which is an open-source, finite element-based numerical framework to solve the linearised (magneto)hydrodynamic equations for a three-dimensional force- and thermally…
We present a fully-coupled, implicit-in-time framework for solving a thermodynamically-consistent Cahn-Hilliard Navier-Stokes system that models two-phase flows. In this work, we extend the block iterative method presented in Khanwale et…
Numerical simulations of two-phase flow and fluid structure interaction problems are of great interest in many environmental problems and engineering applications. To capture the complex physical processes involved in these problems, a high…
The governing equations and numerical solution strategy to solve porohyperelastic problems as multiscale multiphysics media are provided in this contribution. The problem starts from formulating and non-dimensionalising a Fluid-Solid…
In this work, we aim to develop a phase-field based lattice Boltzmann (LB) method for simulating two-phase electrohydrodynamics (EHD) flows, which allows for different properties (densities, viscosities, conductivity and permittivity) of…
We consider the numerical approximation of a sharp-interface model for two-phase flow, which is given by the incompressible Navier-Stokes equations in the bulk domain together with the classical interface conditions on the interface. We…