Related papers: A consistent and conservative volume distribution …
We introduce a family of hybrid discretisations for the numerical approximation of optimal control problems governed by the equations of immiscible displacement in porous media. The proposed schemes are based on mixed and discontinuous…
In this paper, we derive two bound-preserving and mass-conserving schemes based on the fractional-step method and high-order compact (HOC) finite difference method for nonlinear convection-dominated diffusion equations. We split the…
In this paper, we propose high order numerical methods to solve a 2D advection diffusion equation, in the highly oscillatory regime. We use an integrator strategy that allows the construction of arbitrary high-order schemes {leading} to an…
We study in this paper the convergence of the random splitting method for Allen-Cahn equation in a background flow that plays as a simplified model for phase separation in multiphase flows. The model does not own the gradient flow structure…
Phase-transition models are an important family of non-equilibrium continuum traffic flow models, offering properties like replicating complex traffic phenomena, maintaining anisotropy, and promising potentials for accommodating automated…
We present a reduction-consistent and thermodynamically consistent formulation and an associated numerical algorithm for simulating the dynamics of an isothermal mixture consisting of $N$ ($N\geqslant 2$) immiscible incompressible fluids…
In this work, high order asymptotic preserving schemes are constructed and analysed for kinetic equations under a diffusive scaling. The framework enables to consider different cases: the diffusion equation, the advection-diffusion equation…
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 extend the positivity-preserving method of Zhang & Shu (2010, JCP, 229, 3091-3120) to simulate the advection of neutral particles in phase space using curvilinear coordinates. The ability to utilize these coordinates is important for…
Degenerate Cahn-Hilliard phase-field models provide a robust approximation of surface-diffusion-driven interface motion without explicit front tracking. In computations, however, the geometric volume enclosed by the interface -- the region…
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…
The phase-field crystal equation, a parabolic, sixth-order and nonlinear partial differential equation, has generated considerable interest as a possible solution to problems arising in molecular dynamics. This is because the phase-field…
This article provides a reduced-order modelling framework for turbulent compressible flows discretized by the use of finite volume approaches. The basic idea behind this work is the construction of a reduced-order model capable of providing…
In this paper, a fractional step lattice Boltzmann method is proposed to model two-phase flows with large density differences by solving Cahn-Hilliard phase-field equation and the incompressible Navier-Stokes equations.In order to maintain…
This paper presents an algorithm that solves the AC power flow problem for balanced, three-phase transmission systems at steady state. The algorithm extends the "fixed-point power flow" algorithm in the literature to include transmission…
The computation of multiphase flows presents a subtle energetic equilibrium between potential (i.e., surface) and kinetic energies. The use of traditional interface-capturing schemes provides no control over such a dynamic balance. In the…
Geometric flux-based Volume-of-Fluid (VOF) methods are widely considered consistent in handling two-phase flows with high density ratios. However, although the conservation of mass and momentum is consistent for two-phase incompressible…
We are interested in simulating blood flow in arteries with variable elasticity with a one dimensional model. We present a well-balanced finite volume scheme based on the recent developments in shallow water equations context. We thus get a…
We consider conservation laws with discontinuous flux where the initial datum, the flux function, and the discontinuous spatial dependency coefficient are subject to randomness. We establish a notion of random adapted entropy solutions to…
In this paper, a strongly mass conservative and stabilizer free scheme is designed and analyzed for the coupled Brinkman-Darcy flow and transport. The flow equations are discretized by using a strongly mass conservative scheme in mixed…