Related papers: Hypocoercivity and diffusion limit of a finite vol…
This paper focusses on finite volume schemes for solving multilayer diffusion problems. We develop a finite volume method that addresses a deficiency of recently proposed finite volume/difference methods, which consider only a limited…
In this article, we design a fully spectral method in both space and velocity for a linear inhomogeneous kinetic equation with mass, momentum and energy conservation. We focus on the linear BGK equation with a confinement potential $\Phi$,…
This paper investigates the diffusion limit of a kinetic BGK-type equation, focusing on its relaxation to a nonlinear aggregation-diffusion equation, where the diffusion exhibits a porous-medium-type nonlinearity. Unlike previous studies by…
A finite volume scheme for the (Patlak-) Keller-Segel model in two space dimensions with an additional cross-diffusion term in the elliptic equation for the chemical signal is analyzed. The main feature of the model is that there exists a…
This paper presents a hybrid numerical method for linear collisional kinetic equations with diffusive scaling. The aim of the method is to reduce the computational cost of kinetic equations by taking advantage of the lower dimensionality of…
The Active Flux (AF) method is a compact, high-order finite volume scheme that enhances flexibility by introducing point values at cell interfaces as additional degrees of freedom alongside cell averages. The method of lines is employed…
We introduce some approximation schemes for linear and fully non-linear diffusion equations of Bellman-Isaacs type. Although they are not monotone one can prove their convergence to the viscosity solution of the problem. Effective…
We develop and study an asymptotic-preserving (AP) numerical scheme for a linear kinetic equation in a large deviation regime. After applying a Hopf-Cole transform to the distribution function, the system exhibits the behavior of rare…
The continuum description of active particle systems is an efficient instrument to analyze a finite size particle dynamics in the limit of a large number of particles. However, it is often the case that such equations appear as nonlinear…
In the present work, the Eulerian Large Eddy Simulation of dilute disperse phase flows is investigated. By highlighting the main advantages and drawbacks of the available approaches in the literature, a choice is made in terms of modelling:…
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…
A novel hybrid computational method based on the discrete-velocity (DV) approximation, including the lattice-Boltzmann (LB) technique, is proposed. Numerical schemes for the kinetic equations are used in regions of rarefied flows, and LB…
For linear transport and radiative heat transfer equations with random inputs, we develop new generalized polynomial chaos based Asymptotic-Preserving stochastic Galerkin schemes that allow efficient computation for the problems that…
A model of progression of Alzheimer's disease (AD) incorporating the interactions of A$\beta$-monomers, oligomers, microglial cells and interleukins with neurons is considered. The resulting convection-diffusion-reaction system consists of…
In this work we consider an extension of a recently proposed structure preserving numerical scheme for nonlinear Fokker-Planck-type equations to the case of nonconstant full diffusion matrices. While in existing works the schemes are…
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…
We develop an unconditionally energy-stable tensor-product space-time discretization framework for the solution of a linear kinetic transport equation in one space dimension. The kinetic equation is a simplified model of radiative transfer…
A form of the conservation equations for fluid dynamics is presented, deduced using slightly less restrictive hypothesis than those necessary to obtain the Westervelt equation. This formulation accounts for full wave diffraction,…
We establish a uniform-in-scaling error estimate for the asymptotic preserving scheme proposed in \cite{XW21} for the L\'evy-Fokker-Planck (LFP) equation. The main difficulties stem from not only the interplay between the scaling and…
In this paper, we propose a discretization for the (nonlinearized) compressible Stokes problem with a linear equation of state $\rho=p$, based on Crouzeix-Raviart elements. The approximation of the momentum balance is obtained by usual…