相关论文: A boundary matching micro/macro decomposition for …
We investigate the fractional diffusion approximation of a kinetic equation set in a bounded interval with diffusive reflection conditions at the boundary. In an appropriate singular limit corresponding to small Knudsen number and long time…
An accurate algorithm is proposed to improve the prediction of a particle in collision with a moving wall within the direct simulation Monte Carlo (DSMC) framework for the simulation of unsteady rarefied flows. This algorithm is able to…
In this paper, we prove the existence and uniqueness of the Knudsen layer equation imposed on Maxwell reflection boundary condition with full ranges of cutoff collision kernels and accommodation coefficients (i.e., $- 3 < \gamma \leq 1$ and…
We present the asymptotic transitions from microscopic to macroscopic physics, their computational challenges and the Asymptotic-Preserving (AP) strategies to efficiently compute multiscale physical problems. Specifically, we will first…
In this work we first prove, by formal arguments, that the diffusion limit of nonlinear kinetic equations, where both the transport term and the turning operator are density-dependent, leads to volume-exclusion chemotactic equations. We…
The behavior of active matter under confinement poses significant challenges due to the intricate coupling between dynamics near boundaries and those in the bulk. A defining feature of active matter systems is that a substantial portion of…
This work proposes a novel variational approximation of partial differential equations on moving geometries determined by explicit boundary representations. The benefits of the proposed formulation are the ability to handle large…
Stable computational algorithms for the approximate solution of the Cauchy problem for nonstationary problems are based on implicit time approximations. Computational costs for boundary value problems for systems of coupled multidimensional…
A new framework is introduced for constructing interpretable and truly reliable reduced models for multiscale problems in situations without scale separation. Hydrodynamic approximation to the kinetic equation is used as an example to…
We study, globaly in time, the velocity distribution $f(v,t)$ of a spatially homogeneous system that models a system of electrons in a weakly ionized plasma, subjected to a constant external electric field $E$. The density $f$ satisfies a…
We use the mesoscopic nonequilibrium thermodynamics theory to derive the general kinetic equation of a system in the presence of potential barriers. The result is applied to the description of the evolution of systems whose dynamics is…
The kinetic Boltzmann equation models gas dynamics over a wide range of spatial and temporal scales. Simplified versions of the full Boltzmann collision operator, such as the classical Bhatnagar-Gross-Krook and the closely related…
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 aim of this paper is to propose a novel methodology to deal with micro-structural boundary conditions for the analysis of granular materials. The response of the granular assembly is modelled through the discrete element method (DEM),…
We study overdamped stochastic dynamics confined by hard reflecting boundaries and show that the combination of boundary geometry and an anisotropic diffusion tensor generically generates directed motion. At the level of individual…
We present a novel solution procedure for initial boundary value problems. The procedure is based on an action principle, in which coordinate maps are included as dynamical degrees of freedom. This reparametrization invariant action is…
Kinetic equations model the position-velocity distribution of particles subject to transport and collision effects. Under a diffusive scaling, these combined effects converge to a diffusion equation for the position density in the limit of…
In this note, we demonstrated for the first time that one can derive an expression for the effective diffusion coefficient, equal to the Lifson-Jackson formula, using a subsequent homogenization of the 1D reaction-diffusion-advection…
We demonstrate that a nonthermal distribution of particles described by a kappa distribution can be accurately approximated by a weighted sum of Maxwell-Boltzmann distributions. We apply this method to modeling collision processes in…
In our previous work [29], we proposed a class of high-order asymptotic preserving (AP) finite difference weighted essentially non-oscillatory (WENO) schemes for solving the shallow water equations (SWEs) with bottom topography and Manning…