Related papers: Temporal-Stability-Enhanced and Energy-Stable Dyna…

Time-dependent kinetic models are ubiquitous in computational science and engineering. The underlying integro-differential equations in these models are high-dimensional, comprised of a six--dimensional phase space, making simulations of…

Low-rank methods for kinetic equations have attracted increasing attention due to their effectiveness in reducing the high dimensionality of phase space. In our previous work [G. Wang & J. Hu, J. Comput. Phys. 558 (2026) 114884], we…

We present an explicit scheme for a two-dimensional multilayer shallow water model with density stratification, for general meshes and collocated variables. The proposed strategy is based on a regularized model where the transport velocity…

Kinetic equations model distributions of particles in position-velocity phase space. Often, one is interested in studying the long-time behavior of particles in high-collisional regimes in which an approximate (advection)-diffusion model…

In this paper we classify the pathwise asymptotic behaviour of the discretisation of a general autonomous scalar differential equation which has a unique and globally stable equilibrium. The underlying continuous equation is subjected to a…

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…

Low-rank approximation is a technique to approximate a tensor or a matrix with a reduced rank to reduce the memory required and computational cost for simulation. Its broad applications include dimension reduction, signal processing,…

We consider a Lattice Boltzmann type discrete velocity model in the low Mach number scaling and develop a corresponding numerical scheme that remains uniformly valid across all regimes of the mean free path, from the kinetic to the…

We consider the development of high order asymptotic-preserving linear multistep methods for kinetic equations and related problems. The methods are first developed for BGK-like kinetic models and then extended to the case of the full…

We propose and analyze a linearly stabilized semi-implicit diffusive Crank--Nicolson scheme for the Cahn--Hilliard gradient flow. In this scheme, the nonlinear bulk force is treated explicitly with two second-order stabilization terms. This…

We consider kinetic systems and prove their stability working in weighted spaces in which the systems are symmetric. We prove stability for various explicit and implicit semi-discrete and fully discrete schemes. The applications include…

Kinetic transport models are mesoscopic mathematical descriptions of the transport of particles as well as their interactions with the background media or among themselves, and they have wide applications in many areas of mathematical…

In this paper, we analyze the preservation of asymptotic properties of partially dissipative hyperbolic systems when switching to a discrete setting. We prove that one of the simplest consistent and unconditionally stable numerical methods…

The dynamical low-rank (DLR) approximation is an efficient technique to approximate the solution to matrix differential equations. Recently, the DLR method was applied to radiation transport calculations to reduce memory requirements and…

Computational methods for thermal radiative transfer problems exhibit high computational costs and a prohibitive memory footprint when the spatial and directional domains are finely resolved. A strategy to reduce such computational costs is…

In this paper, a physics-oriented stochastic kinetic scheme will be developed that includes random inputs from both flow and electromagnetic fields via a hybridization of stochastic Galerkin and collocation methods. Based on the BGK-type…

In this article, we are interested in the asymptotic analysis of a finite volume scheme for one dimensional linear kinetic equations, with either Fokker-Planck or linearized BGK collision operator. Thanks to appropriate uniform estimates,…

In this work, we propose a Crank-Nicolson-type scheme with variable steps for the time fractional Allen-Cahn equation. The proposed scheme is shown to be unconditionally stable (in a variational energy sense), and is maximum bound…

In kinetic theory, numerically solving the full Boltzmann equation is extremely expensive. This is because the Boltzmann collision operator involves a high-dimensional, nonlinear integral that must be evaluated at each spatial grid point…

We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…