Related papers: A structure-preserving scheme for computing effect…
Being able to accurately model and predict the dynamics of dispersed inclusions transported by a turbulent flow, remains a challenge with important scientific, environmental and economical issues. One critical and difficult point is to…
We study the notion of stochastic stability with respect to diffusive perturbations for flows with smooth invariant measures. We investigate the question fully for non-singular flows on the circle. We also show that volume-preserving flows…
Extracting governing physical laws from computational or experimental data is crucial across various fields such as fluid dynamics and plasma physics. Many of those physical laws are dissipative due to fluid viscosity or plasma collisions.…
We propose and analyze a structure-preserving parametric finite element method (SP-PFEM) to simulate the motion of closed curves governed by area-conserved generalized mean curvature flow in two dimensions (2D). We first present a…
We consider coupled models for particulate flows, where the disperse phase is made of particles with distinct sizes. We are thus led to a system coupling the incompressible Navier-Stokes equations to the multi-component Vlasov-Fokker-Planck…
A new energy and enstrophy conserving scheme is evaluated using a suite of test cases over the global spherical domain or bounded domains. The evaluation is organized around a set of pre-defined properties: accuracy of individual opeartors,…
Subsurface flows are commonly modeled by advection-diffusion equations. Insufficient measurements or uncertain material procurement may be accounted for by random coefficients. To represent, for example, transitions in heterogeneous media,…
The stochastic dynamics of colloidal particles with surface activity--in the form of catalytic reaction or particle release--and self-phoretic effects is studied analytically. Three different time scales corresponding to inertial effects,…
In this paper we present a complete framework for the energy-stable simulation of stratified incompressible flow in channels, using the one-dimensional two-fluid model. Building on earlier energy-conserving work on the basic two-fluid…
Turbulent flows posses broadband, power-law spectra in which multiscale interactions couple high-wavenumber fluctuations to large-scale dynamics. Although diffusion-based generative models offer a principled probabilistic forecasting…
We present a more accurate numerical scheme for the calculation of diffusive shock acceleration of cosmic rays using Stochastic Differential Equations. The accuracy of this scheme is demonstrated using a simple analytical flow profile that…
We investigate fluid transport in random velocity fields with unsteady drift. First, we propose to quantify fluid transport between flow regimes of different characteristic motion, by escape probability and mean residence time. We then…
High mesh quality plays a crucial role in maintaining the stability of solutions in geometric flow problems. Duan and Li [Duan & Li, SIAM J. Sci. Comput. 46 (1) (2024) A587-A608] applied the minimal deformation (MD) formulation to propose…
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
In this paper, we introduce and analyze a numerical scheme for solving the Cauchy-Dirichlet problem associated with fractional nonlinear diffusion equations. These equations generalize the porous medium equation and the fast diffusion…
We propose an efficient numerical strategy for simulating fluid flow through porous media with highly oscillatory characteristics. Specifically, we consider non-linear diffusion models. This scheme is based on the classical homogenization…
Infiltration of diffusing particles from one material to another where the diffusion mechanism is either normal or anomalous is a widely observed phenomena. When the diffusion is anomalous we find interesting behaviors: diffusion may lead…
This paper aims at developing a systematic study for the weak rate of convergence of the Euler-Maruyama scheme for stochastic differential equations with very irregular drift and constant diffusion coefficients. We apply our method to…
Recent advances in data-driven modeling have shown that diffusion models can successfully generate synthetic Lagrangian trajectories in turbulent flows. Building on this progress, we extend the method to the joint generation of pairs of…
We prove several properties of the EMCEL scheme, which is capable of approximating one-dimensional continuous strong Markov processes in distribution on the path space (the scheme is briefly recalled). Special cases include irregular…