Related papers: Spline Moment Models for the one-dimensional Boltz…
Multi-species BGK models describe the dynamics of rarefied gases with constituent particles of different elements or compounds with potentially non-trivial velocity distributions. In this paper, moment equations for the bulk velocities,…
We present a further theoretical extension to the kinetic theory based formulation of the lattice Boltzmann method of Shan et al (2006). In addition to the higher order projection of the equilibrium distribution function and a sufficiently…
We propose a hybrid moment method for the multi-scale kinetic equations in the framework of the regularized moment method [7]. In this method, the fourth order moment system is chosen as the governing equations in the fluid region. When…
An original spectral study of the compressible hybrid lattice Boltzmann method (HLBM) on standard lattice is proposed. In this framework, the mass and momentum equations are addressed using the lattice Boltzmann method (LBM), while finite…
Given a stochastic dynamical system modelled via stochastic differential equations (SDEs), we evaluate the safety of the system through characterizations of its exit time moments. We lift the (possibly nonlinear) dynamics into the space of…
The high-order hybridizable discontinuous Galerkin (HDG) method combining with an implicit iterative scheme is used to find the steady-state solution of the Boltzmann equation with full collision integral on two-dimensional triangular…
Shallow water equations (SWE) are fundamental nonlinear hyperbolic PDE-based models in fluid dynamics that are essential for studying a wide range of geophysical and engineering phenomena. Therefore, stable and accurate numerical methods…
A simple stochastic model of solute drag by moving grain boundaries (GBs) is presented. Using a small number of parameters, the model describes solute interactions with GBs and captures nonlinear GB dynamics, solute saturation in the…
The mean-field stochastic partial differential equation (SPDE) corresponding to a mean-field super-Brownian motion (sBm) is obtained and studied. In this mean-field sBm, the branching-particle lifetime is allowed to depend upon the…
We propose a novel Skew Gradient Embedding (SGE) framework for systematically reformulating thermodynamically consistent partial differential equation (PDE) models-capturing both reversible and irreversible processes-as generalized gradient…
In this paper, we discuss the incorporation of dynamic subgrid scale (SGS) models in the lattice-Boltzmann method (LBM) for large-eddy simulation (LES) of turbulent flows. The use of a dynamic procedure, which involves sampling or…
A new kinetic model for multiphase flow was presented under the framework of the discrete Boltzmann method (DBM). Significantly different from the previous DBM, a bottom-up approach was adopted in this model. The effects of molecular size…
In this thesis, we extend the recently introduced theory of stochastic modified equations (SMEs) for stochastic gradient optimization algorithms. In Ch. 3 we study time-inhomogeneous SDEs driven by Brownian motion. For certain SDEs we prove…
Many physical systems are described by probability distributions that evolve in both time and space. Modeling these systems is often challenging to due large state space and analytically intractable or computationally expensive dynamics. To…
We survey a number of moment hierarchies and test their performances in computing one-dimensional shock structures. It is found that for high Mach numbers, the moment hierarchies are either computationally expensive or hard to converge,…
Dense stellar systems such as globular clusters, galactic nuclei and nuclear star clusters are ideal loci to study stellar dynamics due to the very high densities reached, usually a million times higher than in the solar neighborhood; they…
In this paper, we consider the Boltzmann equation with respect to orthonormal vielbein fields in conservative form. This formalism allows the use of arbitrary coordinate systems to describe the space geometry, as well as of an adapted…
This is the third paper in a series in which we develop machine learning (ML) moment closure models for the radiative transfer equation (RTE). In our previous work \cite{huang2021gradient}, we proposed an approach to learn the gradient of…
Prediction of non-equilibrium flows is critical to space flight. In the present work we demonstrate that the recently developed spectral multiple-relaxation-time (SMRT) lattice Boltzmann (LB) model is theoretically equivalent to Grad's…
We present a new deterministic approach for the solution of the Boltzmann kinetic equation based on nodal discontinuous Galerkin (DG) discretizations in velocity space. In the new approach the collision operator has the form of a bilinear…