Related papers: A Bi-fidelity numerical method for velocity discre…
To simulate non-equilibrium compressible flows, a new discrete Boltzmann model, discrete Ellipsoidal Statistical(ES)-BGK model, is proposed. Compared with the original discrete BGK model, the discrete ES-BGK has a flexible Prandtl number.…
We present a robust scheme for solving the electrokinetic equations. This goal is achieved by combining the lattice-Boltzmann method (LB) with a discrete solution of the convection-diffusion equation for the different charged and neutral…
We propose a new approach to discretize the von Neumann equation, which is efficient in the semi-classical limit. This method is first based on the so called Weyl's variables to address the stiffness associated with the equation. Then, by…
This paper presents a data-driven finite volume method for solving 1D and 2D hyperbolic partial differential equations. This work builds upon the prior research incorporating a data-driven finite-difference approximation of smooth solutions…
Lattice Boltzmann Method(LBM) has achieved considerable success on simulating complex flows. However, how to impose correct boundary conditions on the fluid-solid interface with complex geometries is still an open question. Here we proposed…
A simple and efficient one-dimensional discrete Boltzmann method is developed for compressible flows with tunable specific heat ratios by incorporating extra degrees of freedom. To guarantee Galilean invariance in numerical simulations, a…
Efficient and accurate numerical approximation of the full Boltzmann equation has been a longstanding challenging problem in kinetic theory. This is mainly due to the high dimensionality of the problem and the complicated collision…
Several different approaches are proposed for solving fully implicit discretizations of a simplified Boltzmann-Poisson system with a linear relaxation-type collision kernel. This system models the evolution of free electrons in…
We present a free energy lattice Boltzmann model capable of simulating fluid systems with an arbitrary number of immiscible components in principle. Our method is strictly reduction consistent, ensuring that absent fluid components do not…
We propose a control variate multilevel Monte Carlo method for the kinetic BGK model of the Boltzmann equation subject to random inputs. The method combines a multilevel Monte Carlo technique with the computation of the optimal control…
A detailed analysis is presented to demonstrate the capabilities of the lattice Boltzmann method. Thorough comparisons with other numerical solutions for the two-dimensional, driven cavity flow show that the lattice Boltzmann method gives…
In some recent works [G. Dimarco, L. Pareschi, Hybrid multiscale methods I. Hyperbolic Relaxation Problems, Comm. Math. Sci., 1, (2006), pp. 155-177], [G. Dimarco, L. Pareschi, Hybrid multiscale methods II. Kinetic equations, SIAM…
The simulation of geometrically resolved rigid particles in a fluid relies on coupling algorithms to transfer momentum both ways between the particles and the fluid. In this article, the fluid flow is modeled with a parallel Lattice…
This work presents the application of a recently developed parametric, non-intrusive, and multi-fidelity reduced-order modeling method on high-dimensional displacement and stress fields arising from the structural analysis of geometries…
Surrogate modeling for systems with high-dimensional quantities of interest remains challenging, particularly when training data are costly to acquire. This work develops multifidelity methods for multiple-input multiple-output linear…
Two of the most significant challenges in uncertainty quantification pertain to the high computational cost for simulating complex physical models and the high dimension of the random inputs. In applications of practical interest, both of…
We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining…
The lattice Boltzmann equation describes the evolution of the velocity distribution function on a lattice in a manner that macroscopic fluid dynamical behavior is recovered. Although the equation is a derivative of lattice gas automata, it…
We apply the collision-based hybrid introduced in \cite{hauck} to the Boltzmann equation with the BGK operator and a hyperbolic scaling. An implicit treatment of the source term is used to handle stiffness associated with the BGK operator.…
Bilevel optimization (BO) has recently gained prominence in many machine learning applications due to its ability to capture the nested structure inherent in these problems. Recently, many hypergradient methods have been proposed as…