相关论文: A Bi-fidelity numerical method for velocity discre…
In this paper, we study the multiscale Boltzmann equation with multi-dimensional random parameters by a bi-fidelity stochastic collocation (SC) method developed in [A. Narayan, C. Gittelson and D. Xiu, SIAM J. Sci. Comput., 36 (2014); X.…
In this paper, we consider the development of efficient numerical methods for linear transport equations with random parameters and under the diffusive scaling. We extend to the present case the bi-fidelity stochastic collocation method…
In this paper, we conduct uniform error estimates of the bi-fidelity method for multi-scale kinetic equations. We take the Boltzmann and the linear transport equations as important examples. The main analytic tool is the hypocoercivity…
This paper introduces a Bi-fidelity Asymptotic-Preserving Neural Network (BI-APNNs) framework, designed to efficiently solve forward and inverse problems for the semiconductor Boltzmann equation. Our approach builds upon the…
A deterministic method is proposed for solving the Boltzmann equation. The method employs a Galerkin discretization of the velocity space and adopts, as trial and test functions, the collocation basis functions based on weights and roots of…
We propose an entropic Fourier method for the numerical discretization of the Boltzmann collision operator. The method, which is obtained by modifying a Fourier Galerkin method to match the form of the discrete velocity method, can be…
In this paper we present a numerical method for the Boltzmann equation. It is a spectral discretization in the velocity and a discontinuous Galerkin discretization in physical space. To obtain uniform approximation properties in the mach…
The construction of efficient methods for uncertainty quantification in kinetic equations represents a challenge due to the high dimensionality of the models: often the computational costs involved become prohibitive. On the other hand,…
We point out an equivalence between the discrete velocity method of solving the Boltzmann equation, of which the lattice Boltzmann equation method is a special example, and the approximations to the Boltzmann equation by a Hermite…
In traffic flow modeling, incorporating uncertainty is crucial for accurately capturing the complexities of real-world scenarios. In this work we focus on kinetic models of traffic flow, where a key step is to design effective numerical…
We present an efficient nodal discontinuous Galerkin method for approximating nearly incompressible flows using the Boltzmann equations. The equations are discretized with Hermite polynomials in velocity space yielding a first order…
The discretization of velocity space plays a crucial role in the accuracy and efficiency of multiscale Boltzmann solvers. Conventional velocity space discretization methods suffer from uneven node distribution and mismatch issues, limiting…
We propose a new second-order accurate lattice Boltzmann scheme that solves the quasi-static equations of linear elasticity in two dimensions. In contrast to previous works, our formulation solves for a single distribution function with a…
The Lattice Boltzmann Method (LBM) has emerged as a powerful tool in computational fluid dynamics and material science. However, standard LBM formulation imposes some limitations on the applications of the method, particularly compressible…
In this work, we propose and compare several approaches to solve the Boltzmann equation with uncertain parameters, including multi-level Monte Carlo and multi-fidelity methods that employ an asymptotic-preserving-hybrid (APH) scheme (Filbet…
The Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation allows for efficient flow simulations, especially in the transition regime between continuum and high rarefaction. However, ensuring efficient performances for multiscale…
A hybrid lattice Boltzmann method (LBM) for binary mixtures based on the free-energy approach is proposed. Non-ideal terms of the pressure tensor are included as a body force in the LBM kinetic equations, used to simulate the continuity and…
Kinetic or Boltzmann schemes are interesting alternatives to the macroscopic numerical methods for solving the hyperbolic conservation laws of gas dynamics. They utilize the particle-based description instead of the wave propagation models.…
In this paper, we first extend the micro-macro decomposition method for multiscale kinetic equations from the BGK model to general collisional kinetic equations, including the Boltzmann and the Fokker-Planck Landau equations. The main idea…
A type of discrete Boltzmann model for simulating shallow water flows is derived by using the Hermite expansion approach. Through analytical analysis, we study the impact of truncating distribution function and discretizing particle…