Numerical Regularized Moment Method of Arbitrary Order for Boltzmann-BGK Equation
Zhenning Cai,Ruo Li +1 more
TLDR
A conservative projection operator is defined and a fast implementation is proposed, which makes it convenient to add up two distributions and provides more efficient flux calculations compared with the classic method using explicit expressions of flux functions.Abstract:
We introduce a numerical method for solving Grad's moment equations or regularized moment equations for an arbitrary order of moments. In our algorithm, we do not explicitly need the moment equations. Instead, we directly start from the Boltzmann equation and perform Grad's moment method [H. Grad, Commun. Pure Appl. Math., 2 (1949), pp. 331-407] and the regularization technique [H. Struchtrup and M. Torrilhon, Phys. Fluids, 15 (2003), pp. 2668-2680] numerically. We define a conservative projection operator and propose a fast implementation, which makes it convenient to add up two distributions and provides more efficient flux calculations compared with the classic method using explicit expressions of flux functions. For the collision term, the BGK model is adopted so that the production step can be done trivially based on the Hermite expansion. Extensive numerical examples for one- and two-dimensional problems are presented. Convergence in moments can be validated by the numerical results for different numbers of moments.read more
Citations
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Modeling Nonequilibrium Gas Flow Based on Moment Equations
TL;DR: In this article, the development of continuum models to describe processes in gases in which the particle collisions cannot maintain thermal equilibrium is discussed, and typical results are reviewed for channel flow, cavity flow, and flow past a sphere in the low-Mach number setting for which both evolution equations and boundary conditions are well established.
Journal ArticleDOI
Globally Hyperbolic Regularization of Grad's Moment System
Zhenning Cai,Yuwei Fan,Ruo Li +2 more
TL;DR: In this article, a globally hyperbolic regularization to the general Grad's moment system in multidimensional spaces is proposed, which is consistent with the simple one-dimensional case discussed in 1.
Journal ArticleDOI
Globally Hyperbolic Regularization of Grad's Moment System in One Dimensional Space
Zhenning Cai,Yuwei Fan,Ruo Li +2 more
TL;DR: In this paper, a regularization of 1D Grad's moment system is proposed based on the observation that the characteristic polynomial of the Jacobian of the flux in the system is independent of the intermediate moments.
Journal ArticleDOI
Uniformly accurate machine learning-based hydrodynamic models for kinetic equations.
TL;DR: In this article, a framework is introduced for constructing interpretable and reliable reduced models for multiscale problems in situations without scale separation, and the reduced system takes the form of a conventional moment system and works regardless of the numerical discretization used.
Journal ArticleDOI
A Framework on Moment Model Reduction for Kinetic Equation
Zhenning Cai,Yuwei Fan,Ruo Li +2 more
TL;DR: A uniform framework for the derivation of reduced models from general kinetic equations for the Boltzmann equation is proposed and the resulting model appears as a symmetric hyperbolic moment system.
References
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A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems
TL;DR: In this paper, a kinetic theory approach to collision processes in ionized and neutral gases is presented, which is adequate for the unified treatment of the dynamic properties of gases over a continuous range of pressures from the Knudsen limit to the high pressure limit where the aerodynamic equations are valid.
Small amplitude processes in charged and neutral one-component systems
TL;DR: In this article, a kinetic theory approach to collision processes in ionized and neutral gases is presented, which is adequate for the unified treatment of the dynamic properties of gases over a continuous range of pressures from the Knudsen limit to the high pressure limit where the aerodynamic equations are valid.
Book
Riemann Solvers and Numerical Methods for Fluid Dynamics
TL;DR: In this article, the authors present references and index Reference Record created on 2004-09-07, modified on 2016-08-08 and a reference record created on 2003-09 -07.