NUMERICAL SIMULATION OF MICROFLOWS USING HERMITE SPECTRAL METHODS

被引：14

作者：

Hu, Zhicheng ^{[1
]}

Cai, Zhenning ^{[2
]}

Wang, Yanli ^{[3
]}

机构：

[1] Nanjing Univ Aeronaut & Astronaut, Dept Math, Coll Sci, Nanjing 210016, Peoples R China

[2] Natl Univ Singapore, Dept Math, Level 4,Block S17,10 Lower Kent Ridge Rd, Singapore 119076, Singapore

[3] Peking Univ, Dept Engn, Beijing 100871, Peoples R China

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2020年 / 42卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Boltzmann equation; Hermite spectral method; microflow; BOLTZMANN COLLISION OPERATOR; REGULARIZED MOMENT METHOD; EQUATION; MODEL; SOLVER; SPHERE; ORDER;

D O I：

10.1137/18M120066X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose a Hermite spectral method for the spatially inhomogeneous Boltzmann equation. For the inverse-power-law model, we generalize a class of approximate quadratic collision operators defined in the normalized and dimensionless setting to operators for arbitrary distribution functions. An efficient algorithm with a fast transform is introduced to discretize the new collision operators. The method is tested for one- and two-dimensional benchmark microflow problems.

引用

页码：B105 / B134

页数：30

共 50 条

[1] Hermite spectral and pseudospectral methods for numerical differentiation
Zhao, Zhenyu
Liu, Junfeng
APPLIED NUMERICAL MATHEMATICS, 2011, 61 (12) : 1322 - 1330
[2] NRxx SIMULATION OF MICROFLOWS WITH SHAKHOV MODEL
Cai, Zhenning
Li, Ruo
Qiao, Zhonghua
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2012, 34 (01) : A339 - A369
[3] NUMERICAL SIMULATION OF MICROFLOWS BY A DOM WITH STREAMING AND COLLISION PROCESSES
Yang, L. M.
Shu, C.
Wu, J.
PROCEEDINGS OF THE ASME 5TH INTERNATIONAL CONFERENCE ON MICRO/NANOSCALE HEAT AND MASS TRANSFER, 2016, VOL 2, 2016,
[4] Numerical simulation of particulate processes for control and estimation by spectral methods
Bueck, Andreas
Klaunick, Guenter
Kumar, Jitendra
Peglow, Mirko
Tsotsas, Evangelos
AICHE JOURNAL, 2012, 58 (08) : 2309 - 2319
[5] Simulation of microflows using the lattice Boltzmann method on nonuniform meshes
Rahmati, A. R. (ar_rahmati@kashanu.ac.ir), 1600, Begell House Inc. (03): : 77 - 97
[6] Numerical Simulation of Gas Microflows by Solving Relaxation-Type Kinetic Equations
Kudryavtsev, Alexey
Shershnev, Anton
Ivanov, Mikhail
MNHMT2009, VOL 1, 2010, : 357 - 366
[7] A Numerical Method for Simulation of Microflows by Solving Directly Kinetic Equations with WENO Schemes
Kudryavtsev, A. N.
Shershnev, A. A.
JOURNAL OF SCIENTIFIC COMPUTING, 2013, 57 (01) : 42 - 73
[8] Approximation of the Boltzmann collision operator based on hermite spectral method
Wang, Yanli
Cai, Zhenning
JOURNAL OF COMPUTATIONAL PHYSICS, 2019, 397
[9] ON THE SIMULATION OF VISCOELASTIC FLOW PAST A SPHERE USING SPECTRAL METHODS
GERVANG, B
DAVIES, AR
PHILLIPS, TN
JOURNAL OF NON-NEWTONIAN FLUID MECHANICS, 1992, 44 : 281 - 306
[10] Modern lattice Boltzmann methods for multiphase microflows
Falcucci, G.
Ubertini, S.
Chiappini, D.
Succi, S.
IMA JOURNAL OF APPLIED MATHEMATICS, 2011, 76 (05) : 712 - 725

← 1 2 3 4 5 →