A Numerical Method for Simulation of Microflows by Solving Directly Kinetic Equations with WENO Schemes
A numerical method for simulation of transitional-regime gas flows in microdevices is presented. The method is based on solving relaxation-type kinetic equations using high-order shock capturing weighted essentially non-oscillatory (WENO) schemes in the coordinate space and the discrete ordinate tec...
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| Published in | Journal of scientific computing Vol. 57; no. 1; pp. 42 - 73 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Boston
Springer US
01.10.2013
Springer Nature B.V |
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| Abstract | A numerical method for simulation of transitional-regime gas flows in microdevices is presented. The method is based on solving relaxation-type kinetic equations using high-order shock capturing weighted essentially non-oscillatory (WENO) schemes in the coordinate space and the discrete ordinate techniques in the velocity space. In contrast to the direct simulation Monte Carlo (DSMC) method, this approach is not subject to statistical scattering and is equally efficient when simulating both steady and unsteady flows. The presented numerical method is used to simulate some classical problems of rarefied gas dynamics as well as some microflows of practical interest, namely shock wave propagation in a microchannel and steady and unsteady flows in a supersonic micronozzle. Computational results are compared with Navier–Stokes and DSMC solutions. |
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| AbstractList | A numerical method for simulation of transitional-regime gas flows in microdevices is presented. The method is based on solving relaxation-type kinetic equations using high-order shock capturing weighted essentially non-oscillatory (WENO) schemes in the coordinate space and the discrete ordinate techniques in the velocity space. In contrast to the direct simulation Monte Carlo (DSMC) method, this approach is not subject to statistical scattering and is equally efficient when simulating both steady and unsteady flows. The presented numerical method is used to simulate some classical problems of rarefied gas dynamics as well as some microflows of practical interest, namely shock wave propagation in a microchannel and steady and unsteady flows in a supersonic micronozzle. Computational results are compared with Navier–Stokes and DSMC solutions. |
| Author | Shershnev, A. A. Kudryavtsev, A. N. |
| Author_xml | – sequence: 1 givenname: A. N. surname: Kudryavtsev fullname: Kudryavtsev, A. N. organization: Laboratory of Computational Aerodynamics, Khristianovich Institute of Theoretical and Applied Mechanics – sequence: 2 givenname: A. A. surname: Shershnev fullname: Shershnev, A. A. email: antony@itam.nsc.ru organization: Laboratory of Computational Aerodynamics, Khristianovich Institute of Theoretical and Applied Mechanics |
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| Cites_doi | 10.1016/S0021-9991(03)00065-2 10.1063/1.1706887 10.1016/j.apnum.2010.11.005 10.1016/j.compfluid.2005.04.012 10.1006/jcph.1997.5745 10.1063/1.1761862 10.1063/1.1761077 10.1016/j.jcp.2009.11.027 10.1016/j.compfluid.2007.01.009 10.1146/annurev.fluid.30.1.469 10.1115/1.2822013 10.1007/s00231-009-0558-x 10.1080/00411459608220707 10.1007/BF01017539 10.1063/1.1758217 10.1134/S0015462811030124 10.1007/s00193-006-0023-4 10.1137/0125019 10.1007/BF01029546 10.1006/jcph.1996.0130 10.1017/S0022112076002693 10.1016/S0997-7546(00)01103-1 10.1023/B:JCEL.0000011455.74817.35 10.1007/978-94-010-0866-2 10.1063/1.868989 10.1063/1.2140710 10.1007/s00193-003-0191-4 10.1016/S0898-1221(97)00269-1 10.1063/1.1706147 10.1063/1.1761728 10.1063/1.1761920 10.1063/1.1691944 10.1016/j.jcp.2003.08.022 10.1016/j.jcp.2006.09.021 10.1016/j.jcp.2010.10.037 10.1017/S0022112076001912 10.1063/1.869204 10.1146/annurev.fluid.30.1.579 10.1137/S0036142998343300 10.1023/A:1023000406921 10.1063/1.1692299 10.1134/S096554250603016X 10.1006/jcph.2000.6548 10.1007/s00161-008-0068-y 10.1134/S0965542506020138 10.1063/1.1692921 10.1063/1.1705910 10.1134/S0965542509070112 10.1007/BF02697944 10.1103/PhysRev.94.511 10.1006/jcph.1995.1168 10.4208/cicp.110510.150511s 10.1093/oso/9780198561958.001.0001 10.1007/3-540-32386-4 10.1007/b138784 10.1063/1.3562766 10.1134/S0965542510120146 10.1063/1.1921267 10.2514/4.866586 10.1016/B978-1-4832-2858-7.50009-0 10.1007/978-0-387-21738-3 |
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| Keywords | Finite-difference scheme Kinetic models Transitional regime Gas microflows |
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| References | Alsmeyer (CR2) 1976; 74 Brull, Schneider (CR10) 2008; 20 Gilbarg, Paolucci (CR20) 1953; 2 Tcheremissine (CR57) 1998; 35 Bhatnagar, Gross, Krook (CR7) 1954; 94 Egorov, Erofeev (CR15) 1997; 32 CR32 CR31 Teagan, Springer (CR60) 1968; 11 Holway (CR23) 1966; 9 Suresh, Hyunh (CR56) 1997; 136 Welander (CR67) 1954; 7 Zeitoun, Burtschell (CR70) 2006; 15 Robben, Talbot (CR43) 1966; 9 Chigullapalli, Venkattraman, Ivanov, Alexeenko (CR13) 2010; 229 Filbet, Russo (CR18) 2003; 186 Rykov, Titarev, Shakhov (CR45) 2011; 46 Brouillette (CR9) 2004; 13 Mieussens (CR33) 2000; 162 Mirels (CR35) 1963; 6 CR48 Chu (CR12) 1965; 8 Li, Zhang (CR30) 2004; 193 Titarev (CR62) 2007; 36 Huang, Hartley (CR24) 1969; 12 Yen (CR69) 1966; 9 Alekseenko (CR1) 2011; 61 Richter (CR42) 1973; 25 Pullin, Harvey (CR41) 1976; 78 Aoki, Kanba, Takata (CR4) 1997; 9 Segal Ben (CR46) 1971 Kolobov, Arslanbekov, Aristov, Frolova, Zabelok (CR29) 2007; 223 Aristov, Frolova, Zabelok (CR6) 2012; 11 Elizarova, Shirokov, Montero (CR17) 2005; 17 Varghese (CR66) 2011; 230 Morinishi (CR36) 2006; 35 CR16 CR59 Zheng, Struchtrup (CR71) 2005; 17 Pareschi, Perthame (CR39) 1996; 25 Bird (CR8) 1994 Shakhov (CR47) 1973; 8 CR55 Mieussens, Struchtrup (CR34) 2004; 16 CR53 CR52 Roshko (CR44) 1960; 3 CR50 Titarev (CR63) 2009; 49 Tcheremissine (CR58) 2006; 46 Andries, Le Tallec, Perlat, Perthame (CR3) 2000; 19 Jiang, Shu (CR27) 1996; 126 Huang, Hwang (CR25) 1970; 13 Palczewski, Schneider (CR38) 1998; 91 Graur, Polikarpov (CR21) 2009; 46 Shakhov (CR49) 1968; 3 Shu, Osher (CR51) 1988; 77 Ohwada (CR37) 1996; 8 Yang, Huang (CR68) 1995; 120 Carrillo, Gamba, Majorana, Shu (CR11) 2003; 2 Aristov (CR5) 2001 Ho, Tai (CR22) 1998; 30 Pareschi, Russo (CR40) 2000; 37 Karniadakis, Beskok, Aluru (CR28) 2005 CR65 Titarev, Shakhov (CR64) 2006; 50 Ivanov, Gimelshein (CR26) 1998; 30 Duff (CR14) 1959; 2 Gad-el-Hak (CR19) 1999; 121 Struchtrup (CR54) 2005 Titarev, Shakhov (CR61) 2006; 46 VA Titarev (9694_CR61) 2006; 46 L Mieussens (9694_CR34) 2004; 16 IV Egorov (9694_CR15) 1997; 32 JY Yang (9694_CR68) 1995; 120 9694_CR48 F Robben (9694_CR43) 1966; 9 S Chigullapalli (9694_CR13) 2010; 229 DI Pullin (9694_CR41) 1976; 78 ZH Li (9694_CR30) 2004; 193 P Welander (9694_CR67) 1954; 7 CM Ho (9694_CR22) 1998; 30 CK Chu (9694_CR12) 1965; 8 AB Huang (9694_CR24) 1969; 12 M Brouillette (9694_CR9) 2004; 13 F Filbet (9694_CR18) 2003; 186 9694_CR53 9694_CR55 Y Zheng (9694_CR71) 2005; 17 9694_CR50 AM Alekseenko (9694_CR1) 2011; 61 9694_CR52 S Brull (9694_CR10) 2008; 20 9694_CR51 D Gilbarg (9694_CR20) 1953; 2 L Pareschi (9694_CR40) 2000; 37 9694_CR17 R Duff (9694_CR14) 1959; 2 IA Graur (9694_CR21) 2009; 46 9694_CR16 9694_CR59 PL Bhatnagar (9694_CR7) 1954; 94 EM Shakhov (9694_CR49) 1968; 3 K Morinishi (9694_CR36) 2006; 35 K Aoki (9694_CR4) 1997; 9 SM Yen (9694_CR69) 1966; 9 FG Tcheremissine (9694_CR57) 1998; 35 9694_CR65 VI Kolobov (9694_CR29) 2007; 223 VV Aristov (9694_CR5) 2001 T Ohwada (9694_CR37) 1996; 8 P Varghese (9694_CR66) 2011; 230 AB Huang (9694_CR25) 1970; 13 H Mirels (9694_CR35) 1963; 6 VA Titarev (9694_CR62) 2007; 36 VV Aristov (9694_CR6) 2012; 11 D Zeitoun (9694_CR70) 2006; 15 A Roshko (9694_CR44) 1960; 3 JA Carrillo (9694_CR11) 2003; 2 M Gad-el-Hak (9694_CR19) 1999; 121 L Pareschi (9694_CR39) 1996; 25 L Mieussens (9694_CR33) 2000; 162 G Karniadakis (9694_CR28) 2005 9694_CR32 9694_CR31 EM Shakhov (9694_CR47) 1973; 8 MS Ivanov (9694_CR26) 1998; 30 H Struchtrup (9694_CR54) 2005 G Richter (9694_CR42) 1973; 25 GA Bird (9694_CR8) 1994 P Andries (9694_CR3) 2000; 19 G-S Jiang (9694_CR27) 1996; 126 FG Tcheremissine (9694_CR58) 2006; 46 A Palczewski (9694_CR38) 1998; 91 H Alsmeyer (9694_CR2) 1976; 74 VA Rykov (9694_CR45) 2011; 46 WP Teagan (9694_CR60) 1968; 11 VA Titarev (9694_CR63) 2009; 49 VA Titarev (9694_CR64) 2006; 50 M Segal Ben (9694_CR46) 1971 LH Holway (9694_CR23) 1966; 9 A Suresh (9694_CR56) 1997; 136 |
| References_xml | – volume: 186 start-page: 457 year: 2003 end-page: 480 ident: CR18 article-title: High order numerical methods for the space non-homogeneous Boltzmann equation publication-title: J. Comput. Phys. doi: 10.1016/S0021-9991(03)00065-2 – ident: CR16 – volume: 6 start-page: 1201 year: 1963 end-page: 1214 ident: CR35 article-title: Test time in low pressure shock tube publication-title: Phys. Fluids doi: 10.1063/1.1706887 – volume: 61 start-page: 410 year: 2011 end-page: 427 ident: CR1 article-title: Numerical properties of high order discrete velocity solutions to the BGK kinetic equation publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2010.11.005 – volume: 35 start-page: 978 year: 2006 end-page: 985 ident: CR36 article-title: Numerical simulation for gas microflows using Boltzmann equation publication-title: Comput. Fluids doi: 10.1016/j.compfluid.2005.04.012 – volume: 136 start-page: 83 year: 1997 end-page: 99 ident: CR56 article-title: Accurate monotonicity-preserving schemes with Runge-Kutta stepping publication-title: J. Comput. Phys. doi: 10.1006/jcph.1997.5745 – volume: 9 start-page: 1417 year: 1966 end-page: 1418 ident: CR69 article-title: Temperature overshoot in shock waves publication-title: Phys. Fluids doi: 10.1063/1.1761862 – volume: 8 start-page: 12 year: 1965 end-page: 22 ident: CR12 article-title: Kinetic-theoretic description of the formation of a shock wave publication-title: Phys. Fluids doi: 10.1063/1.1761077 – volume: 229 start-page: 2139 year: 2010 end-page: 2158 ident: CR13 article-title: Entropy considerations in numerical simulations of non-equilibrium rarefied flows publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2009.11.027 – year: 2005 ident: CR54 publication-title: Macroscopic Transport Equations for Rarefied Gas Flows – volume: 36 start-page: 1446 year: 2007 end-page: 1459 ident: CR62 article-title: Conservative numerical methods for model kinetic equations publication-title: Comput. Fluids doi: 10.1016/j.compfluid.2007.01.009 – volume: 30 start-page: 469 year: 1998 end-page: 505 ident: CR26 article-title: Computational hypersonic rarefied flows publication-title: Ann. Rev. Fluid Mech. doi: 10.1146/annurev.fluid.30.1.469 – volume: 50 start-page: 2131 year: 2006 end-page: 2144 ident: CR64 article-title: Nonisothermal gas flow in a long channel analyzed on the basis of the kinetic S-model publication-title: Comput. Math. Math. Phys. – volume: 121 start-page: 5 year: 1999 end-page: 33 ident: CR19 article-title: The fluid mechanics of microdevices—the Freeman scholar lecture publication-title: J. Fluids Eng. doi: 10.1115/1.2822013 – volume: 46 start-page: 237 year: 2009 end-page: 244 ident: CR21 article-title: Comparison of different kinetic models for the heat transfer problem publication-title: Heat Mass Transf. doi: 10.1007/s00231-009-0558-x – volume: 25 start-page: 369 year: 1996 end-page: 383 ident: CR39 article-title: A Fourier spectral method for homogeneous Boltzmann equations publication-title: Transp. Theory Stat. Phys. doi: 10.1080/00411459608220707 – volume: 8 start-page: 275 year: 1973 end-page: 281 ident: CR47 article-title: Longitudinal rarefied gas flow over a plate publication-title: Fluid Dyn. doi: 10.1007/BF01017539 – volume: 16 start-page: 2797 year: 2004 ident: CR34 article-title: Numerical comparison of BhatnagarGrossKrook models with proper Prandtl number publication-title: Phys. Fluids doi: 10.1063/1.1758217 – volume: 46 start-page: 456 issue: 3 year: 2011 end-page: 466 ident: CR45 article-title: Rarefied Poiseuille flow in elliptical and rectangular tubes publication-title: Fluid Dyn doi: 10.1134/S0015462811030124 – year: 1994 ident: CR8 publication-title: Molecular Gas Dynamics and Direct Simulation of Gas Flows – volume: 15 start-page: 241 year: 2006 end-page: 246 ident: CR70 article-title: Navier-Stokes computations in micro shock tubes publication-title: Shock Waves doi: 10.1007/s00193-006-0023-4 – volume: 25 start-page: 149 issue: 2 year: 1973 end-page: 157 ident: CR42 article-title: On the convergence of the discrete ordinate method in kinetic theory publication-title: SIAM J. Appl. Math doi: 10.1137/0125019 – ident: CR50 – year: 1971 ident: CR46 publication-title: Shock wave Structure Using Nonlinear Model Boltzmann Equations – volume: 3 start-page: 95 year: 1968 end-page: 96 ident: CR49 article-title: Generalization of the Krook kinetic relaxation equation publication-title: Fluid Dyn. doi: 10.1007/BF01029546 – volume: 126 start-page: 202 year: 1996 end-page: 228 ident: CR27 article-title: Efficient implementation of weighted ENO schemes publication-title: J. Comput. Phys. doi: 10.1006/jcph.1996.0130 – volume: 78 start-page: 689 year: 1976 end-page: 707 ident: CR41 article-title: A numerical simulation of the rarefied hypersonic flat-plate problem publication-title: J. Fluid Mech. doi: 10.1017/S0022112076002693 – volume: 19 start-page: 813 year: 2000 end-page: 830 ident: CR3 article-title: The Gaussian-BGK model of Boltzmann equation with small Prandtl numbers publication-title: Eur. J. Mech. B Fluids doi: 10.1016/S0997-7546(00)01103-1 – volume: 2 start-page: 375 year: 2003 end-page: 380 ident: CR11 article-title: A direct solver for 2D non-stationary Boltzmann-Poisson systems for semiconductor devices: a MESFET simulation by WENO-Boltzmann schemes publication-title: J. Comput. Electron. doi: 10.1023/B:JCEL.0000011455.74817.35 – ident: CR32 – year: 2001 ident: CR5 publication-title: Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows doi: 10.1007/978-94-010-0866-2 – volume: 8 start-page: 2153 year: 1996 end-page: 2160 ident: CR37 article-title: Heat flow and temperature and density distributions in a rarefied gas between parallel plates with different temperatures. Finite-difference analysis of the nonlinear Boltzmann equation for hard-sphere molecules publication-title: Phys. Fluids doi: 10.1063/1.868989 – volume: 17 start-page: 127103 year: 2005 ident: CR71 article-title: Ellipsoidal statistical Bhatnagar-Gross-Krook model with velocity-dependent collision frequency publication-title: Phys. Fluids doi: 10.1063/1.2140710 – volume: 13 start-page: 3 year: 2004 end-page: 12 ident: CR9 article-title: Shock waves at microscales publication-title: Shock Waves doi: 10.1007/s00193-003-0191-4 – volume: 35 start-page: 215 year: 1998 end-page: 221 ident: CR57 article-title: Conservative evaluation of Boltzmann collision integral in discrete coordinates approximation publication-title: Comput. Math. Appl. doi: 10.1016/S0898-1221(97)00269-1 – volume: 3 start-page: 835 year: 1960 end-page: 842 ident: CR44 article-title: On flow duration in low pressure shock tube publication-title: Phys. Fluids doi: 10.1063/1.1706147 – ident: CR53 – volume: 9 start-page: 633 year: 1966 end-page: 643 ident: CR43 article-title: Measurement of shock wave thickness by electron beam fluorescence method publication-title: Phys. Fluids doi: 10.1063/1.1761728 – volume: 9 start-page: 1658 year: 1966 end-page: 1673 ident: CR23 article-title: New statistical models for kinetic theory: methods of construction publication-title: Phys. Fluids doi: 10.1063/1.1761920 – volume: 11 start-page: 497 year: 1968 end-page: 506 ident: CR60 article-title: Heat-transfer and density distribution measurements between parallel plates in the transition regime publication-title: Phys. Fluids doi: 10.1063/1.1691944 – volume: 193 start-page: 708 year: 2004 end-page: 738 ident: CR30 article-title: Study on gas kinetic unified algorithm for flows from rarefied transition to continuum publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2003.08.022 – volume: 223 start-page: 589 year: 2007 end-page: 608 ident: CR29 article-title: Unified solver for rarefied and continuum flows with adaptive mesh and algorithm refinement publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2006.09.021 – volume: 7 start-page: 507 year: 1954 end-page: 553 ident: CR67 article-title: On the temperature jump in a rarefied gas publication-title: Ark. Fys. – volume: 230 start-page: 1265 year: 2011 end-page: 1280 ident: CR66 article-title: Monte Carlo solution of the Boltzmann equation via a discrete velocity model publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2010.10.037 – volume: 74 start-page: 497 year: 1976 end-page: 513 ident: CR2 article-title: Density profiles in argon and nitrogen shock waves measured by the absorbtion of an electron beam publication-title: J. Fluid Mech. doi: 10.1017/S0022112076001912 – volume: 9 start-page: 1144 year: 1997 end-page: 1161 ident: CR4 article-title: Numerical analysis of a supersonic rarefied gas flow past a flat plate publication-title: Phys. Fluids doi: 10.1063/1.869204 – ident: CR48 – ident: CR65 – volume: 30 start-page: 579 year: 1998 end-page: 612 ident: CR22 article-title: Micro-electro-mechanical systems (MEMS) and fluid flows publication-title: Ann. Rev. Fluid Mech. doi: 10.1146/annurev.fluid.30.1.579 – volume: 37 start-page: 1217 year: 2000 end-page: 1245 ident: CR40 article-title: Numerical solution of the Boltzmann equation. I. Spectrally accurate approximation of the collision operator publication-title: SIAM J. Numer. Anal. doi: 10.1137/S0036142998343300 – volume: 91 start-page: 307 issue: 1–2 year: 1998 end-page: 326 ident: CR38 article-title: Existence, stability, and convergence of solutions of discrete velocity models to the Boltzmann equation publication-title: J. Stat. Phys. doi: 10.1023/A:1023000406921 – ident: CR52 – ident: CR31 – volume: 11 start-page: 1334 year: 2012 end-page: 1346 ident: CR6 article-title: Supersonic flows with nontraditional transport described by kinetic methods publication-title: Commun. Comput. Phys. – volume: 12 start-page: 96 year: 1969 end-page: 108 ident: CR24 article-title: Kinetic theory of the sharp leading edge problem in supersonic flow publication-title: Phys. Fluids doi: 10.1063/1.1692299 – volume: 46 start-page: 505 year: 2006 end-page: 513 ident: CR61 article-title: Numerical analysis of the spiral couette flow of a rarefied gas between coaxial cylinders publication-title: Comput. Math. Math. Phys. doi: 10.1134/S096554250603016X – volume: 17 start-page: 068101 issue: 6 year: 2005 ident: CR17 article-title: Numerical simulation of shock-wave structure for argon and helium publication-title: Phys. Fluids – volume: 162 start-page: 429 year: 2000 end-page: 466 ident: CR33 article-title: Discrete velocity models and numerical schemes for the Boltzmann-BGK equation in plane and axisymmetric geometries publication-title: J. Comput. Phys. doi: 10.1006/jcph.2000.6548 – volume: 20 start-page: 63 issue: 2 year: 2008 end-page: 74 ident: CR10 article-title: A new approach for the ellipsoidal statistical model publication-title: Cont. Mech. Thermodyn. doi: 10.1007/s00161-008-0068-y – volume: 46 start-page: 315 year: 2006 end-page: 329 ident: CR58 article-title: Solution to the Boltzmann kinetic equation for high-speed flows publication-title: Comput. Math. Math. Phys. doi: 10.1134/S0965542506020138 – year: 2005 ident: CR28 publication-title: Mictoflows and Nanoflows, Fundamentals and Simulation – volume: 13 start-page: 309 year: 1970 end-page: 317 ident: CR25 article-title: Supersonic leading edge problem according to the ellipsoidal model publication-title: Phys. Fluids doi: 10.1063/1.1692921 – volume: 2 start-page: 207 year: 1959 end-page: 216 ident: CR14 article-title: Shock-tube performance at low initial pressure publication-title: Phys. Fluids doi: 10.1063/1.1705910 – ident: CR55 – volume: 49 start-page: 1197 year: 2009 end-page: 1211 ident: CR63 article-title: Numerical method for computing two-dimensional unsteady rarefied gas flows in arbitrarily shaped domains publication-title: Comput. Math. Math. Phys. doi: 10.1134/S0965542509070112 – volume: 77 start-page: 439 year: 1988 end-page: 471 ident: CR51 article-title: Efficient implementation of essentially non-oscillatory shockcapturing schemes publication-title: J. Comp. Phys. – ident: CR59 – volume: 32 start-page: 112 year: 1997 end-page: 122 ident: CR15 article-title: Continuum and kinetic approaches to the simulation of the hypersonic flow past a flat plate publication-title: Fluid Dyn. doi: 10.1007/BF02697944 – volume: 2 start-page: 617 year: 1953 end-page: 642 ident: CR20 article-title: The structure of shock waves in the continuum theory of fluids publication-title: J. Rat. Mech. Anal. – volume: 94 start-page: 511 year: 1954 end-page: 525 ident: CR7 article-title: A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems publication-title: Phys. Rev. doi: 10.1103/PhysRev.94.511 – volume: 120 start-page: 323 year: 1995 end-page: 339 ident: CR68 article-title: Rarefied flow computations using nonlinear model boltzmann equations publication-title: J. Comput. Phys doi: 10.1006/jcph.1995.1168 – volume: 9 start-page: 1658 year: 1966 ident: 9694_CR23 publication-title: Phys. Fluids doi: 10.1063/1.1761920 – volume: 30 start-page: 579 year: 1998 ident: 9694_CR22 publication-title: Ann. Rev. Fluid Mech. doi: 10.1146/annurev.fluid.30.1.579 – volume: 3 start-page: 835 year: 1960 ident: 9694_CR44 publication-title: Phys. Fluids doi: 10.1063/1.1706147 – volume: 11 start-page: 1334 year: 2012 ident: 9694_CR6 publication-title: Commun. Comput. Phys. doi: 10.4208/cicp.110510.150511s – volume: 46 start-page: 456 issue: 3 year: 2011 ident: 9694_CR45 publication-title: Fluid Dyn doi: 10.1134/S0015462811030124 – volume-title: Molecular Gas Dynamics and Direct Simulation of Gas Flows year: 1994 ident: 9694_CR8 doi: 10.1093/oso/9780198561958.001.0001 – volume: 2 start-page: 375 year: 2003 ident: 9694_CR11 publication-title: J. Comput. Electron. doi: 10.1023/B:JCEL.0000011455.74817.35 – volume: 6 start-page: 1201 year: 1963 ident: 9694_CR35 publication-title: Phys. Fluids doi: 10.1063/1.1706887 – volume-title: Macroscopic Transport Equations for Rarefied Gas Flows year: 2005 ident: 9694_CR54 doi: 10.1007/3-540-32386-4 – volume: 30 start-page: 469 year: 1998 ident: 9694_CR26 publication-title: Ann. Rev. Fluid Mech. doi: 10.1146/annurev.fluid.30.1.469 – ident: 9694_CR50 doi: 10.1007/b138784 – volume: 25 start-page: 369 year: 1996 ident: 9694_CR39 publication-title: Transp. Theory Stat. Phys. doi: 10.1080/00411459608220707 – volume: 223 start-page: 589 year: 2007 ident: 9694_CR29 publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2006.09.021 – ident: 9694_CR31 doi: 10.1063/1.3562766 – volume: 2 start-page: 207 year: 1959 ident: 9694_CR14 publication-title: Phys. Fluids doi: 10.1063/1.1705910 – volume: 20 start-page: 63 issue: 2 year: 2008 ident: 9694_CR10 publication-title: Cont. Mech. Thermodyn. doi: 10.1007/s00161-008-0068-y – volume: 136 start-page: 83 year: 1997 ident: 9694_CR56 publication-title: J. Comput. Phys. doi: 10.1006/jcph.1997.5745 – volume: 15 start-page: 241 year: 2006 ident: 9694_CR70 publication-title: Shock Waves doi: 10.1007/s00193-006-0023-4 – volume: 8 start-page: 2153 year: 1996 ident: 9694_CR37 publication-title: Phys. Fluids doi: 10.1063/1.868989 – volume: 25 start-page: 149 issue: 2 year: 1973 ident: 9694_CR42 publication-title: SIAM J. Appl. Math doi: 10.1137/0125019 – volume: 120 start-page: 323 year: 1995 ident: 9694_CR68 publication-title: J. Comput. Phys doi: 10.1006/jcph.1995.1168 – volume: 19 start-page: 813 year: 2000 ident: 9694_CR3 publication-title: Eur. J. Mech. B Fluids doi: 10.1016/S0997-7546(00)01103-1 – volume: 13 start-page: 309 year: 1970 ident: 9694_CR25 publication-title: Phys. Fluids doi: 10.1063/1.1692921 – volume: 8 start-page: 12 year: 1965 ident: 9694_CR12 publication-title: Phys. Fluids doi: 10.1063/1.1761077 – ident: 9694_CR55 – volume: 126 start-page: 202 year: 1996 ident: 9694_CR27 publication-title: J. Comput. Phys. doi: 10.1006/jcph.1996.0130 – volume-title: Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows year: 2001 ident: 9694_CR5 doi: 10.1007/978-94-010-0866-2 – ident: 9694_CR52 – volume: 50 start-page: 2131 year: 2006 ident: 9694_CR64 publication-title: Comput. Math. Math. Phys. doi: 10.1134/S0965542510120146 – volume: 229 start-page: 2139 year: 2010 ident: 9694_CR13 publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2009.11.027 – volume: 35 start-page: 215 year: 1998 ident: 9694_CR57 publication-title: Comput. Math. Appl. doi: 10.1016/S0898-1221(97)00269-1 – volume-title: Shock wave Structure Using Nonlinear Model Boltzmann Equations year: 1971 ident: 9694_CR46 – volume: 13 start-page: 3 year: 2004 ident: 9694_CR9 publication-title: Shock Waves doi: 10.1007/s00193-003-0191-4 – volume: 49 start-page: 1197 year: 2009 ident: 9694_CR63 publication-title: Comput. Math. Math. Phys. doi: 10.1134/S0965542509070112 – ident: 9694_CR17 doi: 10.1063/1.1921267 – volume: 36 start-page: 1446 year: 2007 ident: 9694_CR62 publication-title: Comput. Fluids doi: 10.1016/j.compfluid.2007.01.009 – ident: 9694_CR16 – volume: 12 start-page: 96 year: 1969 ident: 9694_CR24 publication-title: Phys. Fluids doi: 10.1063/1.1692299 – volume: 11 start-page: 497 year: 1968 ident: 9694_CR60 publication-title: Phys. Fluids doi: 10.1063/1.1691944 – ident: 9694_CR32 doi: 10.2514/4.866586 – volume: 9 start-page: 1417 year: 1966 ident: 9694_CR69 publication-title: Phys. Fluids doi: 10.1063/1.1761862 – volume: 91 start-page: 307 issue: 1–2 year: 1998 ident: 9694_CR38 publication-title: J. Stat. Phys. doi: 10.1023/A:1023000406921 – volume: 7 start-page: 507 year: 1954 ident: 9694_CR67 publication-title: Ark. Fys. – ident: 9694_CR51 – volume: 9 start-page: 633 year: 1966 ident: 9694_CR43 publication-title: Phys. Fluids doi: 10.1063/1.1761728 – ident: 9694_CR48 – volume: 162 start-page: 429 year: 2000 ident: 9694_CR33 publication-title: J. Comput. Phys. doi: 10.1006/jcph.2000.6548 – volume: 3 start-page: 95 year: 1968 ident: 9694_CR49 publication-title: Fluid Dyn. doi: 10.1007/BF01029546 – ident: 9694_CR65 – volume: 32 start-page: 112 year: 1997 ident: 9694_CR15 publication-title: Fluid Dyn. doi: 10.1007/BF02697944 – volume: 16 start-page: 2797 year: 2004 ident: 9694_CR34 publication-title: Phys. Fluids doi: 10.1063/1.1758217 – ident: 9694_CR59 doi: 10.1016/B978-1-4832-2858-7.50009-0 – volume: 2 start-page: 617 year: 1953 ident: 9694_CR20 publication-title: J. Rat. Mech. Anal. – volume: 94 start-page: 511 year: 1954 ident: 9694_CR7 publication-title: Phys. Rev. doi: 10.1103/PhysRev.94.511 – volume: 46 start-page: 505 year: 2006 ident: 9694_CR61 publication-title: Comput. Math. Math. Phys. doi: 10.1134/S096554250603016X – volume-title: Mictoflows and Nanoflows, Fundamentals and Simulation year: 2005 ident: 9694_CR28 – volume: 9 start-page: 1144 year: 1997 ident: 9694_CR4 publication-title: Phys. Fluids doi: 10.1063/1.869204 – volume: 186 start-page: 457 year: 2003 ident: 9694_CR18 publication-title: J. Comput. Phys. doi: 10.1016/S0021-9991(03)00065-2 – volume: 46 start-page: 315 year: 2006 ident: 9694_CR58 publication-title: Comput. Math. Math. Phys. doi: 10.1134/S0965542506020138 – volume: 17 start-page: 127103 year: 2005 ident: 9694_CR71 publication-title: Phys. Fluids doi: 10.1063/1.2140710 – volume: 78 start-page: 689 year: 1976 ident: 9694_CR41 publication-title: J. Fluid Mech. doi: 10.1017/S0022112076002693 – volume: 46 start-page: 237 year: 2009 ident: 9694_CR21 publication-title: Heat Mass Transf. doi: 10.1007/s00231-009-0558-x – volume: 37 start-page: 1217 year: 2000 ident: 9694_CR40 publication-title: SIAM J. Numer. Anal. doi: 10.1137/S0036142998343300 – volume: 193 start-page: 708 year: 2004 ident: 9694_CR30 publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2003.08.022 – volume: 230 start-page: 1265 year: 2011 ident: 9694_CR66 publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2010.10.037 – volume: 35 start-page: 978 year: 2006 ident: 9694_CR36 publication-title: Comput. Fluids doi: 10.1016/j.compfluid.2005.04.012 – volume: 121 start-page: 5 year: 1999 ident: 9694_CR19 publication-title: J. Fluids Eng. doi: 10.1115/1.2822013 – volume: 74 start-page: 497 year: 1976 ident: 9694_CR2 publication-title: J. Fluid Mech. doi: 10.1017/S0022112076001912 – volume: 61 start-page: 410 year: 2011 ident: 9694_CR1 publication-title: Appl. Numer. Math. doi: 10.1016/j.apnum.2010.11.005 – ident: 9694_CR53 doi: 10.1007/978-0-387-21738-3 – volume: 8 start-page: 275 year: 1973 ident: 9694_CR47 publication-title: Fluid Dyn. doi: 10.1007/BF01017539 |
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| SubjectTerms | Algorithms Boundary conditions Computation Computational Mathematics and Numerical Analysis Direct simulation Monte Carlo method Equilibrium Gas flow Gases Kinetic equations Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Microchannels Numerical methods Rarefied gas dynamics Rarefied gases Shock capturing Shock wave propagation Simulation Theoretical Unsteady flow Velocity Viscosity |
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| Title | A Numerical Method for Simulation of Microflows by Solving Directly Kinetic Equations with WENO Schemes |
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