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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 楊照彥 | |
dc.contributor.author | Bagus Putra Muljadi | en |
dc.contributor.author | 李念達 | zh_TW |
dc.date.accessioned | 2021-06-07T18:04:31Z | - |
dc.date.copyright | 2012-08-01 | |
dc.date.issued | 2012 | |
dc.date.submitted | 2012-07-27 | |
dc.identifier.citation | Bibliography
[1] S. O. S. R. C. A. Harten, B. Engquist. Uniformly high order accurate essentially non-oscillatory schemes. J. Comput. Phys, 71:231, 1987. 51 [2] M. Abramowitz and I. A. Stegun. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, New York, ninth dover printing, tenth gpo printing edition, 1964. 29, 30 [3] B. M. Aftosmis, M.J. and J. Melton. Robust and efficient cartesian mesh generation for component based geometry. AIAA-97-0196, 1997. 42 [4] M. G. Ancona and G. J. Iafrate. Quantum correction to the equation of state of an electron gas in a semiconductor. Phys. Rev. B, 39(13):9536– 9540, May 1989. 2 [5] M. G. Ancona and H. F. Tiersten. Macroscopic physics of the silicon inversion layer. Phys. Rev. B, 35(15):7959–7965, May 1987. 2 [6] P. K. Bayyuk, A.A. and B. van Leer. A simulation technique for 2d unsteady inviscid flows around arbitrarily moving and deforming bodies of arbitrarily geometry. AIAA Paper 93-3391-CP, 1993. 42 [7] M. Bennoune, M. Lemou, and L. Mieussens. Uniformly stable numerical schemes for the boltzmann equation preserving the compressible navierstokes asymptotics. Journal of Computational Physics, 227(8):3781 – 3803, 2008. 115 [8] M. Berger and R. LeVeque. An adaptive cartesian mesh algorithm for the euler euations in arbitrary geometries. AIAA-89-1930-CP, year = June, 1989. 42 146 Bibliography [9] P. L. Bhatnagar, E. P. Gross, and M. Krook. A model for collision processes in gases. i: small amplitude processes in charged and neutral one-component system. Phys. Rev., 94:511, 1954. 8, 113 [10] P. L. Bhatnagar, E. P. Gross, and M. Krook. A model for collision processes in gases. i. small amplitude processes in charged and neutral one-component systems. Phys. Rev., 94(3):511–525, May 1954. 3 [11] G. A. Bird. Molecular gas dynamics and the direct simulation of gas flows. Oxford University Press, Oxford, 1994. 15 [12] G. Boole and J. F. Moulton. A Treatise on the Calculus of Finite Differences, 2nd ed. Dover, New York, 1960. 30 [13] J. A. Carrillo, I. M. Gamba, A. Majorana, and C.-W. Shu. A weno-solver for the 1d non-stationary boltzmann-poisson system for semiconductor devices. Journal of Computational Electronics, 1:365–370, 2002. 3 [14] J. A. Carrillo, I. M. Gamba, A. Majorana, and C.-W. Shu. A direct solver for 2d non-stationary boltzmann-poisson systems for semiconductor devices: A mesfet simulation by weno-boltzmann schemes. Journal of Computational Electronics, 2:375–380, 2003. 3 [15] J. A. Carrillo, I. M. Gamba, A. Majorana, and C.-W. Shu. A wenosolver for the transients of boltzmann-poisson system for semiconductor devices: performance and comparisons with monte carlo methods. Journal of Computational Physics, 184(2):498 – 525, 2003. 3 [16] C. Cercignani. Mathematical Methods in Kinetic Theory. Springer, Heidelberg, 1 edition, 1995. 86 Bibliography 147 [17] S. C. Chang. The method of space-time conservation element and solution element–a new approach for solving the navier-stokes and euler equations. Journal of Computational Physics, 119(2):295 – 324, 1995. 120, 121, 122, 123 [18] S. C. Chang and W. M. To. A new numerical framework for solving conservation laws: The method of space-time conservation element and solution element. NASA TM, (104495), August 1991. 117 [19] S. C. Chang and X. Y. Wang. Multi-dimensional courant number insensitive ce/se euler solvers for applications involving highly nonuniform meshes. In AIAA-2003-5285, 2003. 123 [20] S. C. Chang, X. Y. Wang, and W. M. To. Application of the space-time conservation element and solution element method to onedimensional convection-diffusion problems. Journal of Computational Physics, 165(1):189 – 215, 2000. 117 [21] S.-M. Chang and K.-S. Chang. On the shockavortex interaction in Schardin’s problem. Shock Waves, 10:333–343, 2000. 94 [22] S. Chapman and T. G. Cowling. The mathematical theory of nonuniform gases: an account of the kinetic theory of viscosity, thermal conduction, and diffusion in gases. Cambridge University Press, 1970. 2, 19 [23] G. Chen. Nanoscale Energy Transport and Conversion: A Parallel Treatment of Electrons, Molecules, Phonons, and Photons (Mit- Pappalardo Series in Mechanical Engineering). Oxford University Press, USA, Mar. 2005. 2, 3 148 Bibliography [24] S. Chou and D. Baganoff. Kinetic Fluc-Vector Splitting for the Navier- Stokes Equations. Journal of Computational Physics, 130:217–230, 1997. 8 [25] C. K. Chu. Physics of Fluids, 1965. 8 [26] J. Clunie. On bose-einstein functions. Proceedings of the Physical Society. Section A, 67(7):632, 1954. 129 [27] W. Coirier and K. Powell. Solution adaptive cartesian cell approach for viscous and inviscid flows. AIAA, 34:938–945, 1996. 42 [28] J. P. Croissille and P. Villedieu. Kinetic Flux Splitting Schemes for Hyperbolic Flows. Lecture Notes in Physics, Springer-Verlag, 414, 1992. 8 [29] S. M. Deshpande. A second-order accurate kinetic-theory-based method for inviscid compressible flows. NASA Langley Tech. paper No. 2613, 1986. 8 [30] D. DeZeeuw and K. Powell. An adaptively refined cartesian mesh solver for the euler equations. AIAA-91-1542-CP, 1991. 42 [31] B. Einfeldt, C. D. Munz, P. L. Roe, and B. Sjoegreen. On godunovtype methods near low densities. Journal of Computational Physics, 92(2):273 – 295, 1991. 71, 72 [32] T. Elizarova and B. Chetverushkin. Kinetic Algorithms for Calculating Gas Dynamic Flows. J. Comput. Math. and Math. Phys, 25:1526–1533, 1985. 8 Bibliography 149 [33] E. Fatemi and F. Odeh. Upwind finite difference solution of boltzmann equation applied to electron transport in semiconductor devices. Journal of Computational Physics, 108(2):209 – 217, 1993. 3 [34] F. Filbet and S. Jin. A class of asymptotic-preserving schemes for kinetic equations and related problems with stiff sources. Journal of Computational Physics, 229(20):7625 – 7648, 2010. 115 [35] G. H. Findenegg. P.c.riedi: Thermal physics. macmillan press, london 1976. 318 seiten. Berichte der Bunsengesellschaft for physikalische Chemie, 81(2):249–249, 1977. 28 [36] C. L. Gardner. The quantum hydrodynamic model for semiconductor devices. SIAM J. Appl. Math., 54(2):409–427, 1994. 2 [37] S. K. Godunov. Finite difference methods for numerical computation of discontinous solutions of the equations of fluid dynamics. Mat. Sbornik, 47:271–295, 1959. 49 [38] A. Harten. High resolution schemes for hyperbolic conservation laws. Journal of Computational Physics, 49(3):357 – 393, 1983. 4, 39, 44, 51, 97 [39] C. Hirsch. Numerical Computation of Internal and External Flows. Wiley, New York, 1988. 47 [40] X. Y. Hu and B. C. Khoo. Kinetic energy fix for low internal energy flows. Journal of Computational Physics, 193(1):243 – 259, 2004. 72 [41] A. B. Huang and D. P. Giddens. The Discrete Ordinate Method for the Linearized Boundary Value Problems in Kinetic Theory of Gases. In 150 Bibliography C. L. Brundin, editor, Rarefied Gas Dynamics, Volume 1, pages 481–+, 1967. 27 [42] . Y. S. Jameson, A. Lower-upper implicit schemes with multiple grids for the euler equations. AIAA, 25(7):929–935, 1987. 46 [43] S. Jin. Runge-kutta methods for hyperbolic conservation laws with stiff relaxation terms. J. Comput. Phys, 122:51–67, 1995. 53, 77 [44] S. Jin. Efficient asymptotic-preserving (ap) schemes for some multiscale kinetic equations. SIAM Journal on Scientific Computing, 21(2):441– 454, 1999. 115 [45] S. Jin and C. D. Levermore. Numerical schemes for hyperbolic conservation laws with stiff relaxation terms. J. Comput. Phys, 126:449–467, 1996. 53, 77, 115 [46] S. Jin and Z. P. Xin. The relaxation schemes for systems of conservation laws in arbitrary space dimensions. Communications on Pure and Applied Mathematics, 48:235, 2006. 53, 77, 115 [47] a. A. J. K. Xu, L. Martinelli. Gas-Kinetic Finite Volume Methods, Flux-Vector Splitting and Artificial Diffusion. Journal of Computational Physics, 120:48–65, 1995. 8 [48] L. M. a. A. J. K. Xu, C. Kim. Gas-Kinetic Finite Volume Methods, Flux-Vector Splitting and Artificial Diffusion. Int. J. Comput. Fluid Dynamics, 7:213–235, 1996. 8 [49] L. P. Kadanoff and G. Baym. Quantum Statistical Mechanics. Benjamin, New York, 1962. 2, 15 Bibliography 151 [50] S. Kaniel. A Kinetic Model for the Compressible Flow Equations. Journal of Computational Physics, 27:537–563, 1988. 8 [51] C. Kim and A. Jameson. A Robust and Accurate LED-BGK Solver on Unstructured Adaptive Meshes. Journal of Computational Physics, 1997. 8 [52] P. D. Lax and X. D. Liu. Solution of two dimensional riemann problem of gas dynamics by positive schemes. SIAM J. Sci. Comput, 19:319–340, 1995. 73, 75, 78 [53] M. Lemou. Relaxed micro macro schemes for kinetic equations. Comptes Rendus Mathematique, 348(7a8):455 – 460, 2010. 115 [54] Z.-H. Li and H.-X. Zhang. Numerical investigation from rarefied flow to continuum by solving the boltzmann model equation. Intern. J. Numer. Fluids, 42:361–382, 2003. 5 [55] Z.-H. Li and H.-X. Zhang. Study on gas kinetic unified algorithm for flows from rarefied transition to continuum. Journal of Computational Physics, 193:708–738, 2004. 5 [56] Z.-H. Li and H.-X. Zhang. Study on gas kinetic unified algorithm for flows from rarefied transition to continuum. Journal of Computational Physics, 193(2):708 – 738, 2004. 100 [57] M. Lundstrom. Fundamentals of Carrier Transport. Cambridge University Press, 2nd edition, 2000. 3 [58] M. Macrossan. The Equilibrium Flux Method for the Calculation of Flows with Non-Equilibrium Chemical Reactions. Journal of Computational Physics, 80:204–231, 1989. 8 152 Bibliography [59] A. Majorana and R. M. Pidatella. A finite difference scheme solving the boltzmann-poisson system for semiconductor devices: Volume 174, number 2 (2001), pages 649-668. Journal of Computational Physics, 177(2):450 – 450, 2002. 3 [60] P. A. Markowich, C. A. Ringhofer, and C. Schmeiser. Semiconductor Equations. Springer, 1 edition, 2002. 3 [61] J. C. Maxwell. On stresses in rarified gases arising from inequalities of temperature. Philosophical Transactions of the Royal Society of London, 170:231–256, 1879. 55 [62] E. F. Melton, J.E. and M. Berger. 3d automatic cartesian grid generation for euler flows. AIAA Paper 93-3386-CP, 1993. 42 [63] J. Moschetta and D. Pullin. A Robust Low Diffusive Kinetic Scheme for the Navier-Stokes/Euler Equations. Journal of Computational Physics, 133:193–204, 1997. 8 [64] B. P. Muljadi and J.-Y. Yang. Simulation of shock wave diffraction by a square cylinder in gases of arbitrary statistics using a semiclassical boltzmann bhatnagar gross krook equation solver. Proc. R. Soc. A, 468:651 – 670, 2012. 9, 101 [65] B. P. Muljadi and J.-Y. Yang. Space time ce/se and discrete ordinate method for solving gas flows. Computers and Fluids, 63:184 – 188, 2012. 5, 9, 71, 101, 117 [66] T. Nikuni and A. Griffin. Hydrodynamic damping in trapped bose gases. Journal of Low Temperature Physics, 111:793–814, 1998. 2, 19 Bibliography 153 [67] T. Nikuni and A. Griffin. Hydrodynamic damping in trapped bose gases. Journal of Low Temperature Physics, 111(5):793–814, Jun 1998. 15 [68] R. Pathria. Statistical Mechanics. Elsevier Pte Ltd., 2006. 130 [69] A. Pattamatta and C. K. Madnia. Modeling electron-phonon nonequilibrium in gold films using boltzmann transport model. Journal of Heat Transfer, 131:082401–1, 2009. 3 [70] B. Perthame. Second-Order Boltzmann schemes for compressible Euler equation in one and two space dimensions. SIAM J. Numer. Anal., 29(1), 1992. 8 [71] K. H. Prendergast and K. Xu. Numerical hydrodynamics from gaskinetic theory. Journal of Computational Physics, 109(1):53 – 66, 1993. 8, 25 [72] D. I. Pullin. Direct simulation methods for compressible inviscid idealgas flow. Journal of Computational Physics, 34:231–244, 1980. 8 [73] R. D. Reitz. One-dimensional compressible gas dynamics calculations using the Boltzmann equation. Journal of Computational Physics, 42:108–123, 1981. 8 [74] K. H. Sanders, R. H. Prendergast. The Possible Relation of the 3- KILOPARSEC Arm to Explosions in the Galactic Nucleus. Astrophysical Journal, 188:489–500, 1974. 8 [75] S. Scaldaferri, G. Curatola, and G. Iannaccone. Direct solution of the boltzmann transport equation and poisson schrodinger equation for nanoscale mosfets. IEEE Transaction on Electron Devices, 54:2901, 2007. 3 154 Bibliography [76] C. W. Schultz-Rinne, J. P. Collins, and H. M. Glaz. Numerical solution of the riemann problem for two-dimensional gas dynamics. SIAM J. Sci. Comput., 14(6):1394–1414, 1993. 73 [77] J. Sherman and W. J. Morrison. Adjustment of an inverse matrix corresponding to a change in one element of a given matrix. Ann. Math. Stat., 21:124–127, 1950. 60 [78] Y.-H. Shi. Kinetic Numerical Methods for the semiclassical Boltzmann Equation. PhD thesis, National Taiwan University, 2008. 9, 75 [79] Y. H. Shi and J. Y. Yang. A gas kinetic bgk scheme for semiclassical boltzmann hydrodynamic transport. Journal of Computational Physics, 227(22):9389 – 9407, 2008. 9, 20 [80] T. I. P. Shih and W. J. Chyu. AIAA, 29(10):1759, 1991. 48 [81] B. Shizgal. A gaussian quadrature procedure for use in the solution of the boltzmann equation and related problems. Journal of Computational Physics, 41(2):309 – 328, 1981. 27 [82] G. Strang. On the construction and comparison of difference schemes. SIAM J. Numer. Anal., 5(3):506–517, 1968. 49 [83] H. Struchtrup. Macroscopic Transport Equations for Rarefied Gas Flows: Approximation Methods in Kinetic Theory Interaction of Mechanics and Mathematics. Springer, Heidelberg, 1 edition, 2005. 56 [84] M. Sun and K. Takayama. Vorticity production in shock diffraction. Journal of Fluid Mechanics, 478:237–256, 2003. 96 Bibliography 155 [85] M. Torrilhon and H. Struchtrup. Boundary conditions for regularized 13- moment-equations for micro-channel-flows. Journal of Computational Physics, 227(3):1982 – 2011, 2008. 83 [86] E. A. Uehling. Transport phenomena in einstein-bose and fermi-dirac gases. ii. Phys. Rev., 46(10):917–929, Nov 1934. 6 [87] E. A. Uehling and G. E. Uhlenbeck. Transport phenomena in einsteinbose and fermi-dirac gases. i. Phys. Rev., 43(7):552–561, Apr 1933. 2 [88] E. A. Uehling and G. E. Uhlenbeck. Transport phenomena in einsteinbose and fermi-dirac gases. i. Phys. Rev., 43(7):552–561, Apr 1933. 6 [89] B. van Leer. Towards the ultimate conservative difference scheme. v. a second-order sequel to godunov’s method. Journal of Computational Physics, 32(1):101 – 136, 1979. 39, 44, 97 [90] Z. J. Wang, R. F. C. Phen, N. Hariharan, and A. J. Przekwas. A 2n tree based automated viscous cartesian grid methodology for feature capturing. AIAA-99-3300, 1999. 42 [91] E. T. Whittaker and G. Robinson. The Newton-Cotes Formulae of Integration in The Calculus of Observations: A Treatise on Numerical Mathematics, 4th ed. Dover, New York, 1967. 30 [92] E. Wigner. On the quantum correction for thermodynamic equilibrium. Phys. Rev., 40(5):749–759, Jun 1932. 2 [93] D. L. Woolard, H. Tian, M. A. Littlejohn, K. W. Kim, R. J. Trew, M. K. Ieong, and T. W. Tang. Construction of higher-moment terms in the hydrodynamic electron transport model. Journal of Applied Physics, 74(10):6197 –6207, nov 1993. 2 156 Bibliography [94] K. Xu. Numerical Hydrodynamics from Gas-Kinetic Theory. PhD thesis, Columbia University, 1993. 8 [95] Z. Xu and C.-W. Shu. Anti-diffusive flux corrections for high order finite difference weno schemes. Journal of Computational Physics, 205(2):458 – 485, 2005. 4 [96] J. Y. Yang, T. Hsieh, and Y. H. Shi. Kinetic flux vector splitting schemes for ideal quantum gas dynamics. SIAM J. Sci. Comput., 29(1):221–244, 2007. 20, 116 [97] J. Y. Yang, T. Y. Hsieh, and Y. H. Shi. Kinetic flux vector splitting schemes for ideal quantum gas dynamics. SIAM J. Sci. Comput., 29(1):221–244, 2007. 9 [98] J. Y. Yang and C. A. Hsu. High-resolution, nonoscillatory schemes for unsteady compressible flows. AIAA, 30:1570, 1992. 51 [99] J. Y. Yang and J. C. Huang. Rarefied flow computations using nonlinear model boltzmann equations. Journal of Computational Physics, 120(2):323 – 339, 1995. 4, 8, 9, 29, 30, 49, 51, 56, 100 [100] J. Y. Yang and L. H. Hung. Lattice uehling-uhlenbeck boltzmannbhatnagar- gross-krook hydrodynamics of quantum gases. Phys. Rev. E, 79(5):056708, May 2009. 9, 116 [101] J. Y. Yang, L. H. Hung, and S. H. Hu. semiclassical lattice hydrodynamics of rarefied channel flows. Applied Mathematics and Computation, In Press, Corrected Proof:–, 2010. 9, 116 Bibliography 157 [102] J. Y. Yang, L. H. Hung, and Y. T. Kuo. semiclassical axisymmetric lattice boltzmann method. Adv. Appl. Math. Mech., 2(5):626–639, Oct 2010. 9, 116 [103] J.-Y. Yang and B. P. Muljadi. Simulation of shock wave diffraction over 90 degree sharp corner in gases of arbitrary statistics. J. Stat. Phys, 145:1674 – 1688, 2011. 9, 101 [104] J. Y. Yang and Y. H. Shi. A kinetic beam scheme for ideal quantum gas dynamics. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 462(2069):1553–1572, 2006. 9, 20, 75, 116 [105] Z. C. Zhang, S. T. J. Yu, and S. C. Chang. A space-time conservation element and solution element method for solving the two- and threedimensional unsteady euler equations using quadrilateral and hexahedral meshes. Journal of Computational Physics, 175(1):168 – 199, 2002. 117 | |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/16193 | - |
dc.description.abstract | 本文對於求解不同統計粒子流動問題提出一種新的通用計算解法。三種統計粒子
分別遵循Maxwell-Boltzmann、 Fermi-Dirac 以及 Bose-Einstein 統計。基於BGK 方法 (Bhatnagar-Gross-Krook method) 利用鬆弛時間近似處理相空間中應用於廣 泛Knudsen 數範圍內的氣體動力學問題。 本數值方法使用離散座標法(discrete ordinate method)對於半古典分布函數中的速 度空間做處理,使其轉換為一組含有源項的純量守恆律。使用高階方法包含全變 量消逝法(Total Variation Diminishing / TVD) 、基本不振盪法 (Essentially Non-Oscillatory)、加權型基本不振盪法 (Weighted Essentially Non-Oscillatory schemes) 以及CE/SE (Conservation Element/Solution Element) 方法來演算物理 空間與時間內的解。本文發展出在卡氏座標以及通用座標中求解多維度問題的顯 式與隱式算則。 數值實驗包含 (1) 不同統計粒子在各種Knudsen 數和鬆弛時間下的一維震波管 問題 (2) 正交和非正交格點下使用不同鬆弛時間的二維穩態及暫態氣體流動問 題。針對初始及邊界值問題測試了各種顯式及隱式求解器。由數值實驗結果可知, 本文所提出的數值方法為可行且可靠的方法。 | zh_TW |
dc.description.abstract | This dissertation aims to provide a novel unified computational method to solve gas flows problems of arbitrary particle statistics namely, Maxwell-Boltzmann,
Fermi-Dirac and Bose-Einstein statistics. The relaxation time approximation based on Bhatnagar-Gross-Krook method was implemented in phase space in order to tackle gas dynamics problems in a wide range of Knudsen numbers. The numerical method is based on the discrete ordinate method to render the velocity space of the semiclassical distribution function resulting in a set of scalar conservation laws with source terms. High resolution methods comprising Total Variation Diminishing (TVD), Essentially Non-Oscillatory, Weighted Essentially Non-Oscillatory schemes (ENO/WENO) and Conservation Element / Solution Element (CE/SE) were used for evolving the solution in physical space and time. The classes of explicit and implicit schemes for solving multi-dimensional problems in Cartesian and general coordinate were developed. The computational experiments include (1) One-dimensional shock tube problem in which the range of Knudsen numbers and relaxation times were tested for gases obeying the three statistics, (2) Two-dimensional gas flow problems covering both transient and steady state cases on Cartesian and curvilinear grids and various relaxation times. The variants of explicit and implicit solvers were tested on initial and boundary value problems. The results from the computational experiments shows the feasibility and robustness of the current method. | en |
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dc.description.tableofcontents | Contents
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1 Introduction 1 1.1 Background and Overview . . . . . . . . . . . . . . . . . . . . 2 1.2 Objectives and Scope of the Dissertation . . . . . . . . . . . . 4 1.3 Organization of Thesis . . . . . . . . . . . . . . . . . . . . . . 5 2 Semiclassical Kinetic Theory 7 2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Semiclassical Gas Dynamics . . . . . . . . . . . . . . . . . . . 10 2.3 Semiclassical Boltzmann - BGK Equation . . . . . . . . . . . 15 2.4 Semiclassical Hydrodynamic Equations . . . . . . . . . . . . . 17 2.5 Classical limit . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.6 Normalization . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3 Discrete Ordinate Method 27 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2 Quadrature Methods . . . . . . . . . . . . . . . . . . . . . . . 29 3.3 Application of Discrete Ordinate Method . . . . . . . . . . . . 31 4 Numerical Methods 35 4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.2 Computational Methods for One-Dimensional Case . . . . . . 37 4.2.1 Implementation of Upwind Based WENO and TVD Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 ii Contents 4.2.2 Implementation of Space-Time CE/SE w .. . . . . . 40 4.3 Computational Methods for Two-Dimensional Case . . . . . . 41 4.4 Numerical Methods on Cartesian Grid . . . . . . . . . . . . . 41 4.4.1 Explicit Methods on Cartesian Coordinate . . . . . . . 42 4.4.2 Implicit Methods on Cartesian Coordinate . . . . . . . 45 4.5 Numerical Methods on Curvilinear Grid . . . . . . . . . . . . 48 4.5.1 Explicit Methods on Curvilinear Coordinate . . . . . . 50 4.5.2 Implicit Methods on Curvilinear Coordinate . . . . . . 53 4.6 Adiabatic, Absorbing and Maxwellian types of Boundary Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.7 Boundary Condition for Implicit Schemes . . . . . . . . . . . . 56 5 Numerical Results 61 5.1 One Dimensional Gas-Flow Problems . . . . . . . . . . . . . . 62 5.1.1 Mesh refinement tests . . . . . . . . . . . . . . . . . . 62 5.1.2 Application of constant relaxation time values . . . . . 63 5.1.3 Application of varying Knudsen numbers . . . . . . . . 65 5.1.4 Recovery to classical limit . . . . . . . . . . . . . . . . 66 5.1.5 Comparison with TVD scheme . . . . . . . . . . . . . . 68 5.1.6 Application of Space Time Conservation Element Solution Element schemes . . . . . . . . . . . . . . . . . . . 71 5.2 Two Dimensional Gas-Flow Problems . . . . . . . . . . . . . . 73 5.2.1 Initial Value Problems . . . . . . . . . . . . . . . . . . 73 5.2.2 Boundary Value Problems . . . . . . . . . . . . . . . . 78 6 Conclusions and Future Work 113 6.1 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . 113 6.2 Future works . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Contents iii A Space-Time Conservation Element/Solution Element (CE/SE) w .. scheme 117 A.0.1 a .. scheme . . . . . . . . . . . . . . . . . . . . . . . 120 A.0.2 a .. ' and c scheme . . . . . . . . . . . . . . . . . . . . 121 A.0.3 Wiggle-suppressing terms . . . . . . . . . . . . . . . . 123 A.0.4 c .. c scheme . . . . . . . . . . . . . . . . . . . . . . . 124 A.0.5 Algorithm summary . . . . . . . . . . . . . . . . . . . 126 B Bose and Fermi Functions 129 C Gauss-Hermite Quadrature Points 131 Bibliography 145 | |
dc.language.iso | en | |
dc.title | 量子統計稀薄氣體直接解法研究 | zh_TW |
dc.title | Development of Direct Solver for Rarefied Flow of Gases of Arbitrary Statistics | en |
dc.type | Thesis | |
dc.date.schoolyear | 100-2 | |
dc.description.degree | 博士 | |
dc.contributor.oralexamcommittee | 林昭安,劉通敏,吳宗信,許文翰,黃俊誠 | |
dc.subject.keyword | 半古典氣體動力學,統計粒子,離散座標法,Maxwell-Boltzmann,Fermi-Dirac,Bose-Einstein, | zh_TW |
dc.subject.keyword | semiclassical gas dynamics,arbitrary particle statistics,discrete ordinate method,Maxwell-Boltzmann,Fermi-Dirac,Bose-Einstein, | en |
dc.relation.page | 157 | |
dc.rights.note | 未授權 | |
dc.date.accepted | 2012-07-27 | |
dc.contributor.author-college | 工學院 | zh_TW |
dc.contributor.author-dept | 應用力學研究所 | zh_TW |
顯示於系所單位: | 應用力學研究所 |
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ntu-101-1.pdf 目前未授權公開取用 | 17.24 MB | Adobe PDF |
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