- Previous Article
- KRM Home
- This Issue
-
Next Article
Large-time decay of the soft potential relativistic Boltzmann equation in $\mathbb{R}^3_x$
Unique moment set from the order of magnitude method
1. | Department of Mechanical Engineering, University of Victoria, Victoria BC V8W 3P6, Canada |
References:
[1] |
A. V. Bobylëv, The Chapman-Enskog and Grad methods for solving the Boltzmann equation, Sov. Phys. Dokl., 27 (1982), 29-31. |
[2] |
S. Chapman and T. G. Cowling, "The Mathematical Theory of Non-Uniform Gases. An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases,'' Third edition, prepared in co-operation with D. Burnett, Cambridge University Press, London, 1970. |
[3] |
H. Grad, Principles of the Kinetic Theory of Gases, in "1958 Handbuch der Physik" (ed. S. Flügge), Bd. 12, Thermodynamik der Gase, Springer-Verlag, Berlin-Göttingen-Heidelberg, (1958), 205-294. |
[4] |
P. Kauf, M. Torrilhon and M. Junk, Scale-induced closure for approximations of kinetic equations, J. Stat. Phys., 141 (2010), 848-888.
doi: 10.1007/s10955-010-0073-y. |
[5] |
M. Frank and B. Seibold, Optimal prediction for radiative transfer: A new perspective on moment closure, Kinetic and Related Models, 4 (2011), 717-733.
doi: 10.3934/krm.2011.4.717. |
[6] |
Y. Sone, "Kinetic Theory and Fluid Dynamics,'' Modeling and Simulation in Science, Engineering and Technology, Birkhäuser Boston, Inc., Boston, MA, 2002. |
[7] |
H. Struchtrup and M. Torrilhon, Regularization of Grad's 13 moment equations: Derivation and linear analysis, Phys. Fluids, 15 (2003), 2668-2680.
doi: 10.1063/1.1597472. |
[8] |
H. Struchtrup, Stable transport equations for rarefied gases at high orders in the Knudsen number, Phys. Fluids, 16 (2004), 3921-3934.
doi: 10.1063/1.1782751. |
[9] |
H. Struchtrup, Derivation of 13 moment equations for rarefied gas flow to second order accuracy for arbitrary interaction potentials, Multiscale Model. Simul., 3 (2004/05), 211-243. |
[10] |
H. Struchtrup, Failures of the Burnett and super-Burnett equations in steady state processes, Cont. Mech. Thermodyn., 17 (2005), 43-50.
doi: 10.1007/s00161-004-0186-0. |
[11] |
H. Struchtrup, "Macroscopic Transport Equations for Rarefied Gas Flows. Approximation Methods in Kinetic Theory,'' Interaction of Mechanics and Mathematics, Springer, Berlin, 2005. |
[12] |
H. Struchtrup, Linear kinetic heat transfer: Moment equations, boundary conditions, and Knudsen layers, Physica A, 387 (2008), 1750-1766.
doi: 10.1016/j.physa.2007.11.044. |
[13] |
H. Struchtrup and P. Taheri, Macroscopic transport models for rarefied gas flows: A brief review, IMA J. Appl. Math., 76 (2011), 672-697.
doi: 10.1093/imamat/hxr004. |
[14] |
M. Schäfer, M. Frank and C. D. Levermore, Diffusive correction to $P_N-$ approximations, Multiscale. Model. Simul., 9 (2011), 1-28.
doi: 10.1137/090764542. |
[15] |
Y. Zheng and H. Struchtrup, Burnett equations for the ellipsoidal statistical BGK Model, Cont. Mech. Thermodyn., 16 (2004), 97-108.
doi: 10.1007/s00161-003-0143-3. |
show all references
References:
[1] |
A. V. Bobylëv, The Chapman-Enskog and Grad methods for solving the Boltzmann equation, Sov. Phys. Dokl., 27 (1982), 29-31. |
[2] |
S. Chapman and T. G. Cowling, "The Mathematical Theory of Non-Uniform Gases. An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases,'' Third edition, prepared in co-operation with D. Burnett, Cambridge University Press, London, 1970. |
[3] |
H. Grad, Principles of the Kinetic Theory of Gases, in "1958 Handbuch der Physik" (ed. S. Flügge), Bd. 12, Thermodynamik der Gase, Springer-Verlag, Berlin-Göttingen-Heidelberg, (1958), 205-294. |
[4] |
P. Kauf, M. Torrilhon and M. Junk, Scale-induced closure for approximations of kinetic equations, J. Stat. Phys., 141 (2010), 848-888.
doi: 10.1007/s10955-010-0073-y. |
[5] |
M. Frank and B. Seibold, Optimal prediction for radiative transfer: A new perspective on moment closure, Kinetic and Related Models, 4 (2011), 717-733.
doi: 10.3934/krm.2011.4.717. |
[6] |
Y. Sone, "Kinetic Theory and Fluid Dynamics,'' Modeling and Simulation in Science, Engineering and Technology, Birkhäuser Boston, Inc., Boston, MA, 2002. |
[7] |
H. Struchtrup and M. Torrilhon, Regularization of Grad's 13 moment equations: Derivation and linear analysis, Phys. Fluids, 15 (2003), 2668-2680.
doi: 10.1063/1.1597472. |
[8] |
H. Struchtrup, Stable transport equations for rarefied gases at high orders in the Knudsen number, Phys. Fluids, 16 (2004), 3921-3934.
doi: 10.1063/1.1782751. |
[9] |
H. Struchtrup, Derivation of 13 moment equations for rarefied gas flow to second order accuracy for arbitrary interaction potentials, Multiscale Model. Simul., 3 (2004/05), 211-243. |
[10] |
H. Struchtrup, Failures of the Burnett and super-Burnett equations in steady state processes, Cont. Mech. Thermodyn., 17 (2005), 43-50.
doi: 10.1007/s00161-004-0186-0. |
[11] |
H. Struchtrup, "Macroscopic Transport Equations for Rarefied Gas Flows. Approximation Methods in Kinetic Theory,'' Interaction of Mechanics and Mathematics, Springer, Berlin, 2005. |
[12] |
H. Struchtrup, Linear kinetic heat transfer: Moment equations, boundary conditions, and Knudsen layers, Physica A, 387 (2008), 1750-1766.
doi: 10.1016/j.physa.2007.11.044. |
[13] |
H. Struchtrup and P. Taheri, Macroscopic transport models for rarefied gas flows: A brief review, IMA J. Appl. Math., 76 (2011), 672-697.
doi: 10.1093/imamat/hxr004. |
[14] |
M. Schäfer, M. Frank and C. D. Levermore, Diffusive correction to $P_N-$ approximations, Multiscale. Model. Simul., 9 (2011), 1-28.
doi: 10.1137/090764542. |
[15] |
Y. Zheng and H. Struchtrup, Burnett equations for the ellipsoidal statistical BGK Model, Cont. Mech. Thermodyn., 16 (2004), 97-108.
doi: 10.1007/s00161-003-0143-3. |
[1] |
Céline Baranger, Marzia Bisi, Stéphane Brull, Laurent Desvillettes. On the Chapman-Enskog asymptotics for a mixture of monoatomic and polyatomic rarefied gases. Kinetic and Related Models, 2018, 11 (4) : 821-858. doi: 10.3934/krm.2018033 |
[2] |
Vincent Giovangigli, Wen-An Yong. Volume viscosity and internal energy relaxation: Symmetrization and Chapman-Enskog expansion. Kinetic and Related Models, 2015, 8 (1) : 79-116. doi: 10.3934/krm.2015.8.79 |
[3] |
Pierre Degond, Amic Frouvelle, Jian-Guo Liu. From kinetic to fluid models of liquid crystals by the moment method. Kinetic and Related Models, 2022, 15 (3) : 417-465. doi: 10.3934/krm.2021047 |
[4] |
Kaifang Liu, Lunji Song, Shan Zhao. A new over-penalized weak galerkin method. Part Ⅰ: Second-order elliptic problems. Discrete and Continuous Dynamical Systems - B, 2021, 26 (5) : 2411-2428. doi: 10.3934/dcdsb.2020184 |
[5] |
Sho Matsumoto, Jonathan Novak. A moment method for invariant ensembles. Electronic Research Announcements, 2018, 25: 60-71. doi: 10.3934/era.2018.25.007 |
[6] |
Vincent Giovangigli, Wen-An Yong. Erratum: ``Volume viscosity and internal energy relaxation: Symmetrization and Chapman-Enskog expansion''. Kinetic and Related Models, 2016, 9 (4) : 813-813. doi: 10.3934/krm.2016018 |
[7] |
Gilberto M. Kremer, Wilson Marques Jr.. Fourteen moment theory for granular gases. Kinetic and Related Models, 2011, 4 (1) : 317-331. doi: 10.3934/krm.2011.4.317 |
[8] |
Pierre Lissy. Construction of gevrey functions with compact support using the bray-mandelbrojt iterative process and applications to the moment method in control theory. Mathematical Control and Related Fields, 2017, 7 (1) : 21-40. doi: 10.3934/mcrf.2017002 |
[9] |
Giacomo Dimarco. The moment guided Monte Carlo method for the Boltzmann equation. Kinetic and Related Models, 2013, 6 (2) : 291-315. doi: 10.3934/krm.2013.6.291 |
[10] |
Lunji Song, Wenya Qi, Kaifang Liu, Qingxian Gu. A new over-penalized weak galerkin finite element method. Part Ⅱ: Elliptic interface problems. Discrete and Continuous Dynamical Systems - B, 2021, 26 (5) : 2581-2598. doi: 10.3934/dcdsb.2020196 |
[11] |
Jiantao Jiang, Jing An, Jianwei Zhou. A novel numerical method based on a high order polynomial approximation of the fourth order Steklov equation and its eigenvalue problems. Discrete and Continuous Dynamical Systems - B, 2022 doi: 10.3934/dcdsb.2022066 |
[12] |
Luciano Pandolfi. Riesz systems and moment method in the study of viscoelasticity in one space dimension. Discrete and Continuous Dynamical Systems - B, 2010, 14 (4) : 1487-1510. doi: 10.3934/dcdsb.2010.14.1487 |
[13] |
Shigeru Takata, Hitoshi Funagane, Kazuo Aoki. Fluid modeling for the Knudsen compressor: Case of polyatomic gases. Kinetic and Related Models, 2010, 3 (2) : 353-372. doi: 10.3934/krm.2010.3.353 |
[14] |
Christopher Bose, Rua Murray. The exact rate of approximation in Ulam's method. Discrete and Continuous Dynamical Systems, 2001, 7 (1) : 219-235. doi: 10.3934/dcds.2001.7.219 |
[15] |
Chen Li, Fajie Wei, Shenghan Zhou. Prediction method based on optimization theory and its application. Discrete and Continuous Dynamical Systems - S, 2015, 8 (6) : 1213-1221. doi: 10.3934/dcdss.2015.8.1213 |
[16] |
Palash Sarkar, Shashank Singh. A unified polynomial selection method for the (tower) number field sieve algorithm. Advances in Mathematics of Communications, 2019, 13 (3) : 435-455. doi: 10.3934/amc.2019028 |
[17] |
Feng Ma, Mingfang Ni. A two-phase method for multidimensional number partitioning problem. Numerical Algebra, Control and Optimization, 2013, 3 (2) : 203-206. doi: 10.3934/naco.2013.3.203 |
[18] |
Sergio Grillo, Leandro Salomone, Marcela Zuccalli. Explicit solutions of the kinetic and potential matching conditions of the energy shaping method. Journal of Geometric Mechanics, 2021, 13 (4) : 629-646. doi: 10.3934/jgm.2021022 |
[19] |
Aleksa Srdanov, Radiša Stefanović, Aleksandra Janković, Dragan Milovanović. "Reducing the number of dimensions of the possible solution space" as a method for finding the exact solution of a system with a large number of unknowns. Mathematical Foundations of Computing, 2019, 2 (2) : 83-93. doi: 10.3934/mfc.2019007 |
[20] |
Xiaojun Chen, Guihua Lin. CVaR-based formulation and approximation method for stochastic variational inequalities. Numerical Algebra, Control and Optimization, 2011, 1 (1) : 35-48. doi: 10.3934/naco.2011.1.35 |
2020 Impact Factor: 1.432
Tools
Metrics
Other articles
by authors
[Back to Top]