-
Previous Article
New insights into the numerical solution of the Boltzmann transport equation for photons
- KRM Home
- This Issue
- Next Article
On hyperbolicity of 13-moment system
1. | CAPT & School of Mathematical Sciences, Peking University, Yiheyuan Road 5, 100871 Beijing, China |
2. | School of Mathematical Sciences, Peking University, Yiheyuan Road 5, 100871 Beijing, China |
3. | HEDPS, CAPT & School of Mathematical Sciences, Peking University, Yiheyuan Road 5, 100871 Beijing, China |
References:
[1] |
G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Clarendon Press, Oxford, 1995. |
[2] |
S. Chapman and T. G. Cowling, The Mathematical Theory of Non-uniform Gases, $3^{rd}$ edition, Cambridge University Press, Cambridge, 1990. |
[3] |
H. Grad, Note on $N$-dimensional Hermite polynomials, Comm. Pure Appl. Math., 2 (1949), 325-330.
doi: 10.1002/cpa.3160020402. |
[4] |
H. Grad, On the kinetic theory of rarefied gases, Comm. Pure Appl. Math., 2 (1949), 331-407.
doi: 10.1002/cpa.3160020403. |
[5] |
S. Jin, L. Pareschi and M. Slemrod, A relaxation scheme for solving the Boltzmann equation based on the Chapman-Enskog expansion, Acta Math. Appl. Sin.-E., 18 (2002), 37-62.
doi: 10.1007/s102550200003. |
[6] |
S. Jin and M. Slemrod, Regularization of the Burnett equations via relaxation, J. Stat. Phys., 103 (2001), 1009-1033.
doi: 10.1023/A:1010365123288. |
[7] |
G. Karniadakis, A. Beskok and N. Aluru, Microflows and Nanoflows: Fundamentals and Simulation, Springer, New York, 2005. |
[8] |
I. Müller and T. Ruggeri, Rational Extended Thermodynamics, $2^{nd}$ edition, Springer Tracts in Natural Philosophy, Vol. 37, Springer-Verlag, New York, 1998.
doi: 10.1007/978-1-4612-2210-1. |
[9] |
L. Mieussens and H. Struchtrup, Numerical comparison of Bhatnagar-Gross-Krook models with proper Prandtl number, Phys. Fluids, 16 (2004), 2797-2813.
doi: 10.1063/1.1758217. |
[10] |
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. |
[11] |
H. Struchtrup, Derivation of 13 moment equations for rarefied gas flow to second order accuracy for arbitrary interaction potentials,, Multiscale Model. Simul., 3 (): 221.
doi: 10.1137/040603115. |
[12] |
M. Torrilhon, Regularized 13-moment-equations, in Proceedings of Rarefied Gas Dynamics: 25th International Symposium (eds. M. S. Ivanov and A. K. Rebrov), 2006, 167-172. |
[13] |
M. Torrilhon, Hyperbolic moment equations in kinetic gas theory based on multi-variate Pearson-IV-distributions, Commun. Comput. Phys., 7 (2010), 639-673.
doi: 10.4208/cicp.2009.09.049. |
[14] |
Wolfram Research, Mathematica 9,, , ().
|
show all references
References:
[1] |
G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Clarendon Press, Oxford, 1995. |
[2] |
S. Chapman and T. G. Cowling, The Mathematical Theory of Non-uniform Gases, $3^{rd}$ edition, Cambridge University Press, Cambridge, 1990. |
[3] |
H. Grad, Note on $N$-dimensional Hermite polynomials, Comm. Pure Appl. Math., 2 (1949), 325-330.
doi: 10.1002/cpa.3160020402. |
[4] |
H. Grad, On the kinetic theory of rarefied gases, Comm. Pure Appl. Math., 2 (1949), 331-407.
doi: 10.1002/cpa.3160020403. |
[5] |
S. Jin, L. Pareschi and M. Slemrod, A relaxation scheme for solving the Boltzmann equation based on the Chapman-Enskog expansion, Acta Math. Appl. Sin.-E., 18 (2002), 37-62.
doi: 10.1007/s102550200003. |
[6] |
S. Jin and M. Slemrod, Regularization of the Burnett equations via relaxation, J. Stat. Phys., 103 (2001), 1009-1033.
doi: 10.1023/A:1010365123288. |
[7] |
G. Karniadakis, A. Beskok and N. Aluru, Microflows and Nanoflows: Fundamentals and Simulation, Springer, New York, 2005. |
[8] |
I. Müller and T. Ruggeri, Rational Extended Thermodynamics, $2^{nd}$ edition, Springer Tracts in Natural Philosophy, Vol. 37, Springer-Verlag, New York, 1998.
doi: 10.1007/978-1-4612-2210-1. |
[9] |
L. Mieussens and H. Struchtrup, Numerical comparison of Bhatnagar-Gross-Krook models with proper Prandtl number, Phys. Fluids, 16 (2004), 2797-2813.
doi: 10.1063/1.1758217. |
[10] |
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. |
[11] |
H. Struchtrup, Derivation of 13 moment equations for rarefied gas flow to second order accuracy for arbitrary interaction potentials,, Multiscale Model. Simul., 3 (): 221.
doi: 10.1137/040603115. |
[12] |
M. Torrilhon, Regularized 13-moment-equations, in Proceedings of Rarefied Gas Dynamics: 25th International Symposium (eds. M. S. Ivanov and A. K. Rebrov), 2006, 167-172. |
[13] |
M. Torrilhon, Hyperbolic moment equations in kinetic gas theory based on multi-variate Pearson-IV-distributions, Commun. Comput. Phys., 7 (2010), 639-673.
doi: 10.4208/cicp.2009.09.049. |
[14] |
Wolfram Research, Mathematica 9,, , ().
|
[1] |
Manuel Torrilhon. H-Theorem for nonlinear regularized 13-moment equations in kinetic gas theory. Kinetic and Related Models, 2012, 5 (1) : 185-201. doi: 10.3934/krm.2012.5.185 |
[2] |
Jessy Mallet, Stéphane Brull, Bruno Dubroca. General moment system for plasma physics based on minimum entropy principle. Kinetic and Related Models, 2015, 8 (3) : 533-558. doi: 10.3934/krm.2015.8.533 |
[3] |
Yi Zhang, Yuyun Zhao, Tao Xu, Xin Liu. $p$th Moment absolute exponential stability of stochastic control system with Markovian switching. Journal of Industrial and Management Optimization, 2016, 12 (2) : 471-486. doi: 10.3934/jimo.2016.12.471 |
[4] |
Peter Bella, Arianna Giunti. Green's function for elliptic systems: Moment bounds. Networks and Heterogeneous Media, 2018, 13 (1) : 155-176. doi: 10.3934/nhm.2018007 |
[5] |
Teddy Pichard. A moment closure based on a projection on the boundary of the realizability domain: 1D case. Kinetic and Related Models, 2020, 13 (6) : 1243-1280. doi: 10.3934/krm.2020045 |
[6] |
Sho Matsumoto, Jonathan Novak. A moment method for invariant ensembles. Electronic Research Announcements, 2018, 25: 60-71. doi: 10.3934/era.2018.25.007 |
[7] |
Paweł Lubowiecki, Henryk Żołądek. The Hess-Appelrot system. I. Invariant torus and its normal hyperbolicity. Journal of Geometric Mechanics, 2012, 4 (4) : 443-467. doi: 10.3934/jgm.2012.4.443 |
[8] |
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 |
[9] |
Swann Marx, Tillmann Weisser, Didier Henrion, Jean Bernard Lasserre. A moment approach for entropy solutions to nonlinear hyperbolic PDEs. Mathematical Control and Related Fields, 2020, 10 (1) : 113-140. doi: 10.3934/mcrf.2019032 |
[10] |
Laurent Baratchart, Sylvain Chevillard, Douglas Hardin, Juliette Leblond, Eduardo Andrade Lima, Jean-Paul Marmorat. Magnetic moment estimation and bounded extremal problems. Inverse Problems and Imaging, 2019, 13 (1) : 39-67. doi: 10.3934/ipi.2019003 |
[11] |
Henning Struchtrup. Unique moment set from the order of magnitude method. Kinetic and Related Models, 2012, 5 (2) : 417-440. doi: 10.3934/krm.2012.5.417 |
[12] |
Darryl D. Holm, Cesare Tronci. Geodesic Vlasov equations and their integrable moment closures. Journal of Geometric Mechanics, 2009, 1 (2) : 181-208. doi: 10.3934/jgm.2009.1.181 |
[13] |
Miroslava Růžičková, Irada Dzhalladova, Jitka Laitochová, Josef Diblík. Solution to a stochastic pursuit model using moment equations. Discrete and Continuous Dynamical Systems - B, 2018, 23 (1) : 473-485. doi: 10.3934/dcdsb.2018032 |
[14] |
Florian Méhats, Olivier Pinaud. A problem of moment realizability in quantum statistical physics. Kinetic and Related Models, 2011, 4 (4) : 1143-1158. doi: 10.3934/krm.2011.4.1143 |
[15] |
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 |
[16] |
Julian Koellermeier, Giovanni Samaey. Projective integration schemes for hyperbolic moment equations. Kinetic and Related Models, 2021, 14 (2) : 353-387. doi: 10.3934/krm.2021008 |
[17] |
Radosław Kurek, Paweł Lubowiecki, Henryk Żołądek. The Hess-Appelrot system. Ⅲ. Splitting of separatrices and chaos. Discrete and Continuous Dynamical Systems, 2018, 38 (4) : 1955-1981. doi: 10.3934/dcds.2018079 |
[18] |
Quyen Tran, Harbir Antil, Hugo Díaz. Optimal control of parameterized stationary Maxwell's system: Reduced basis, convergence analysis, and a posteriori error estimates. Mathematical Control and Related Fields, 2022 doi: 10.3934/mcrf.2022003 |
[19] |
Henri Schurz. Moment attractivity, stability and contractivity exponents of stochastic dynamical systems. Discrete and Continuous Dynamical Systems, 2001, 7 (3) : 487-515. doi: 10.3934/dcds.2001.7.487 |
[20] |
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 |
2020 Impact Factor: 1.432
Tools
Metrics
Other articles
by authors
[Back to Top]