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Approximating the $M_2$ method by the extended quadrature method of moments for radiative transfer in slab geometry
1. | Department of Mathematics RWTH Aachen University, Aachen, Germany |
2. | CAPT, LMAM & School of Mathematical Sciences, Peking University, Beijing, China |
3. | School of Mathematical Sciences, Peking University, Beijing, China |
References:
[1] |
G. W. Alldredge, C. D. Hauck, D. P. O'Leary and A. L. Tits, Adaptive change of basis in entropy-based moment closures for linear kinetic equations,, Journal of Computational Physics, 258 (2014), 489.
doi: 10.1016/j.jcp.2013.10.049. |
[2] |
G. W. Alldredge, C. D. Hauck and A. L. Tits, High-order entropy-based closures for linear transport in slab geometry ii: A computational study of the optimization problem,, SIAM Journal on Scientific Computing, 34 (2012).
doi: 10.1137/11084772X. |
[3] |
C. Berthon, P. Charrier and B. Dubroca, An hllc scheme to solve the $M_1$ model of radiative transfer in two space dimensions,, Journal of Scientific Computing, 31 (2007), 347.
doi: 10.1007/s10915-006-9108-6. |
[4] |
T. A. Brunner, Forms of Approximate Radiation Transport,, Tech. Rep SAND2002-1778, (2002), 2002. Google Scholar |
[5] |
T. A. Brunner and J. P. Holloway, One-dimensional riemann solvers and the maximum entropy closure,, Journal of Quantitative Spectroscopy and Radiative Transfer, 69 (2001), 543.
doi: 10.1016/S0022-4073(00)00099-6. |
[6] |
R. Curto and L. Fialkow, Recursiveness, positivity and truncated moment problems,, Houston J. Math, 17 (1991), 603.
|
[7] |
B. Dubroca and J.-L. Fuegas, Étude théorique et numérique d'une hiérarchie de modèles aus moments pour le transfert radiatif,, C.R. Acad. Sci. Paris, 329 (1999), 915.
doi: 10.1016/S0764-4442(00)87499-6. |
[8] |
C. K. Garrett, C. Hauck and J. Hill, Optimization and large scale computation of an entropy-based moment closure,, Journal of Computational Physics, 302 (2015), 573.
|
[9] |
C. D. Levermore, Moment closure hierarchies for kinetic theories,, Journal of Statistical Physics, 83 (1996), 1021.
doi: 10.1007/BF02179552. |
[10] |
E. E. Lewis and W. F. Miller, Jr, Computational Methods in Neutron Transport,, John Wiley and Sons, (1984). Google Scholar |
[11] |
R. G. McClarren, J. P. Holloway and T. A. Brunner, On solutions to the $P_n$ equations for thermal radiative transfer,, Journal of Computational Physics, 227 (2008), 2864.
doi: 10.1016/j.jcp.2007.11.027. |
[12] |
E. Olbrant, C. D. Hauck and M. Frank, A realizability-preserving discontinuous galerkin method for the m1 model of radiative transfer,, Journal of Computational Physics, 231 (2012), 5612.
doi: 10.1016/j.jcp.2012.03.002. |
[13] |
G. C. Pomraning, The Equations of Radiation Hydrodynamics,, Courier Dover Publications, (1973). Google Scholar |
[14] |
B. Su and G. L. Olson, An analytical benchmark for non-equilibrium radiative transfer in an isotropically scattering medium,, Annals of Nuclear Energy, 24 (1997), 1035.
doi: 10.1016/S0306-4549(96)00100-4. |
[15] |
E. F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction,, Springer Science & Business Media, (2009).
doi: 10.1007/b79761. |
[16] |
V. Vikas, C. D. Hauck, Z. J. Wang and R. O. Fox, Radiation transport modeling using extended quadrature method of moments,, Journal of Computational Physics, 246 (2013), 221.
doi: 10.1016/j.jcp.2013.03.028. |
show all references
References:
[1] |
G. W. Alldredge, C. D. Hauck, D. P. O'Leary and A. L. Tits, Adaptive change of basis in entropy-based moment closures for linear kinetic equations,, Journal of Computational Physics, 258 (2014), 489.
doi: 10.1016/j.jcp.2013.10.049. |
[2] |
G. W. Alldredge, C. D. Hauck and A. L. Tits, High-order entropy-based closures for linear transport in slab geometry ii: A computational study of the optimization problem,, SIAM Journal on Scientific Computing, 34 (2012).
doi: 10.1137/11084772X. |
[3] |
C. Berthon, P. Charrier and B. Dubroca, An hllc scheme to solve the $M_1$ model of radiative transfer in two space dimensions,, Journal of Scientific Computing, 31 (2007), 347.
doi: 10.1007/s10915-006-9108-6. |
[4] |
T. A. Brunner, Forms of Approximate Radiation Transport,, Tech. Rep SAND2002-1778, (2002), 2002. Google Scholar |
[5] |
T. A. Brunner and J. P. Holloway, One-dimensional riemann solvers and the maximum entropy closure,, Journal of Quantitative Spectroscopy and Radiative Transfer, 69 (2001), 543.
doi: 10.1016/S0022-4073(00)00099-6. |
[6] |
R. Curto and L. Fialkow, Recursiveness, positivity and truncated moment problems,, Houston J. Math, 17 (1991), 603.
|
[7] |
B. Dubroca and J.-L. Fuegas, Étude théorique et numérique d'une hiérarchie de modèles aus moments pour le transfert radiatif,, C.R. Acad. Sci. Paris, 329 (1999), 915.
doi: 10.1016/S0764-4442(00)87499-6. |
[8] |
C. K. Garrett, C. Hauck and J. Hill, Optimization and large scale computation of an entropy-based moment closure,, Journal of Computational Physics, 302 (2015), 573.
|
[9] |
C. D. Levermore, Moment closure hierarchies for kinetic theories,, Journal of Statistical Physics, 83 (1996), 1021.
doi: 10.1007/BF02179552. |
[10] |
E. E. Lewis and W. F. Miller, Jr, Computational Methods in Neutron Transport,, John Wiley and Sons, (1984). Google Scholar |
[11] |
R. G. McClarren, J. P. Holloway and T. A. Brunner, On solutions to the $P_n$ equations for thermal radiative transfer,, Journal of Computational Physics, 227 (2008), 2864.
doi: 10.1016/j.jcp.2007.11.027. |
[12] |
E. Olbrant, C. D. Hauck and M. Frank, A realizability-preserving discontinuous galerkin method for the m1 model of radiative transfer,, Journal of Computational Physics, 231 (2012), 5612.
doi: 10.1016/j.jcp.2012.03.002. |
[13] |
G. C. Pomraning, The Equations of Radiation Hydrodynamics,, Courier Dover Publications, (1973). Google Scholar |
[14] |
B. Su and G. L. Olson, An analytical benchmark for non-equilibrium radiative transfer in an isotropically scattering medium,, Annals of Nuclear Energy, 24 (1997), 1035.
doi: 10.1016/S0306-4549(96)00100-4. |
[15] |
E. F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction,, Springer Science & Business Media, (2009).
doi: 10.1007/b79761. |
[16] |
V. Vikas, C. D. Hauck, Z. J. Wang and R. O. Fox, Radiation transport modeling using extended quadrature method of moments,, Journal of Computational Physics, 246 (2013), 221.
doi: 10.1016/j.jcp.2013.03.028. |
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