Free Access
Volume 54, Number 5, September-October 2020
Page(s) 1465 - 1490
Published online 26 June 2020
  1. J.W. Bates, D.A. Knoll, W.J. Rider, R.B. Lowrie and V.A. Mousseau, On consistent time-integration methods for radiation hydrodynamics in the equilibrium diffusion limit: low-energy-density regime. J. Comput. Phys. 167 (2001) 99–130. [Google Scholar]
  2. P.N. Brown, D.E. Shumaker and C.S. Woodward, Fully implicit solution of large-scale non-equilibrium radiation diffusion with high order time integration. J. Comput. Phys. 204 (2005) 760–783. [Google Scholar]
  3. X. Cui and J.Y. Yue, Property analysis and quick solutions for nonlinear discrete schemes for conservative diffusion equation. Math. Numer. Sin. 37 (2015) 227–246. [Google Scholar]
  4. X. Cui, G.W. Yuan and Z.J. Shen, Asymptotic analysis of discrete schemes for nonequilibrium radiation diffusion. J. Comput. Phys. 313 (2016) 415–429. [Google Scholar]
  5. X. Cui, G.W. Yuan and J.Y. Yue, Numerical analysis and iteration acceleration of a fully implicit scheme for nonlinear diffusion problem with second-order time evolution. Numer. Meth. Part. D. E. 32 (2016) 121–140. [CrossRef] [Google Scholar]
  6. X. Cui, Z.J. Shen and G.W. Yuan, Asymptotic-preserving discrete schemes for non-equilibrium radiation diffusion problem in spherical and cylindrical symmetrical geometries. Commun. Comput. Phys. 23 (2018) 198–229. [Google Scholar]
  7. J.D. Densmore and E.W. Larsen, Asymptotic equilibrium diffusion analysis of time-dependent Monte Carlo methods for grey radiative transfer. J. Comput. Phys. 199 (2004) 175–204. [Google Scholar]
  8. J. Droniou, R. Eymard, T. Gallouët, C. Guichard and R. Herbin, The gradient discretisation method: a framework for the discretisation and numerical analysis of linear and nonlinear elliptic and parabolic problems. In Maths & Applications. Springer (2017). [Google Scholar]
  9. L. Even-Dar Mandel and S. Schochet, Uniform discrete Sobolev estimates of solutions to finite difference schemes for singular limits of nonlinear PDEs. ESAIM: M2AN 51 (2017) 727–757. [CrossRef] [EDP Sciences] [Google Scholar]
  10. K.E. Kang, P1 nonconforming finite element multigrid method for radiation transport. SIAM J. Sci. Comput. 25 (2003) 369–384. [Google Scholar]
  11. C.T. Kelley, Solving Nonlinear Equations with Newton’s Method. SIAM, Philadephia (2003). [CrossRef] [Google Scholar]
  12. D.A. Knoll, W.J. Rider and G.L. Olson, An efficient nonlinear solution method for non-equilibrium radiation diffusion. J. Quant. Spectrosc. Radiat. Transfer 63 (1999) 15–29. [CrossRef] [Google Scholar]
  13. D.A. Knoll, W.J. Rider and G.L. Olson, Nonlinear convergence, accuracy, and time step control in non-equilibrium radiation diffusion. J. Quant. Spectrosc. Radiat. Transfer 70 (2001) 25–36. [CrossRef] [Google Scholar]
  14. D.A. Knoll, R.B. Lowrie and J.E. Morel, Numerical analysis of time integration errors for nonequilibrium radiation diffusion. J. Comput. Phys. 226 (2007) 1332–1347. [Google Scholar]
  15. O.A. Ladyzhenskaya, V.A. Solonnikov and N.N. Uraltseva, Linear and Quasilinear Equations of Parabolic Type. American Math. Society (1968). [CrossRef] [Google Scholar]
  16. C.F. Li, Y.R. Yuan and H.L. Song, A mixed volume element with upwind multistep mixed volume element and convergence analysis for numerical simulation of nuclear waste contaminant disposal. J. Comput. Appl. Math. 356 (2019) 164–181. [Google Scholar]
  17. V.A. Mousseau and D.A. Knoll, Temporal accuracy of the nonequilibrium radiation diffusion equations applied to two-dimensional multimaterial simulation. Nucl. Sci. Eng. 154 (2006) 174–189. [Google Scholar]
  18. V.A. Mousseau, D.A. Knoll and W.J. Rider, Physics-based preconditioning and the Newton-Krylov method for non-equilibrium radiation diffusion. J. Comput. Phys. 160 (2000) 743–765. [Google Scholar]
  19. C.Y. Nie, S. Shu, X.D. Hang and J. Cheng, SFVE schemes for radiative heat conduction problems in cylindrical coordinates and numerical simulations. J. Syst. Simul. 24 (2012) 275–283. [Google Scholar]
  20. G.L. Olson, Efficient solution of multi-dimensional flux-limited nonequilibrium radiation diffusion coupled to material conduction with second-order time discretization. J. Comput. Phys. 226 (2007) 1181–1195. [Google Scholar]
  21. M. Pernice and B. Philip, Solution of equilibrium radiation diffusion problems using implicit adaptive mesh refinement. SIAM J. Sci. Comput. 27 (2006) 1709–1726. [Google Scholar]
  22. R.M. Rauenzahn, V.A. Mousseau and D.A. Knoll, Temporal accuracy of the nonequilibrium radiation diffusion equations employing a Saha ionization model. Comput. Phys. Commun. 172 (2005) 109–118. [Google Scholar]
  23. W.J. Rider, D.A. Knoll and G.L. Olson, A multigrid Newton-Krylov method for multidimensional equilibrium radiation diffusion. J. Comput. Phys. 152 (1999) 164–191. [Google Scholar]
  24. Z.Q. Sheng, J.Y. Yue and G.W. Yuan, Monotone finite volume schemes of nonequilibrium radiation diffusion equations on distorted meshes. SIAM J. Sci. Comput. 31 (2009) 2915–2934. [Google Scholar]
  25. A.I. Shestakov, J.L. Milovich and M.K. Prasad, Combining cell- and point-centered methods in 3D, unstructured-grid radiation-hydrodynamic codes. J. Comput. Phys. 170 (2001) 81–111. [Google Scholar]
  26. K.A. Winkler, M.L. Norman and D. Mihalas, Implicit adaptive-grid radiation hydrodynamics. In: Multiple Time Scales. Academic Press, New York (1985). [Google Scholar]
  27. X.B. Yang, W.Z. Huang and J.X. Qiu, A moving mesh finite difference method for equilibrium radiation diffusion equations. J. Comput. Phys. 298 (2015) 661–677. [Google Scholar]
  28. G.W. Yuan and X.D. Hang, Acceleration methods of nonlinear iteration for nonlinear parabolic equations. J. Comput. Math. 24 (2006) 412–424. [Google Scholar]
  29. G.W. Yuan, X.D. Hang, Z.Q. Sheng and J.Y. Yue, Progress in numerical methods for radiation diffusion equations. Chin. J. Comput. Phys. 26 (2009) 475–500. [Google Scholar]
  30. G.W. Yuan, Z.Q. Sheng, X.D. Hang, Y.Z. Yao, L.N. Chang and J.Y. Yue, Computational Methods for Diffusion Equation, Science Press, Beijing (2015). [Google Scholar]
  31. G.W. Yuan, J.Y. Yue, Z.Q. Sheng and L.J. Shen, The computational method for nonlinear parabolic equation. Sci. China Ser. A. 43 (2013) 235–248. [Google Scholar]
  32. J.Y. Yue and G.W. Yuan, Picard-Newton iterative method with time step control for multimaterial non-equilibrium radiation diffusion problem. Commun. Comput. Phys. 10 (2011) 844–866. [Google Scholar]
  33. Q.H. Zeng, W.B. Pei, J. Cheng and H. Yong, Extension of Kershaw diffusion scheme on multi-block grids. Chin. J. Comput. Phys. 28 (2011) 641–648. [Google Scholar]
  34. R.P. Zhang, X.J. Yu and J. Zhu, Solution of multimaterial equilibrium radiation diffusion problems by using the discontinuous Galerkin method. Chin. Phys. Lett. 29 (2012) 110201. [CrossRef] [Google Scholar]
  35. S.C. Zhang, A special problem in the calculation of fluid dynamic equations with radiation. Acta Mech. Sinica 17 (1985) 379–382. [Google Scholar]
  36. X.K. Zhao, Y.L. Chen, Y.N. Gao, C.H. Yu and Y.H. Li, Finite volume element methods for nonequilibrium radiation diffusion equations. Int. J. Numer. Meth. Fluids 73 (2013) 1059–1080. [Google Scholar]
  37. Y.L. Zhou, Applications of Discrete Functional Analysis to the Finite Difference Method. Inter. Acad. Pub, Beijing (1990) [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you