Volume 23, Issue 1
Asymptotic-Preserving Discrete Schemes for Non-Equilibrium Radiation Diffusion Problem in Spherical and Cylindrical Symmetrical Geometries

Xia Cui, Zhi-Jun Shen & Guang-Wei Yuan

Commun. Comput. Phys., 23 (2018), pp. 198-229.

Published online: 2018-01

Preview Full PDF 388 1057
Export citation
  • Abstract

We study the asymptotic-preserving fully discrete schemes for nonequilibrium radiation diffusion problem in spherical and cylindrical symmetric geometry. The research is based on two-temperature models with Larsen’s flux-limited diffusion operators. Finite volume spatially discrete schemes are developed to circumvent the singularity at the origin and the polar axis and assure local conservation. Asymmetric second order accurate spatial approximation is utilized instead of the traditional first order one for boundary flux-limiters to consummate the schemes with higher order global consistency errors. The harmonic average approach in spherical geometry is analyzed, and its second order accuracy is demonstrated. By formal analysis, we prove these schemes and their corresponding fully discrete schemes with implicitly balanced and linearly implicit time evolutions have first order asymptoticpreserving properties. By designing associated manufactured solutions and reference solutions, we verify the desired performance of the fully discrete schemes with numerical tests, which illustrates quantitatively they are first order asymptotic-preserving and basically second order accurate, hence competent for simulations of both equilibrium and non-equilibrium radiation diffusion problems.

  • Keywords

Poisson-Boltzmann equation, DG methods, global projection, energy error estimates, L2 error estimates.

  • AMS Subject Headings

65D15, 65N30, 35J05, 35J25

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • References
  • Hide All
    View All

@Article{CiCP-23-198, author = {}, title = {Asymptotic-Preserving Discrete Schemes for Non-Equilibrium Radiation Diffusion Problem in Spherical and Cylindrical Symmetrical Geometries}, journal = {Communications in Computational Physics}, year = {2018}, volume = {23}, number = {1}, pages = {198--229}, abstract = {

We study the asymptotic-preserving fully discrete schemes for nonequilibrium radiation diffusion problem in spherical and cylindrical symmetric geometry. The research is based on two-temperature models with Larsen’s flux-limited diffusion operators. Finite volume spatially discrete schemes are developed to circumvent the singularity at the origin and the polar axis and assure local conservation. Asymmetric second order accurate spatial approximation is utilized instead of the traditional first order one for boundary flux-limiters to consummate the schemes with higher order global consistency errors. The harmonic average approach in spherical geometry is analyzed, and its second order accuracy is demonstrated. By formal analysis, we prove these schemes and their corresponding fully discrete schemes with implicitly balanced and linearly implicit time evolutions have first order asymptoticpreserving properties. By designing associated manufactured solutions and reference solutions, we verify the desired performance of the fully discrete schemes with numerical tests, which illustrates quantitatively they are first order asymptotic-preserving and basically second order accurate, hence competent for simulations of both equilibrium and non-equilibrium radiation diffusion problems.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2016-0153}, url = {http://global-sci.org/intro/article_detail/cicp/10525.html} }
Copy to clipboard
The citation has been copied to your clipboard