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 528 2085
Export citation
  • Abstract

We study the asymptotic-preserving fully discrete schemes for non-equilibrium 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 asymptotic-preserving 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

Spherical symmetrical geometry, cylindrical symmetrical geometry, non-equilibrium radiation diffusion problem, fully discrete schemes, asymptotic-preserving, second order accuracy.

  • AMS Subject Headings

65M08, 80M35, 65M12

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@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 non-equilibrium 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 asymptotic-preserving 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} }
TY - JOUR T1 - Asymptotic-Preserving Discrete Schemes for Non-Equilibrium Radiation Diffusion Problem in Spherical and Cylindrical Symmetrical Geometries JO - Communications in Computational Physics VL - 1 SP - 198 EP - 229 PY - 2018 DA - 2018/01 SN - 23 DO - http://doi.org/10.4208/cicp.OA-2016-0153 UR - https://global-sci.org/intro/article_detail/cicp/10525.html KW - Spherical symmetrical geometry, cylindrical symmetrical geometry, non-equilibrium radiation diffusion problem, fully discrete schemes, asymptotic-preserving, second order accuracy. AB -

We study the asymptotic-preserving fully discrete schemes for non-equilibrium 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 asymptotic-preserving 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.

Xia Cui, Zhi-Jun Shen & Guang-Wei Yuan. (2020). Asymptotic-Preserving Discrete Schemes for Non-Equilibrium Radiation Diffusion Problem in Spherical and Cylindrical Symmetrical Geometries. Communications in Computational Physics. 23 (1). 198-229. doi:10.4208/cicp.OA-2016-0153
Copy to clipboard
The citation has been copied to your clipboard