Uniform convergent scheme for discrete-ordinate radiative transport equation with discontinuous coefficients on unstructured quadrilateral meshes

Yihong Wang (), Min Tang () and Jingyi Fu ()
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Yihong Wang: Shanghai Lixin University of Accounting and Finance
Min Tang: Shanghai Jiao Tong University
Jingyi Fu: Shanghai Jiao Tong University

Partial Differential Equations and Applications, 2022, vol. 3, issue 5, 1-20

Abstract: Abstract In this paper, we construct an asymptotic preserving (AP) scheme for the steady state radiative transport equation (RTE) with discontinuous coefficients on unstructured quadrilateral meshes. There are abundant works of constructing AP schemes for RTE on structured meshes but AP schemes on unstructured or even distorted meshes with discontinuous coefficients are relatively few. When the solution exhibits boundary or interface layers, though the details of fast changes in the layers may not be important, whether the solution remains valid across the layers is not guaranteed by the AP property. Based on the tailored finite point method (TFPM), we proposed an AP scheme on the unstructured mesh that is not only convergent uniformly with respect to the mean free path but also valid up to the boundary and interface layers. We will show analytically that the proposed scheme is AP and demonstrate its numerical performance for problems with/without boundary and interface layers.

Keywords: Radiative transport equation; Tailored finite point method; Distorted quadrilateral meshes; Discontinuous coefficients; Asymptotic preserving; Interface/Boundary layer; 41A30; 41A60; 65D25 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s42985-022-00195-y

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