TY - JOUR
AU - Sun, Wenjun
AB - We propose two spatial second-order schemes for linear radiative transfer equations by using the idea of the unified gas kinetic scheme (UGKS) to construct the numerical boundary fluxes, and show that the proposed schemes are both positive and asymptotic preserving. The UGKS was proposed by Xu and Huang (J Comput Phys 229:7747–7764, 2010) for continuum and rarefied flows firstly, and was then applied to a linear radiative transfer equation by Mieussens in (J Comput Phys 253:138–156, 2013) where the asymptotic preserving property of UGKS is shown. Although it is asymptotic preserving, UGKS can not always keep the positivity of solutions. We first apply UGKS to discretize a linear radiative transfer equation to have a spatial second-order scheme. Then, by a detailed analysis of the numerical boundary fluxes, we are able to find the reasons why the positive preserving property of UGKS fails. Finally, we carefully employ a linear scaling limiter and a flux correction to make UGKS positive-preserving but still asymptotic-preserving. Consequently, we propose two spatial second-order positive and asymptotic preserving unified gas kinetic schemes for the linear radiative transfer equation, thus improving the earlier work (J Comput Phys 444:110546, 2021) where only a first-order positive and asymptotic scheme is developed. The proposed schemes can well capture the solution of the diffusion limit equation in optically thick regions without requiring the cell size being smaller than the photon’s mean free path, while the solution in optically thin regions can also be well resolved in a natural way. To our best knowledge, this is the first time that a spatial second-order positive and asymptotic preserving gas kinetic scheme for linear radiative transfer equations is constructed. Several numerical experiments are included to validate the spatial second-order accuracy, positive- and asymptotic-preserving properties of the proposed schemes.
TI - Spatial Second-Order Positive and Asymptotic Preserving Unified Gas Kinetic Schemes for Radiative Transfer Equations
JF - Journal of Scientific Computing
DO - 10.1007/s10915-023-02305-3
DA - 2023-09-01
UR - https://www.deepdyve.com/lp/springer-journals/spatial-second-order-positive-and-asymptotic-preserving-unified-gas-3elIzLt3P9
VL - 96
IS - 3
DP - DeepDyve
ER -