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• This paper presents a positive and asymptotic preserving scheme for the nonlinear gray radiative transfer equations. • The scheme is almost free of ray effects. • The scheme can reduce the Gibbs phenomena in the spherical harmonics (PN) approximation. This paper presents a positive and asymptotic preserving scheme for the nonlinear gray radiative transfer equations. The scheme is constructed by combining the filtered spherical harmonics (F P N) method for the discretization of angular variable and with the framework of the unified gas kinetic scheme (UGKS) for the spatial- and time-discretization. The constructed scheme is almost free of ray effects and can also mitigate oscillations in the spherical harmonics (P N) approximation. Moreover, it can be shown that the current scheme is asymptotic preserving. Consequently, in the optically thick regimes the current scheme can exactly capture the solution of the diffusion limit equation without requiring the cell size being smaller than the photon's mean free path, while the solution in optically thin regimes can also be well resolved in a natural way. In addition, the F P N angular discretization induces a natural macro-micro decomposition, with this help we can obtain the sufficient conditions that guarantee the positivity of the radiative energy density and material temperature. Then, a linear scaling limiter is given to enforce that sufficient conditions. With the process of such construction, we finally obtain a scheme, called the P P F P N -based UGKS scheme, that is positive and asymptotic preserving. Various numerical experiments are included to validate the robustness, positive- and asymptotic-preserving property as well as the property of almost ray effect free. [ABSTRACT FROM AUTHOR]

• An angular finite element based unified gas kinetic scheme has been developed. • Ray effects can be much mitigated by the scheme. • The scheme possesses the asymptotic preserving property. In order to mitigate the ray effects of the usual discrete ordinate (S N) method for the gray radiative transfer equations, a new numerical approach is constructed in this paper with the angular discretization by a linear finite element (FE) method and the spatial discretization by the method of unified gas kinetic scheme (UGKS). Different from the usual S N -based UGKS for which the propagation directions of photons are discretized with finite points, the angular-FE-based UGKS considers the linear combination of all propagation directions (i.e., the unit sphere) and induces a coupling between the discrete directions. Hence, the angular-FE-based UGKS can much mitigate the ray effects to some extent as was expected, as also shown numerically by a point source problem in this paper. At the same time, it is shown that the current scheme possesses the asymptotic preserving (AP) property, that is, in the optically thick regimes the current scheme can exactly capture the solution of the diffusion limit equation without requiring the cell size being smaller than the photon's mean free path, while the solution in optically thin regimes can also be well resolved in a natural way. Various numerical experiments are included to validate the robustness, accuracy and AP property of the current scheme. [ABSTRACT FROM AUTHOR]

The aim of this paper is to construct a new numerical scheme for the nonlinear gray radiative transfer (GRT) equations, namely, the asymptotic-preserving (AP) $$H_N^T$$ H N T -based unified gas kinetic scheme (UGKS). The constructed scheme is obtained by combing the UGKS for spatial discretization with the hybrid $$H_N^T$$ H N T method for angular discretization. Since the $$H_N^T$$ H N T is a hybrid angular discrete method of both $${P_N}$$ P N and $${S_N}$$ S N methods, the current $$H_N^T$$ H N T -based UGKS can not only mitigate the ray effects of the $${S_N}$$ S N method largely, but also suppress the oscillations of the original $${P_N}$$ P N method. Furthermore, we show that the current $$H_N^T$$ H N T -based UGKS also inherits the AP property of UGKS. A number of one-dimensional and two-dimensional numerical experiments are presented that validate the performance of the current scheme in both optically thin and thick regimes, as well as in mitigating the ray effects. Moreover, it can capture the initial layer solution without requiring additional treatments. [ABSTRACT FROM AUTHOR]