Semi-implicit Hybrid Discrete $$\left( \text {H}^T_N\right) $$ Approximation of Thermal Radiative Transfer

The thermal radiative transfer (TRT) equations form an integro-differential system that describes the propagation and collisional interactions of photons. Computing numerical solutions TRT accurately efficiently is challenging for several reasons, first which defined on a high-dimensional phase space includes independent variables time, space, velocity. In order to reduce dimensionality classical approaches such as P $$_N$$ (spherical harmonics) or S (discrete ordinates) ansatz are often used in literature. this work, we introduce novel approach: hybrid discrete (H $$^T_N$$ ) approximation equations. This approach acquires desirable properties both , indeed reduces each these approximations various limits: H $$^1_N$$ $$\equiv $$ $$^T_0$$ $$_T$$ . We prove results hyperbolic partial differential all $$T\ge 1$$ $$N\ge 0$$ Another challenge solving inherent stiffness due large timescale separation between collisions, especially diffusive (i.e., highly collisional) regime. can be partially overcome via implicit time integration, although fully methods may become computationally expensive strong nonlinearity size. On other hand, explicit time-stepping schemes not also asymptotic-preserving limit require resolving mean-free path making prohibitively expensive. work develop method based nodal discontinuous Galerkin discretization coupled with semi-implicit time. particular, make use second Runge–Kutta scheme streaming term Euler material coupling term. Furthermore, solve energy equation implicitly after predictor corrector step, linearize temperature using Taylor expansion; avoids need iterative procedure, therefore improves efficiency. unphysical oscillation, apply slope limiter step. Finally, conduct experiments verify accuracy, efficiency, robustness discretizations.