Abstract
Recent development of the high-order, low-order (HOLO) method has shown promising results for solving thermal radiative transfer problems. The HOLO algorithm is a moment-based acceleration, similar to the well-known nonlinear diffusion acceleration and coarse-mesh finite difference methods. In this work, we introduce a new spatial-differencing scheme for the low-order (LO) system based on the corner-balance method and analyze an asymptotic diffusion property for a one-dimensional gray equation. An asymptotic analysis indicates that the new spatial-differencing scheme possesses the equilibrium diffusion limit. Numerical examples demonstrate significant improvements in the solution accuracy compared to the LO finite-volume discretization with a discontinuous source reconstruction.
Notes
a CitationEquation (12) becomes linear when the right side is fixed. We also assume the HO and LO systems have the same initial conditions.
b A discretely consistent system gives the same reaction rate. Thus, integral quantities can be directly computed using the LO system. Hence, the LO system can be employed for multiphysics coupling.
c Note that because the consistency terms γ± are defined in terms of the HO variables, we keep the right side of EquationEqs. (46)(46)
(46) and Equation(47)
(47)
(47) as
. Using
-scaling in the right side of EquationEqs. (46)
(46)
(46) and Equation(47)
(47)
(47) yields the identical result.
d We assume that the full- and half-range discrete angular integrations closely approximate the analytic integrals.