Residual distribution schemes for steady radiative transfer equations on unstructured meshes

Abstract

We consider the numerical solution of steady radiative transfer equations on unstructured meshes. The radiative transfer equations belong to a class of integro-differential equations. We apply conservative residual distribution (RD) methods to solve the radiative transfer equations. To achieve this, we first adopt the discrete ordinate method for angular discretization and use the RD methods to solve the resulting system of coupled linear hyperbolic equations. We present some basics and accuracy analysis for the RD schemes. The standard nonlinear limiter is adopted to upgrade the monotonicity preserving first-order scheme for a high-order one. Several numerical experiments show that the proposed RD schemes achieve second-order accuracy and verify the non-oscillatory property of our numerical schemes.