Nyström Method Applied to the Transport Equation in a Semi-Reflective Rectangle

Abstract

Several numerical schemes for solving the transport equation in two-dimensional geometries have been proposed in last decades, but it is still a challenge to build a high accurate and efficient method. In this work, the transport equation in X–Y geometry with semi-reflective boundary conditions and isotropic scattering was solved by Nyström method. The approach consists in discretizing the integral formulation of the transport problem and applying numerical and analytical techniques to deal with singularities, reduce memory storage and optimize computations. The algorithm implemented here was able to compute numerical solutions with several correct significant digits for the scalar fluxes and eigenvalues.

Keywords:

• Transport equation
• integral formulation
• Nyström method