Adaptive Finite Element Simulation of the Time-dependent Simplified PN Equations

TL;DR

This paper presents an adaptive finite element method for solving the two-dimensional time-dependent simplified P_N equations, demonstrating its effectiveness through numerical comparisons with existing models.

Contribution

It introduces an adaptive finite element approach for the time-dependent simplified P_N equations and provides computational results in two dimensions.

Findings

Effective numerical solutions for 2D time-dependent SP_N equations.

Comparative analysis showing advantages over existing models.

Demonstrated adaptability and accuracy of the finite element method.

Abstract

The steady-state simplified $P_N$ approximation to the radiative transport equation has been successfully applied to many problems involving radiation. Recently, time-dependent simplified $P_N$ equations have been derived by an asymptotic analysis similar to the asymptotic derivation of the steady-state $SP_N$ equations \cite{FraKlaLarYas07}. In this paper, we present computational results for the time-dependent $SP_N$ equations in two dimensions, obtained by using an adaptive finite element approach. Several numerical comparisons with other existing models are shown.