论文标题
声子传输方程式和数字的二阶扩散极限
Second-order diffusion limit for the phonon transport equation-asymptotics and numerics
论文作者
论文摘要
我们研究了小型纳德森数制度中声子传输方程的限制方程的数值实现。主要贡献是我们得出实现二阶收敛的极限方程，并提供了计算罗宾系数的数值配方。这些系数是通过求解辅助半空间方程来获得的。从数值上讲，半空间方程是通过一种依赖于偶数分解来消除角点奇异性的光谱方法求解的。数值证据将提出以证明二阶渐近收敛率是合理的。
We investigate the numerical implementation of the limiting equation for the phonon transport equation in the small Knudsen number regime. The main contribution is that we derive the limiting equation that achieves the second order convergence, and provide a numerical recipe for computing the Robin coefficients. These coefficients are obtained by solving an auxiliary half-space equation. Numerically the half-space equation is solved by a spectral method that relies on the even-odd decomposition to eliminate corner-point singularity. Numerical evidences will be presented to justify the second order asymptotic convergence rate.
