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.
翻译:我们调查了小Knudsen 数数制度中磷运输方程限量方程的量化实施情况。 主要贡献在于我们得出了实现第二顺序趋同的限量方程,并为计算罗宾系数提供了一种数字配方。这些系数是通过解决一个辅助半空方程获得的。半空方程的数值是通过光谱法解决的,光谱法依靠的是消除角点奇数的奇数分解法。将提出数字证据来证明第二个顺序的零点趋同率的合理性。