Abstract

In this paper, we design an interpolation-characteristic scheme for the numerical solution of the inhomogeneous transfer equation. The scheme is based on the Hermitian interpolation to reconstruct the value of an unknown function at the point of intersection of the backward characteristic with the cell faces. The Hermitian interpolation to reconstruct the function values ​​uses both the nodal values ​​of the desired function and its derivative. Unlike previous studies also based on the Hermitian interpolation, not only the differential continuation of the transfer equation but also the relationship between the integral averaged values, nodal values, ​​and derivatives according to the Euler-Maclaurin formula is used to transfer information about the derivatives to the next layer. The third-order difference scheme is shown to converge for smooth solutions. The dissipative and dispersive properties of the scheme are considered using numerical examples of solutions with decreasing smoothness.

中文翻译：

---

线性非均匀传递方程的厄米特征格式

摘要

本文针对非均匀传递方程的数值解，设计了一种插值特征格式。该方案基于Hermitian插值，可在后向特性与像元面的交点处重构未知函数的值。埃尔米特插值法用于重建函数值，它既使用所需函数的节点值，又使用其导数。与先前基于Hermitian插值的研究不同，不仅使用传递方程的微分连续，而且根据Euler-Maclaurin公式将积分平均值，节点值和导数之间的关系用于传递有关派生到下一层。示出了三阶差分方案收敛于平滑解。使用具有降低的平滑度的解决方案的数值示例来考虑该方案的耗散和色散特性。