对传输方程的预因子压缩方案的推广
A Generalization of Prefactored Compact Schemes for Advection Equations
AI总结：
本文提出了一种改进的预因子压缩方案，旨在减少计算域并提高计算效率，通过预因子化避免了多对角矩阵求逆的计算负担，同时保持了精度阶数。该方法适用于任意阶数的中心压缩差分方案，并通过线性和非线性输运方程的测试案例展示了其精度保持和计算效率提升。
摘要：
本文提出了一种针对传输方程的预因子压缩方案的推广，旨在减少计算域并提高计算效率。通过引入的预因子化方法，避免了多对角矩阵求逆的计算负担，同时保持了精度阶数。预因子化可以应用于任意阶数的中心压缩差分方案（研究中包括了最高十六阶精度的压缩方案）。一个显著的限制是，所提出的方案只能在预测-校正类型的时间推进框架中使用。两个测试案例，分别对应线性和非线性输运方程，用于展示预因子化压缩方案的精度保持和计算效率的提高。
英文摘要：
A generalized prefactorization of compact schemes aimed at reducing the stencil and improving the computational efficiency is proposed here in the framework of transport equations. By the prefactorization introduced here, the computational load associated with inverting multi-diagonal matrices is avoided, while the order of accuracy is preserved. The prefactorization can be applied to any centered compact difference scheme with arbitrary order of accuracy (results for compact schemes of up to sixteenth order of accuracy are included in the study). One notable restriction is that the proposed schemes can be applied in a predictor-corrector type marching scheme framework. Two test cases, associated with linear and nonlinear advection equations, respectively, are included to show the preservation of the order of accuracy and the increase of the computational efficiency of the prefactored compact schemes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
