求解非定常非线性耦合Burgers方程的四阶精度紧致ADI格式
On the fourth-order accurate compact ADI scheme for solving the unsteady Nonlinear Coupled Burgers' Equations
AI总结：
本文提出并比较了求解二维非定常耦合Burgers方程的四阶紧致ADI格式与Du Fort-Frankel格式，证明前者在精度和效率上更优且稳定。
摘要：
本文采用高阶精度有限差分格式数值求解具有中等至严重梯度的二维非定常耦合Burgers方程，即四阶精度紧致ADI格式和四阶精度Du Fort-Frankel格式。文中给出了数值稳定性和收敛性的讨论。针对具有严重内部梯度和边界梯度的问题，在精度和计算效率方面对两种格式进行了比较。研究表明，四阶紧致ADI格式是稳定且高效的。
英文摘要：
The two-dimensional unsteady coupled Burgers' equations with moderate to severe gradients, are solved numerically using higher-order accurate finite difference schemes; namely the fourth-order accurate compact ADI scheme, and the fourth-order accurate Du Fort Frankel scheme. The question of numerical stability and convergence are presented. Comparisons are made between the present schemes in terms of accuracy and computational efficiency for solving problems with severe internal and boundary gradients. The present study shows that the fourth-order compact ADI scheme is stable and efficient.
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。
