基于指数时间离散化的高效 $p$-多网格方法用于可压缩稳态流
Efficient $p$-multigrid method based on an exponential time discretization for compressible steady flows
AI总结：
本文提出一种高效的多网格框架，结合高阶 $p$-阶多项式模断续 Galerkin 方法，利用指数时间积分方案增强阻尼效果，提升收敛效率，实现二维和三维稳态流的快速收敛。
摘要：
本文开发了一种高效的多网格框架，用于可压缩稳态流的时间推进，采用高阶（$p$-阶多项式）模断续 Galerkin 方法。核心算法基于全局耦合，指数时间积分方案提供强阻尼效应以加速向稳态收敛，同时高频率、高阶空间误差模式通过 $s$-阶段预条件 Runge-Kutta 方法进行平滑。数值研究表明，指数时间积分显著提高了 Runge-Kutta 时间推进的阻尼和传播效率，用于 $p$-多网格方法，实现二维和三维稳态流的快速且 $p$-无关收敛。
英文摘要：
An efficient multigrid framework is developed for the time marching of steady-state compressible flows with a spatially high-order ($p$-order polynomial) modal discontinuous Galerkin method. The core algorithm that based on a global coupling, exponential time integration scheme provides strong damping effects to accelerate the convergence towards the steady state, while high-frequency, high-order spatial error modes are smoothed out with a $s$-stage preconditioned Runge-Kutta method. Numerical studies show that the exponential time integration substantially improves the damping and propagative efficiency of Runge-Kutta time-stepping for use with the $p$-multigrid method, yielding rapid and $p$-independent convergences to steady flows in both two and three dimensions.
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。
