摘要
针对传统高阶数值方法在处理间断问题时易产生非物理振荡的难题,提出一种新型无振荡间断Petrov-Galerkin方法来求解一维Euler方程。采用SSP Runge-Kutta方法进行时间离散,并在每个时间步进后引入一个阻尼算子,通过自适应调节机制抑制数值计算中可能产生的非物理振荡,同时保持间断Petrov-Galerkin方法原有的高精度特性。数值实验结果表明,该方法在光滑区域保持最优收敛阶,在间断附近通过阻尼机制自动调节数值耗散,实现了稳定性和高分辨率的有效平衡。
To address the challenge of non-physical oscillations generated by traditional high-order numerical methods when dealing with discontinuous problems,a new oscillation-free discontinuous Petrov-Galerkin method was proposed to solve one-dimensional Euler equations.The method employed the SSP Runge-Kutta scheme for temporal discretization and incorporated a damping operator at every time step,so that the possible non-physical oscillations in numerical calculations could be suppressed through the adaptive regulation mechanism,while maintaining the original high-precision characteristics of the discontinuous Petrov-Galerkin method.The results of numerical experiments show that this method maintains the optimal convergence order in smooth regions and automatically adjusts the numeri⁃cal dissipation near discontinuities through the damping mechanism,achieving an effective balance be⁃tween stability and high resolution.
作者
王晨焱
高巍
WANG Chenyan;GAO Wei(School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China)
出处
《内蒙古大学学报(自然科学版)》
2025年第6期593-602,共10页
Journal of Inner Mongolia University:Natural Science Edition
基金
内蒙古自治区人才开发基金项目(12000-1300020240)。
