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首页> 外文期刊>Journal of Computational Physics >Adaptive Runge-Kutta discontinuous Galerkin methods using different indicators: One-dimensional case
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Adaptive Runge-Kutta discontinuous Galerkin methods using different indicators: One-dimensional case

机译：使用不同指标的自适应Runge-Kutta不连续Galerkin方法：一维情况

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摘要

In this paper, we systematically investigate adaptive Runge-Kutta discontinuous Galerkin (RKDG) methods for hyperbolic conservation laws with different indicators which were based on the troubled cell indicators studied by Qiu and Shu [J. Qiu, C.-W. Shu, A comparison of troubled-cell indicators for Runge-Kutta discontinuous Galerkin mehtods using weighted essentially non-osillatory limiters, SIAM J. Sci. Comput. 27 (2005) 995-1013]. The emphasis is on comparison of the performance of adaptive RKDG method using different indicators, with an objective of obtaining efficient and reliable indicators to obtain better performance for adaptive computation to save computational cost. Both h-version and r-version adaptive methods are considered in the paper. The idea is to first identify "troubled cells" by different troubled-cell indicators, namely those cells where limiting might be needed and discontinuities might appear, then adopt an adaptive approach in these cells. A detailed numerical study in one-dimensional case is performed, addressing the issues of efficiency (less CPU cost and more accurate), non-oscillatory property, and resolution of discontinuities.
机译：在本文中，我们基于邱和舒研究的问题细胞指标，系统地研究了具有不同指标的双曲守恒律的自适应Runge-Kutta不连续Galerkin（RKDG）方法。邱长华Shu，使用加权的基本非振荡限幅器比较Runge-Kutta不连续Galerkin方法的问题细胞指标，SIAM J. Sci。计算27（2005）995-1013]。重点是比较使用不同指标的自适应RKDG方法的性能，目的是获得高效可靠的指标，以获得更好的自适应计算性能，从而节省计算成本。本文同时考虑了h版本和r版本的自适应方法。这个想法是首先通过不同的故障单元指示符（即可能需要限制并且可能出现不连续性的那些单元）来识别“故障单元”，然后在这些单元中采用自适应方法。在一维情况下进行了详细的数值研究，解决了效率（CPU成本更低且更准确），非振荡特性和不连续性的解决问题。

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