| 基于坏单元指示子的p自适应RKDG算法 |
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| 引用本文： | 袁安安,朱洪强,刘蕊.基于坏单元指示子的p自适应RKDG算法[J].数学的实践与认识,2020(5):165-172. |
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| 作者姓名： | 袁安安 朱洪强 刘蕊 |
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| 作者单位： | 南京邮电大学理学院 |
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| 基金项目： | 国家自然科学基金项目(11401319);江苏省高等学校自然科学研究项目(17KJB110013)。 |
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| 摘 要： | Runge-Kutta间断Galerkin(RKDG)方法是求解双曲守恒律方程的主流方法之一.很多双曲守恒律问题的规模特别巨大,数值计算求解时需要耗费大量的时间和计算机存储空间.为此我们设计了一个基于坏单元指示子的p自适应RKDG算法,它不仅能够保持原RKDG方法在光滑区域的高阶逼近,而且能够有效降低存储空间.同时,这也为后续进一步开展hp自适应RKDG算法的研究奠定了基础.
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| 关 键 词： | 双曲守恒律 自适应算法 间断GALERKIN方法 坏单元指示子 |
A p-Adaptive RKDG Algorithm Based on the Troubled-Cell Indicators |
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| YUAN An-an,ZHU Hong-qiang,LIU Rui.A p-Adaptive RKDG Algorithm Based on the Troubled-Cell Indicators[J].Mathematics in Practice and Theory,2020(5):165-172. |
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| Authors: | YUAN An-an ZHU Hong-qiang LIU Rui |
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| Institution: | (School of Science,Nanjing University of Posts and Telecommunications,Nanjing 210023,China) |
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| Abstract: | The Runge-Kutta discontinuous Galerkin(RKDG)method is one of the main numerical methods for solving equations of hyperbolic conservation laws.Many problems involving conservation laws have a very large scale,and they will cost considerable CPU time and storage.To solve this problem,a p-adaptive RKDG algorithm based on the troubled-cell indicators is designed.This new algorithm not only can maintain high order approximations in the smooth regions as the standard RKDG method,but also can effectively reduce storage.In the meanwhile,this work also builds the foundation of the upcoming research on hpadaptive RKDG algorithm. |
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| Keywords: | hyperbolic conservation laws adaptive algorithm discontinuous Galerkin method troubled-cell indicators |
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