An h-adaptive RKDG method with troubled-cell indicator for one-dimensional detonation wave simulations
An h-adaptive RKDG method with troubled-cell indicator for one-dimensional detonation wave simulations
复制标题
用于一维爆轰波模拟的具有故障单元指示器的 h 自适应 RKDG 方法
DOI：
10.1007/s10444-016-9454-3
复制
发表时间：
2016
影响因子：
1.7
通讯作者：
Gao Zhen
中科院分区：
文献类型：
--
作者：
Zhu Hongqiang;Gao Zhen
在这项工作中，我们讨论了 Zhu 和 Qiu (J. Comput. Phys. 228, 6957-6976 2009) 中自适应技术的扩展，以设计一种 h 自适应龙格-库塔不连续伽辽金 (RKDG) 方法，用于模拟几种经典的一维爆震波。 TVB 故障单元指示器用于检测被认为包含不连续性的故障单元。通过细化有问题的单元并粗化其他单元，在每个时间级别生成自适应网格。设计了一种递归多级网格细化技术，以避免爆炸前沿移动过快而导致在爆炸前沿离开之前没有足够的单元来解析爆炸前沿的问题。我们详细描述了数值实现，包括自适应过程、解重建方法和问题单元指示器。此外，采用高阶正性保持技术来保证我们算法的鲁棒性。大量的数值测试表明了自适应策略的有效性以及我们的自适应方法相对于固定网格 RKDG 方法在节省计算存储和提高解质量方面的优势。
In this work, we discuss an extension of the adaptive technique in Zhu and Qiu (J. Comput. Phys. 228, 6957-6976 2009) to design an h-adaptive Runge-Kutta discontinuous Galerkin (RKDG) method for the simulations of several classical one-dimensional detonation waves. The TVB troubled-cell indicator is employed to detect the troubled cells which are believed to contain the discontinuities. An adaptive mesh is generated at each time-level by refining the troubled cells and coarsening the others. A recursive multi-level mesh refinement technique is designed to avoid the problem that the detonation front moves so fast that there are not enough cells to resolve the detonation front before it leaves. We describe the numerical implementation in detail including the adaptive procedure, solution reconstruction method and troubled-cell indicator. Furthermore, a high order positivity-preserving technique is employed for the robustness of our algorithm. Extensive numerical tests are conducted to show the effectiveness of the adaptive strategy and advantages of our adaptive method over the fixed-mesh RKDG method in saving the computational storage and improving the solution quality.