High-order Runge-Kutta discontinuous Galerkin methods with multi-resolution WENO limiters for solving steady-state problems
High-order Runge-Kutta discontinuous Galerkin methods with multi-resolution WENO limiters for solving steady-state problems
复制标题
具有多分辨率 WENO 限制器的高阶 Runge-Kutta 不连续 Galerkin 方法用于解决稳态问题
DOI：
10.1016/j.apnum.2021.03.011
复制
发表时间：
2021-07
影响因子：
2.8
通讯作者：
Qiu Jianxian
中科院分区：
文献类型：
--
作者：
Zhu Jun;Shu Chi-Wang;Qiu Jianxian
由于经典的韦诺格式[27]可能遭受轻微的激波后振荡，（这是负责数值残差挂在截断误差水平）和新的高阶多分辨率韦诺格式[59]是成功地解决稳态问题，我们应用这些高阶有限体积多分辨率韦诺技术作为高阶Runge-Kutta间断Galerkin（RKDG）的限制器模拟稳态问题的方法。首先，设计了一种新的故障小区指示器，用于精确检测需要进一步限制的小区。然后，采用高阶多分辨率韦诺限制程序的分层L2投影多项式的DG解决方案在故障细胞本身的序列。通过这样做，这些RKDG方法与多分辨率韦诺限制器可以逐渐从最佳的高阶精度下降到一阶精度附近的强间断，抑制轻微的激波后振荡，并推动数值残差定居下来的机器零在稳态模拟。这些新的多分辨率韦诺限制器是非常简单的构造，可以很容易地实现到任意高阶精度，用于解决多维稳态问题。
Since the classical WENO schemes [27] might suffer from slight post-shock oscillations (which are responsible for the numerical residual to hang at a truncation error level) and the new high-order multi-resolution WENO schemes [59] are successful to solve for steady-state problems, we apply these high-order finite volume multi-resolution WENO techniques to serve as limiters for high-order Runge-Kutta discontinuous Galerkin (RKDG) methods in simulating steady-state problems. Firstly, a new troubled cell indicator is designed to precisely detect the cells which would need further limiting procedures. Then the high-order multi-resolution WENO limiting procedures are adopted on a sequence of hierarchical L 2 projection polynomials of the DG solution within the troubled cell itself. By doing so, these RKDG methods with multi-resolution WENO limiters could gradually degrade from the optimal high-order accuracy to the first-order accuracy near strong discontinuities, suppress the slight post-shock oscillations, and push the numerical residual to settle down to machine zero in steady-state simulations. These new multi-resolution WENO limiters are very simple to construct and can be easily implemented to arbitrary high-order accuracy for solving steady-state problems in multi-dimensions.
登录
查看更多内容
影响因子：
2.9
作者：
S. Osher;S. Chakravarthy
通讯作者：
S. Osher;S. Chakravarthy
DOI：
10.1016/j.jcp.2017.06.046
发表时间：
2017-10
期刊：
J. Comput. Phys.
影响因子：
--
作者：
G. Fu;Chi-Wang Shu
通讯作者：
G. Fu;Chi-Wang Shu
DOI：
--
发表时间：
--
期刊：
--
影响因子：
--
作者：
A. Tesdall;R. Sanders;B. Keyfitz
通讯作者：
A. Tesdall;R. Sanders;B. Keyfitz
影响因子：
3.7
作者：
global sci
通讯作者：
global sci
影响因子：
2
作者：
Bernardo Cockburn;S. Hou;Chi-Wang Shu
通讯作者：
Bernardo Cockburn;S. Hou;Chi-Wang Shu