Order-Preserving Interpolation for Summation-by-Parts Operators at Nonconforming Grid Interfaces
Order-Preserving Interpolation for Summation-by-Parts Operators at Nonconforming Grid Interfaces
复制标题
非相容网格接口处分部求和运算符的保序插值
DOI：
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发表时间：
2018
影响因子：
3.1
通讯作者：
J. Werpers
中科院分区：
文献类型：
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作者：
M. Almquist;Siyang Wang;J. Werpers
我们研究了应用于空间二阶导数偏微分方程的分部求和有限差分法的非相容网格接口。为了保持能量稳定性，由于非相容界面处存在较大的截断误差，之前的努力被迫接受全局收敛速度降低一个数量级。我们通过推广接口处理并引入保序插值运算符来避免降阶。我们证明，给定两个对角范数分部求和方案，无论沿界面的网格点分布如何，都保证存在具有必要属性的保序插值算子。新方法保留了一致性接口底层方案的稳定性和全局准确性属性。
We study non-conforming grid interfaces for summation-by-parts finite difference methods applied to partial differential equations with second derivatives in space. To maintain energy stability, previous efforts have been forced to accept a reduction of the global convergence rate by one order, due to large truncation errors at the non-conforming interface. We avoid the order reduction by generalizing the interface treatment and introducing order preserving interpolation operators. We prove that, given two diagonal-norm summation-by-parts schemes, order preserving interpolation operators with the necessary properties are guaranteed to exist, regardless of the grid-point distributions along the interface. The new methods retain the stability and global accuracy properties of the underlying schemes for conforming interfaces.
影响因子：
2.5
作者：
Lucas Friedrich;D. C. D. R. Fernández-D.-C.-D.-R.-Fernández-145704654;A. R. Winters;G. Gassner;D. Zingg;Jason E. Hicken
通讯作者：
Lucas Friedrich;D. C. D. R. Fernández-D.-C.-D.-R.-Fernández-145704654;A. R. Winters;G. Gassner;D. Zingg;Jason E. Hicken