Numerical Simulation of Singularity Propagation Modeled by Linear Convection Equations with Spatially Heterogeneous Nonlocal Interactions
Numerical Simulation of Singularity Propagation Modeled by Linear Convection Equations with Spatially Heterogeneous Nonlocal Interactions
复制标题
DOI：
10.1007/s10915-022-01915-7
复制
发表时间：
2022-01
影响因子：
2.5
通讯作者：
X. Yu;Yan Xu;Q. Du
中科院分区：
文献类型：
--
作者：
X. Yu;Yan Xu;Q. Du
研究了具有空间非局部非均质相互作用的线性对流方程解的奇异性传播。该模型采用空间变化的非局部视界参数来测量非局部相互作用的范围。通过异构定位，这可以导致本地和非本地模型的无缝耦合。我们感兴趣的是了解由于非局部视界和局部和非局部跃迁的非均匀性对奇点传播的影响。我们首先解析推导方程来描述非局部状态下各种形式的非局部视界参数的不同类型奇点的传播。然后，我们使用渐近相容格式对方程进行离散化，并进行数值模拟来说明在不同情况下的传播模式。
We study the propagation of singularities in solutions of linear convection equations with spatially heterogeneous nonlocal interactions. A spatially varying nonlocal horizon parameter is adopted in the model, which measures the range of nonlocal interactions. Via heterogeneous localization, this can lead to the seamless coupling of the local and nonlocal models. We are interested in understanding the impact on singularity propagation due to the heterogeneities of the nonlocal horizon and the local and nonlocal transition. We first analytically derive equations to characterize the propagation of different types of singularities for various forms of nonlocal horizon parameters in the nonlocal regime. We then use asymptotically compatible schemes to discretize the equations and carry out numerical simulations to illustrate the propagation patterns in different scenarios.