论文标题
通过线性对流方程建模的奇异性传播的数值模拟，并具有空间异质性非局部相互作用
Numerical simulation of singularity propagation modeled by linear convection equations with spatially heterogeneous nonlocal interactions
论文作者
论文摘要
我们研究了具有空间异质非局部相互作用的线性对流方程解中奇异性的传播。模型中采用了空间变化的非局部视野参数，该参数测量了非局部相互作用的范围。通过异质定位，这可以导致局部和非局部模型的无缝耦合。我们有兴趣了解由于非局部地平线的异质性以及局部和非局部过渡的异质性而对奇异性传播的影响。我们首先在分析中得出方程式，以表征非局部制度中各种形式的非局部地平线参数的不同类型的奇点的传播。然后，我们使用渐近兼容的方案来离散方程并进行数值模拟，以说明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 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.
