Paper Info
Title
Numerical Simulation of Singularity Propagation Modeled by Linear Convection Equations with Spatially Heterogeneous Nonlocal Interactions
Abstract
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.
Year
DOI
Venue
2022
10.1007/s10915-022-01915-7
Journal of Scientific Computing
Keywords
DocType
Volume
Asymptotically compatible scheme, Nonlocal conservation law, Variable horizon, Propagation of discontinuities, Jump of derivatives
Journal
92
Issue
ISSN
Citations 
2
0885-7474
0
PageRank 
References 
Authors
0.34
8
3
Name
Order
Citations
PageRank
Xiaoxuan Yu100.34
Yan Xu219222.38
Qiang Du31692188.27