@Article{CiCP-38-156,
author = {Kurganov , AlexanderLiu , ZepeiPollack , Michael and Xin , Ruixiao},
title = {Low-Dissipation Central-Upwind Schemes for Elasticity in Heterogeneous Media},
journal = {Communications in Computational Physics},
year = {2025},
volume = {38},
number = {1},
pages = {156--180},
abstract = {<p style="text-align: justify;">We develop new low-dissipation central-upwind (LDCU) schemes for nonlinear elasticity equations in heterogeneous media. In general, central-upwind schemes belong to the class of finite-volume Godunov-type schemes, which consist of three
steps: reconstruction, evolution, and projection onto the original grid. In our new
method, the evolution is performed in the standard way by integrating the system
over the space-time control volumes. However, the reconstruction and projection are
performed in a special manner. First, we take into account the fact that the conservative variables (strain and momentum) are discontinuous across the material interfaces,
while the flux variables (velocity and strain) are continuous there: we therefore reconstruct the flux variables. Second, we use a special projection recently introduced in
[A. Kurganov and R. Xin, J. Sci. Comput., 96, 2023] to complete the derivation of the
LDCU scheme. Our numerical experiments demonstrate that the developed schemes
are capable of accurately resolving waves with dispersive behavior that over a long
period of time evolve into solitary waves.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2024-0117},
url = {http://global-sci.org/intro/article_detail/cicp/24255.html}
}