TY - JOUR
T1 - Low-Dissipation Central-Upwind Schemes for Elasticity in Heterogeneous Media
AU - Kurganov , Alexander
AU - Liu , Zepei
AU - Pollack , Michael
AU - Xin , Ruixiao
JO - Communications in Computational Physics
VL - 1
SP - 156
EP - 180
PY - 2025
DA - 2025/07
SN - 38
DO - http://doi.org/10.4208/cicp.OA-2024-0117
UR - https://global-sci.org/intro/article_detail/cicp/24255.html
KW - Hyperbolic systems of conservation laws, low-dissipation central-upwind schemes, nonlinear elasticity, heterogeneous media, waves with dispersive behavior, solitary waves.
AB - <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>