@Article{AAMM-16-1,
author = {Zhao, Xiaolong and Yu, Xijun and Zupeng, Jia and Zou, Shijun and Qiu, Meilan},
title = {A Vertex-Centered Arbitrary Lagrangian-Eulerian Finite Volume Method with Sub-Cells for Two-Dimensional Compressible Flow},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2024},
volume = {16},
number = {1},
pages = {181--207},
abstract = {<p style="text-align: justify;">In this paper, we present a new vertex-centered arbitrary Lagrangian-Eulerian (ALE) finite volume scheme for two-dimensional compressible flow. In our
scheme, the momentum equation is discretized on the vertex control volume, while
the mass equation and the energy equation are discretized on the sub-cells which are
included in the vertex control volume. We attain the average of the fluid velocity
on the vertex control volume directly by solving the conservation equations. Then
we can obtain the fluid velocity at vertex with the reconstructed polynomial of the
velocity. This fluid velocity is chosen as the mesh velocity, which makes the mesh
move in a Lagrangian manner. Two WENO (Weighted Essentially Non-Oscillatory)
reconstructions for the density (the total energy) and the velocity are used to make
our scheme achieve the anticipated accuracy. Compared with the general vertex-centered schemes, our scheme with the new approach for the space discretization
can simulate some multi-material flows which do not involve large deformations.
In addition, our scheme has good robustness, and some numerical examples are
presented to demonstrate the anticipated accuracy and the good properties of our
scheme.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2022-0085},
url = {https://global-sci.com/article/72806/a-vertex-centered-arbitrary-lagrangian-eulerian-finite-volume-method-with-sub-cells-for-two-dimensional-compressible-flow}
}