@Article{AAMM-15-1,
author = {You , Cheng-ShuHsieh , Po-Wen and Yang , Suh-Yuh},
title = {A Direct-Forcing Immersed Boundary Projection Method for Thermal Fluid-Solid Interaction Problems},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2022},
volume = {15},
number = {1},
pages = {1--29},
abstract = {<p style="text-align: justify;">In this paper, we develop a direct-forcing immersed boundary projection
method for simulating the dynamics in thermal fluid-solid interaction problems. The
underlying idea of the method is that we treat the solid as made of fluid and introduce two virtual forcing terms. First, a virtual fluid force distributed only on the solid
region is appended to the momentum equation to make the region behave like a real
solid body and satisfy the prescribed velocity. Second, a virtual heat source located
inside the solid region near the boundary is added to the energy transport equation to
impose the thermal boundary condition on the solid boundary. We take the implicit
second-order backward differentiation to discretize the time variable and employ the
Choi-Moin projection scheme to split the coupled system. As for spatial discretization,
second-order centered differences over a staggered Cartesian grid are used on the entire domain. The advantages of this method are its conceptual simplicity and ease
of implementation. Numerical experiments are performed to demonstrate the high
performance of the proposed method. Convergence tests show that the spatial convergence rates of all unknowns seem to be super-linear in the 1-norm and 2-norm while
less than linear in the maximum norm.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2021-0165},
url = {http://global-sci.org/intro/article_detail/aamm/21123.html}
}