TY - JOUR
T1 - The Immersed Interface Method for Non-Smooth Rigid Objects in Incompressible Viscous Flows
AU - Liu , Yang
AU - Xu , Sheng
JO - Communications in Computational Physics
VL - 2
SP - 510
EP - 533
PY - 2020
DA - 2020/12
SN - 29
DO - http://doi.org/10.4208/cicp.OA-2020-0023
UR - https://global-sci.org/intro/article_detail/cicp/18470.html
KW - The immersed interface method, boundary condition capturing, non-smooth complex rigid objects, jump conditions.
AB - <p style="text-align: justify;">In the immersed interface method, an object in a flow is formulated as a singular force, and jump conditions caused by the singular force are incorporated into numerical schemes to compute the flow. Previous development of the method considered
only smooth objects. We here extend the method to handle non-smooth rigid objects
with sharp corners in 2D incompressible viscous flows. We represent the boundary of
an object as a polygonal curve moving through a fixed Cartesian grid. We compute
necessary jump conditions to achieve boundary condition capturing on the object. We
incorporate the jump conditions into finite difference schemes to solve the flow on the
Cartesian grid. The accuracy, efficiency and robustness of our method are tested using
canonical flow problems. The results demonstrate that the method has second-order
accuracy for the velocity and first-order accuracy for the pressure in the infinity norm,
and is extremely efficient and robust to simulate flows around non-smooth complex
objects.</p>