TY - JOUR
T1 - A Time Variable Filter Approach for the Fluid-Fluid Interaction
AU - Li , Wei
AU - Huang , Pengzhan
AU - He , Yinnian
JO - Communications in Computational Physics
VL - 5
SP - 1417
EP - 1451
PY - 2025
DA - 2025/05
SN - 37
DO - http://doi.org/10.4208/cicp.OA-2024-0108
UR - https://global-sci.org/intro/article_detail/cicp/24099.html
KW - Fluid-fluid interaction, unconditional energy stability, local $H^1$
stability, time variable filter, error estimate.
AB - <p style="text-align: justify;">This paper analyzes a time variable filter approach for the nonlinear fluid-fluid interaction problem. The method applies a time variable filter to improve numerical solution of a variable time step Euler scheme with explicit second-order extrapolation treatment for nonlinear convection and interface terms. Compared with classical
second-order method in time, the proposed approach improves time accuracy from the
first order to the second order by adding several lines to the code of variable time step
Euler scheme. Theoretically, we prove the unconditional energy stability, local $H^1$ stability and error estimates. Numerically, some numerical experiments are provided to
test the theoretical results, which illustrate the accuracy and efficiency of the presented
method.</p>