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Volume 37, Issue 5
A Time Variable Filter Approach for the Fluid-Fluid Interaction

Wei Li, Pengzhan Huang & Yinnian He

DOI: 10.4208/cicp.OA-2024-0108

Commun. Comput. Phys., 37 (2025), pp. 1417-1451.

Published online: 2025-05

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  • Abstract

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.

  • Keywords

Fluid-fluid interaction, unconditional energy stability, local $H^1$ stability, time variable filter, error estimate.

  • AMS Subject Headings

65M15, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-37-1417, author = {Li , WeiHuang , Pengzhan and He , Yinnian}, title = {A Time Variable Filter Approach for the Fluid-Fluid Interaction}, journal = {Communications in Computational Physics}, year = {2025}, volume = {37}, number = {5}, pages = {1417--1451}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2024-0108}, url = {http://global-sci.org/intro/article_detail/cicp/24099.html} }
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 -

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.

Li , WeiHuang , Pengzhan and He , Yinnian. (2025). A Time Variable Filter Approach for the Fluid-Fluid Interaction. Communications in Computational Physics. 37 (5). 1417-1451. doi:10.4208/cicp.OA-2024-0108
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