{"id":9679,"date":"2026-08-05T21:52:11","date_gmt":"2026-08-05T13:52:11","guid":{"rendered":"\/jase\/?post_type=tkuisotope&#038;p=9679"},"modified":"2026-08-16T13:23:39","modified_gmt":"2026-08-16T05:23:39","slug":"jase-202611-34-009","status":"publish","type":"tkuisotope","link":"\/jase\/?tkuisotope=jase-202611-34-009","title":{"rendered":"Influence of Time Step on Accuracy and Convergence in Fluid\u2013Structure Interaction Analysis"},"content":{"rendered":"\n<div class=\"wp-block-tkuwpbs5-bs5-row row article-info\">\n<div class=\"wp-block-tkuwpbs5-bs5-column col-md-3 align-self-start\">\n<p><i class=\"fa fa-folder\" aria-hidden=\"true\"><\/i>&nbsp;<a href=\"\/jase\/?page_id=807\" data-type=\"page\" data-id=\"807\">2026<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-tkuwpbs5-bs5-column col-md-3 align-self-start\">\n<p><i class=\"fa fa-folder-open\" aria-hidden=\"true\"><\/i>&nbsp;<a href=\"\/jase\/?page_id=9439\" data-type=\"page\" data-id=\"9439\">Volume 34<\/a><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-tkuwpbs5-bs5-column col-md-6 align-self-start\">\n<div class=\"wp-block-tkuwpbs5-bs5-div dv_publish\" data-aos=\"normal\"><div class=\"wp-block-post-date\"><time datetime=\"2026-08-05T21:52:11+08:00\">2026-08-05<\/time><\/div><\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-tkuwpbs5-bs5-row row\">\n<div class=\"wp-block-tkuwpbs5-bs5-column col-md-5 align-self-start\">\n<div class=\"wp-block-tkuwpbs5-bs5-div au-ol\" data-aos=\"normal\">\n<p>Xuan-Thuc Nguyen<sup>1<\/sup>, Ngoc-Quynh Nguyen<sup>1<\/sup>, Le-Minh Nguyen<sup>1<\/sup>, Thi-Tuyet-Nhung Le<sup>2<\/sup>, Dai-Cuong Pham<sup>2<\/sup>, and Dinh-Quy Vu<sup>2<\/sup><a href=\"mailto:quy.vudinh@hust.edu.vn\"><i class=\"fa fa-envelope\"><\/i><\/a> <\/p>\n\n\n\n<p style=\"font-size:14px\"><sup>1<\/sup>Viettel High Technology Industries Corporation\u2013 Viettel Group, Hanoi, Vietnam<\/p>\n\n\n\n<p style=\"font-size:14px\"><sup>2<\/sup>School of Mechanical Engineering, Hanoi University of Science and Technology, Hanoi, Vietnam<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-tkuwpbs5-bs5-div\" style=\"margin-top:var(--wp--preset--spacing--40)\" data-aos=\"normal\">\n<p>Received: March 07, 2026<br>Accepted:&nbsp;July 11, 2026<br>Publication Date:&nbsp;August 05, 2026<\/p>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-tkuwpbs5-bs5-column col-md-7 align-self-start clk=\u5716\u7247\"><img decoding=\"async\" src=\"\/jase\/wp-content\/uploads\/2026\/08\/34_009.jpg\" class=\"img-fluid img-fluid mx-auto d-block\" alt=\"\u4e0a\u50b3\u5716\u7247\">\n\n\n<p class=\"has-text-align-center\">Composite&nbsp;wing&nbsp;model.&nbsp;<\/p>\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-small-font-size\"><i class=\"fab fa-creative-commons\"><\/i>&nbsp;<strong>Copyright&nbsp;<\/strong>The Author(s). This is an open access article distributed under the terms of the&nbsp;<a rel=\"noreferrer noopener\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\" target=\"_blank\">Creative Commons Attribution&nbsp;License (CC BY 4.0)<\/a>, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.<\/p>\n\n\n\n<p>Download Citation:&nbsp; <a href=\"\/jase\/wp-content\/uploads\/2026\/08\/V34.0009.txt\" data-type=\"attachment\" data-id=\"9765\" target=\"_blank\" rel=\"noreferrer noopener\">BibTeX <\/a>| <a rel=\"noreferrer noopener\" href=\"http:\/\/dx.doi.org\/10.6180\/jase.202611_34.009\" target=\"_blank\">http:\/\/dx.doi.org\/10.6180\/jase.202611_34.009<\/a>&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"btn btn-primary article-btn\"><a href=\"\/jase\/wp-content\/uploads\/2026\/08\/009_2026_0474.pdf\" data-type=\"attachment\" data-id=\"9627\" target=\"_blank\" rel=\"noreferrer noopener\">Download PDF<\/a><\/p>\n\n\n\n<div style=\"height:24px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>Fluid\u2013Structure Interaction (FSI) is a multidisciplinary research field that has drawn significant attention across various domains, including aerospace, biomedical engineering, agriculture, industry, and renewable energy. The finite element method (FEM) has become a leading computational tool for investigating these coupled phenomena, enabling more accurate prediction of the interactions between fluids and solids. Although numerical FSI simulations are more economical than physical experiments, they require substantial computational resources. This study focuses on the influence of time step size on the accuracy and convergence of coupled FSI simulations. A cantilever beam model is adopted as the benchmark case and analyzed using the ANSYS software suite. The time step of the fluid solver and the sub-step size of the structural solver are systematically varied to determine the optimal configuration that ensures accuracy while minimizing computation time. The amplitude and frequency responses obtained from the coupled solver are validated against reference results from published literature. The optimized time step and sub-step selection strategy is then applied to more<br>complex FSI simulations, including a cropped delta wing and a lightweight composite UAV wing, to evaluate flutter behavior within their operating envelopes.<\/p>\n\n\n\n<p><em>Keywords:&nbsp;Computational Fluid Dynamics (CFD); Fluid\u2013Structure Interaction (FSI); Time Step, Sub-Step; Convergence<\/em><\/p>\n\n\n\n<div style=\"height:2rem\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-tkuwpbs5-bs5-div ref_ol\" data-aos=\"normal\">\n<ol>\n<li>[1] B. Wang, L. Feng, L. Xu, H. Gao, X. Luo, and N. Qi, (2025) \u201cThree-dimensional fluid\u2013structure interaction modelling of the venous valve using immersed boundary\/finite element method\u201d Computers in Biology and Medicine 185: 109450. DOI: 10.1016\/j.compbiomed.2024.109450.<\/li>\n<li>[2] F. Marcinn\u00f2, C. Vergara, L. Giovannacci, A. Quarteroni, and G. Prouse, (2024) \u201cComputational fluid-structure interaction analysis of the end-to-side radiocephalic arteriovenous fistula\u201d Computer Methods and Programs in Biomedicine 249: 108146. DOI: 10.1016\/j.cmpb.2024.108146.<\/li>\n<li>[3] A. M. Tango, A. Monteleone, A. Ducci, and G. Burriesci, (2025) \u201cAnalysis of the haemodynamic changes caused by surgical and transcatheter aortic valve replacements by means fluid\u2013structure interaction simulations\u201d Computers in Biology and Medicine 186: 109673. DOI: 10.1016\/j.compbiomed.2025.109673.<\/li>\n<li>[4] L. Feng, H. Gao, and X. Luo, (2024) \u201cWhole\u2013heart modelling with valves in a fluid\u2013structure interaction framework\u201d Computer Methods in Applied Mechanics and Engineering 420: 116724. DOI: 10.1016\/j.cma.2023.116724.<\/li>\n<li>[5] S. Qashqaie Abdi and K. Hassani, (2023) \u201cThe study of the relationship between unicuspid aortic valve insufficiency and heart disease by fluid\u2013structure interaction modeling\u201d Biomedical Engineering Advances 5: 100079. DOI: 10.1016\/j.bea.2023.100079.<\/li>\n<li>[6] L. Cai, T. Zhao, Y. Wang, X. Luo, and H. Gao, (2023) \u201cFluid\u2013structure interaction simulation of pathological mitral valve dynamics in a coupled mitral valve-left ventricle model\u201d Intelligent Medicine 3(2): 104\u2013114. DOI: 10.1016\/j.imed.2022.06.005.<\/li>\n<li>[7] A. Souche and K. Valen-Sendstad, (2022) \u201cHigh-fidelity fluid structure interaction simulations of turbulent-like aneurysm flows reveals high-frequency narrowband wall vibrations: A stimulus of mechanobiological relevance?\u201d Journal of Biomechanics 145: 111369. DOI: 10.1016\/j.jbiomech.2022.111369.<\/li>\n<li>[8] Y. Mai, S. Wen, J. Zhang, Y. Lan, and G. Huang, (2025) \u201cAnalysis of the two-way fluid\u2013structure interaction between the rice canopy and the downwash airflow of a quadcopter UAV\u201d Biosystems Engineering 250: 343\u2013364. DOI: 10.1016\/j.biosystemseng.2025.01.005.<\/li>\n<li>[9] H. Cui, C. Wang, X. Liu, X. Liu, J. Yuan, and Y. Liu, (2023) \u201cPrediction of the distribution of airflow within the cotton canopy using fluid\u2013structure interaction simulation and machine-learning methods\u201d Biosystems Engineering 232: 51\u201366. DOI: 10.1016\/j.biosystemseng.2023.06.011.<\/li>\n<li>[10] X. Liao, C. G. Koh, and Y. K. Chow, (2025) \u201cA hybrid strategy for numerical simulations of fluid\u2013structure interaction problems in ocean engineering\u201d Applied Ocean Research 155: 104433. DOI: 10.1016\/j.apor.2025.104433.<\/li>\n<li>[11] I. Pr\u00fcter, F. Spr\u00f6er, K. Keimer, O. Lojek, C. Windt, D. Sch\u00fcrenkamp, H. Bihs, I. Nistor, and N. Goseberg, (2025) \u201cA comprehensive numerical study on the current-induced fluid\u2013structure interaction of flexible submerged vegetation\u201d Journal of Fluids and Structures 133: 104232. DOI: 10.1016\/j.jfluidstructs.2024.104232.<\/li>\n<li>[12] H. K. Sakran, M. S. A. Aziz, and C. Y. Khor, (2024) \u201cBlade Wrap Angle Impact on Centrifugal Pump Performance: Entropy Generation and Fluid-Structure Interaction Analysis\u201d Computer Modeling in Engineering &amp; Sciences 140(1): 109\u2013137. DOI: 10.32604\/cmes.2024.047245.<\/li>\n<li>[13] N. B. Darbamulla and R. K. Jaiman, (2024) \u201cA finite element framework for fluid\u2013structure interaction of turbulent cavitating flows with flexible structures\u201d Computers &amp; Fluids 277: 106283. DOI: 10.1016\/j.compfluid.2024.106283.<\/li>\n<li>[14] M. R. Firdaus, M. R. Mahalik, A. Jusuf, S. Wicaksono, L. Gunawan, and T. Dirgantara, (2024) \u201cModelling Strategies to Simulate the Fluid-Structure Interaction of Amphibious Aircraft Float Structure\u201d Procedia Structural Integrity 52: 309\u2013322. DOI: 10.1016\/j.prostr.2023.12.031.<\/li>\n<li>[15] P. Shakya, M. Thomas, A. C. Seibi, M. Shekaramiz, and M. A. S. Masoum, (2024) \u201cFluid-structure interaction and life prediction of small-scale damaged horizontal axis wind turbine blades\u201d Results in Engineering 23: 102388. DOI: 10.1016\/j.rineng.2024.102388.<\/li>\n<li>[16] L. Yuan, Z. Liu, L. Li, and M. Lin, (2023) \u201cAnalysis of the Influence of the Blade Deformation on Wind Turbine Output Power in the Framework of a Bidirectional Fluid-Structure Interaction Model\u201d Fluid Dynamics &amp; Materials Processing 19(5): 1129\u20131141. DOI: 10.32604\/fdmp.2023.023538.<\/li>\n<li>[17] Y. Cui, L. Wang, J. Ru, and J. Wu, (2023) \u201cAnalysis and Optimization of Flow-Guided Structure Based on Fluid-Structure Interaction\u201d Fluid Dynamics &amp; Materials Processing 19(6): 1573\u20131584. DOI: 10.32604\/fdmp.2023.024873.<\/li>\n<li>[18] M. Mihaila-Andres, C. Rotaru, and P. G. Matei, (2015) \u201cStaggered Approach for Fluid-Structure Interaction Phenomena of an AGARD 445.6 Wing Using Commercial CFD\/CSM Software\u201d Journal of Aerospace Engineering 28(4): DOI: 10.1061\/(asce)as.1943-5525.0000427.<\/li>\n<li>[19] N. Di Domenico, C. Groth, A. Wade, T. Berg, and M. E. Biancolini, (2018) \u201cFluid structure interaction analysis: vortex shedding induced vibrations\u201d Procedia Structural Integrity 8: 422\u2013432. DOI: 10.1016\/j.prostr.2017.12.042.<\/li>\n<li>[20] A. J. Torregrosa, A. Gil, P. Quintero, and A. Cremades, (2022) \u201cOn the effects of orthotropic materials in flutter protection of wind turbine flexible blades\u201d Journal of Wind Engineering and Industrial Aerodynamics 227: 105055. DOI: 10.1016\/j.jweia.2022.105055.<\/li>\n<li>[21] F. Salmon and L. Chatellier, (2022) \u201c3D fluid\u2013structure interaction simulation of an hydrofoil at low Reynolds number\u201d Journal of Fluids and Structures 111: 103573. DOI: 10.1016\/j.jfluidstructs.2022.103573.<\/li>\n<li>[22] W. Guo, Y. Shui, L. Nie, and G. Chen, (2024) \u201cFluid-structure interaction simulation for multi-body flexible morphing structures\u201d Chinese Journal of Aeronautics 37(2): 137\u2013147. DOI: 10.1016\/j.cja.2023.09.009.<\/li>\n<li>[23] J. Pfl\u00fcger and C. Breitsamter, (2024) \u201cGust response of an elasto-flexible morphing wing using fluid\u2013structure interaction simulations\u201d Chinese Journal of Aeronautics 37(2): 45\u201357. DOI: 10.1016\/j.cja.2023.12.017.<\/li>\n<li>[24] Y. Guo, W. Yang, Y. Dong, and D. Xue, (2024) \u201cResonance mechanism of flapping wing based on fluid structure interaction simulation\u201d Chinese Journal of Aeronautics 37(5): 243\u2013262. DOI: 10.1016\/j.cja.2024.01.011.<\/li>\n<li>[25] Y. Dai, Y. Hu, Y. Wu, C. Song, and C. Yang, (2025) \u201cEffect of leading-edge and trailing-edge camber morphing on gust load for an elastic wing\u201d Chinese Journal of Aeronautics 38(4): 103245. DOI: 10.1016\/j.cja.2024.09.021.<\/li>\n<li>[26] T. Schwentner and T.-P. Fries, (2024) \u201cFully Coupled, Higher-Order, Block-Structured Mesh Generation in Fluid\u2013Structure Interaction\u201d International Journal for Numerical Methods in Fluids 97(3): 359\u2013377. DOI: 10.1002\/fld.5355.<\/li>\n<li>[27] M. R. Rajanna, E. L. Johnson, N. Liu, A. Korobenko, Y. Bazilevs, and M.-C. Hsu, (2022) \u201cFluid\u2013structure interaction modeling with nonmatching interface discretizations for compressible flow problems: Computational framework and validation study\u201d Mathematical Models and Methods in Applied Sciences 32(12): 2497\u20132528. DOI: 10.1142\/s0218202522500592.<\/li>\n<li>[28] B. Li, W. Sun, Y. Xie, and W. Yu, (2024) \u201cOptimal L2 Error Analysis of a Loosely Coupled Finite Element Scheme for Thin-Structure Interactions\u201d SIAM Journal on Numerical Analysis 62(4): 1782\u20131813. DOI: 10.1137\/23m1578401.<\/li>\n<li>[29] M. Buka\u010d, G. Fu, A. Seboldt, and C. Trenchea, (2023) \u201cTime-adaptive partitioned method for fluid-structure interaction problems with thick structures\u201d Journal of Computational Physics 473: 111708. DOI: 10.1016\/j.jcp.2022.111708.<\/li>\n<li>[30] J. \u010ce\u010drdle. Whirl Flutter of Turboprop Aircraft Structures. Elsevier, 2015. DOI: 10.1016\/C2014-0-01800-X.<\/li>\n<li>[31] A. K. Slone, K. Pericleous, C. Bailey, and M. Cross, (2002) \u201cDynamic fluid\u2013structure interaction using finite volume unstructured mesh procedures\u201d Computers &amp; Structures 80(5\u20136): 371\u2013390. DOI: 10.1016\/s0045-7949(01)00177-8.<\/li>\n<li>[32] C. Peng and J. Han, (2011) \u201cNumerical investigation of the effects of structural geometric and material nonlinearities on limit-cycle oscillation of a cropped delta wing\u201d Journal of Fluids and Structures 27(4): 611\u2013622. DOI: 10.1016\/j.jfluidstructs.2011.03.015.<\/li>\n<li>[33] A. A. Kumar, N. Manoj, A. K. Onkar, and M. Manjuprasad, (2016) \u201cFluid-Structure Interaction Analysis of a Cropped Delta Wing\u201d Procedia Engineering 144: 1205\u20131212. DOI: 10.1016\/j.proeng.2016.05.102.<\/li>\n<li>[34] W. Wang, Y. Dai, C. Zhang, X. Gao, and M. Zhao, (2016) \u201cMicromechanical Modeling of Fiber-Reinforced Composites with Statistically Equivalent Random Fiber Distribution\u201d Materials 9(8): 624. DOI: 10.3390\/ma9080624.<\/li>\n<li>[35] MakeItFrom.com. 7075-T6 Aluminum Material Properties Database.<\/li>\n<li>[36] Corecell\u2122 M-foam structural core data sheet. Gurit. 2021.<\/li>\n<li>[37] Federal Aviation Administration. Airworthiness Standard FAR Part 23, Part 25. 2024.<\/li>\n<\/ol>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"author":3,"template":"wp-custom-template-detail-4-aricles","meta":{"_uag_custom_page_level_css":""},"categories":[12,1682,6],"tags":[1691],"acf":[],"uagb_featured_image_src":[],"uagb_author_info":{"display_name":"\u6797\u923a\u6db5","author_link":"\/jase\/?author=3"},"uagb_comment_info":0,"uagb_excerpt":"&nbsp;Copyright&nbsp;The Author(s). This is an open access article distributed under the terms of the&nbsp;Creative Commons Attribution&nbsp;License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited. Download Citation:&nbsp; BibTeX | http:\/\/dx.doi.org\/10.6180\/jase.202611_34.009&nbsp;&nbsp; Download PDF Fluid\u2013Structure Interaction (FSI) is a multidisciplinary research field that has drawn&hellip;","_links":{"self":[{"href":"\/jase\/index.php?rest_route=\/wp\/v2\/tkuisotope\/9679"}],"collection":[{"href":"\/jase\/index.php?rest_route=\/wp\/v2\/tkuisotope"}],"about":[{"href":"\/jase\/index.php?rest_route=\/wp\/v2\/types\/tkuisotope"}],"author":[{"embeddable":true,"href":"\/jase\/index.php?rest_route=\/wp\/v2\/users\/3"}],"wp:attachment":[{"href":"\/jase\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9679"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"\/jase\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9679"},{"taxonomy":"post_tag","embeddable":true,"href":"\/jase\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9679"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}