{"title":"Numerical analysis of a 1/2-equation model of turbulence","authors":"Wei-Wei Han , Rui Fang , William Layton","doi":"10.1016/j.physd.2024.134428","DOIUrl":null,"url":null,"abstract":"<div><div>The recent 1/2-equation model of turbulence is a simplification of the standard Kolmogorov–Prandtl 1-equation URANS model. In tests, the 1/2-equation model produced comparable velocity statistics to a full 1-equation model with lower computational complexity. There is little progress in the numerical analysis of URANS models due to the difficulties in treating the coupling between equations and the nonlinearities in highest-order terms. The numerical analysis herein on the 1/2-equation model has independent interest and is also a first numerical analysis step to address the couplings and nonlinearities in a full 1-equation model. This report develops a complete numerical analysis of the 1/2-equation model. Stability, convergence, and error estimates are proven for a semi-discrete and fully discrete approximation. Finally, numerical tests are conducted to validate the predictions of the convergence theory.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"471 ","pages":"Article 134428"},"PeriodicalIF":2.7000,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physica D: Nonlinear Phenomena","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167278924003786","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
The recent 1/2-equation model of turbulence is a simplification of the standard Kolmogorov–Prandtl 1-equation URANS model. In tests, the 1/2-equation model produced comparable velocity statistics to a full 1-equation model with lower computational complexity. There is little progress in the numerical analysis of URANS models due to the difficulties in treating the coupling between equations and the nonlinearities in highest-order terms. The numerical analysis herein on the 1/2-equation model has independent interest and is also a first numerical analysis step to address the couplings and nonlinearities in a full 1-equation model. This report develops a complete numerical analysis of the 1/2-equation model. Stability, convergence, and error estimates are proven for a semi-discrete and fully discrete approximation. Finally, numerical tests are conducted to validate the predictions of the convergence theory.
期刊介绍：
Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.
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