000165015 001__ 165015
000165015 005__ 20251204150238.0
000165015 0247_ $$2doi$$a10.1016/j.cma.2025.118480
000165015 0248_ $$2sideral$$a146470
000165015 037__ $$aART-2025-146470
000165015 041__ $$aeng
000165015 100__ $$0(orcid)0000-0001-7802-3411$$aHauke, Guillermo$$uUniversidad de Zaragoza
000165015 245__ $$aA stable entropy producing formulation of two-equation turbulence models with particular reference to the − model
000165015 260__ $$c2025
000165015 5060_ $$aAccess copy available to the general public$$fUnrestricted
000165015 5203_ $$aConsistency and stability are two essential ingredients in the design of numerical algorithms for partial differential equations. Robust algorithms can be developed by incorporating nonlinear physical stability principles in their design, such as the entropy production inequality (i.e., the Clausius-Duhem inequality or second law of thermodynamics), rather than by simply adding artificial viscosity (a common approach). In the context of two-equation turbulence models we introduce space-time averaged variables, the essential concept which enables identification of an appropriate set of conservation variables. This change of variables, compared with the usual formulations of the model, is also key to the ensuing developments. From these, the correct concept of entropy and a set of entropy variables can be defined which leads to a symmetric system of advective-diffusive equations. The equivalence of quasilinear symmetric, advective-diffusive systems with coupled systems having a nonlinear convex entropy function, established by Mock [25] and Godunov [26], provides the theoretical underpinning of our developments. Positivity and symmetry of the equations require certain constraints on the turbulence diffusivity coefficients and the turbulence source terms that we delineate. With these, we are able to design entropy producing formulations of two-equation turbulence models and, in particular, the model, and numerical formulations that inherit these properties. The accuracy of the original model is maintained and we automatically gain computational stability and robustness due to the guaranteed entropy production property. The results suggest possible formulations of other turbulence models that will enhance their behavior in numerical simulation.
000165015 536__ $$9info:eu-repo/grantAgreement/ES/DGA/T32-23R$$9info:eu-repo/grantAgreement/ES/MICINN/PID2022-138572OB-C44
000165015 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttps://creativecommons.org/licenses/by/4.0/deed.es
000165015 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000165015 700__ $$aHughes, T.J.R.
000165015 7102_ $$15001$$2600$$aUniversidad de Zaragoza$$bDpto. Ciencia Tecnol.Mater.Fl.$$cÁrea Mecánica de Fluidos
000165015 773__ $$g449, Part. B (2025), 118480 [27 pp.]$$pComput. methods appl. mech. eng.$$tComputer Methods in Applied Mechanics and Engineering$$x0045-7825
000165015 8564_ $$s2613852$$uhttps://zaguan.unizar.es/record/165015/files/texto_completo.pdf$$yVersión publicada
000165015 8564_ $$s2017384$$uhttps://zaguan.unizar.es/record/165015/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000165015 909CO $$ooai:zaguan.unizar.es:165015$$particulos$$pdriver
000165015 951__ $$a2025-12-04-14:39:21
000165015 980__ $$aARTICLE