Print Email Facebook Twitter Numerical Methods for the Optimization of Nonlinear Residual-Based Sungrid-Scale Models Using the Variational Germano Identity Title Numerical Methods for the Optimization of Nonlinear Residual-Based Sungrid-Scale Models Using the Variational Germano Identity Author Maher, G.D. Hulshoff, S.J. Faculty Aerospace Engineering Department Aerodynamics, Wind Energy & Propulsion Date 2014-07-20 Abstract The Variational Germano Identity [1, 2] is used to optimize the coefficients of residual-based subgrid-scale models that arise from the application of a Variational Multiscale Method [3, 4]. It is demonstrated that numerical iterative methods can be used to solve the Germano relations to obtain values for the parameters of subgrid-scale models that are nonlinear in their coefficients. Specifically, the Newton-Raphson method is employed. A least-squares minimization formulation of the Germano Identity is developed to resolve issues that occur when the residual is positive and negative over different regions of the domain. In this case a Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm is used to solve the minimization problem. The developed method is applied to the one-dimensional unsteady forced Burgers’ equation and the two-dimensional steady Stokes’ equations. It is shown that the Newton-Raphson method and BFGS algorithm generally solve, or minimize the residual of, the Germano relations in a relatively small number of iterations. The optimized subgridscale models are shown to outperform standard SGS models with respect to a L2 error. Additionally, the nonlinear SGS models tend to achieve lower L2 errors than the linear models. Subject subgrid-scale modelvariational multiscale methodvariational Germano identityoptimizationturbulence To reference this document use: http://resolver.tudelft.nl/uuid:9dff055c-eb6d-4005-a052-fce8aaeea792 Publisher CIMNE ISBN 978-84-942844-7-2 Source Proceedings - WCCM XI: 11th World Congress on Computational Mechanics; ECCM V: 5th European Conference on Computational Mechanics; ECFD VI: 6th European Conference on Computational Fluid Dynamics, Barcelona, Spain, 20-25 July 2014 Part of collection Institutional Repository Document type conference paper Rights © 2014 The Authors Files PDF Maher_2014.pdf 363.64 KB Close viewer /islandora/object/uuid:9dff055c-eb6d-4005-a052-fce8aaeea792/datastream/OBJ/view