Sensitivity analysis of turbulence models using automatic differentiation

• Published in: SIAM journal on scientific computing Vol. 26; no. 2; pp. 510 - 522
• Main Authors: BISCHOF, Christian H, BÜCKER, H. Martin, RASCH, Arno
• Format: Conference Proceeding Journal Article
• Language: English
• Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2004
• Subjects: Algorithmics. Computability. Computer arithmetics; Applied sciences; Approximation; Boundary conditions; Computer science; control theory; systems; Computer simulation; Computers; Decomposition; Exact sciences and technology; Mathematics; Methods of scientific computing (including symbolic computation, algebraic computation); Miscellaneous; Navier-Stokes equations; Numerical analysis. Scientific computation; Reynolds number; Sciences and techniques of general use; Sensitivity analysis; Software; Software engineering; Theoretical computing; Turbulence models; Viscosity; 76F60; 68U20; Sensitivity analysis; Experimental data; k-epsilon turbulence model; Computer simulation; k epsilon turbulence model; 76F30; ADIFOR; 65Y99; Automatic differentiation; Scientific computation; FLUENT; 68N20; ADIFOR 68N19; 68-04; Renormalization group
• ISSN: 1064-8275; 1095-7197
• DOI: 10.1137/S1064827503426723

Turbulence models are examples of computer simulations that parameterize complicated phenomena and depend on artificial model parameters heuristically justified from empirical information and experimental data. To assess the confidence in the results of such a turbulence simulation, a derivative-based sensitivity analysis is carried out. The sensitivities of the flow over a backward-facing step w.r.t. parameters of the turbulence model are investigated. The standard k-$\varepsilon$ model and the renormalization group (RNG) k-$\varepsilon$ model are compared. Both turbulence models are implemented in the FLUENT code to which automatic differentiation is applied using the ADIFOR system. In our case studies, all turbulence models yield results that are rather sensitive to some of the modeling parameters.