Improvement of spectral element methods for simulating transitional and turbulent incompressible flows

• Grant number: 20/10910-8
• Support Opportunities: Regular Research Grants
• Start date: June 01, 2021
• End date: September 30, 2023
• Field of knowledge: Engineering - Aerospace Engineering - Aerodynamics
• Principal Investigator: Rodrigo Costa Moura
• Grantee: Rodrigo Costa Moura
• Host Institution: Divisão de Engenharia Aeronáutica (IEA). Instituto Tecnológico de Aeronáutica (ITA). Ministério da Defesa (Brasil). São José dos Campos , SP, Brazil
• Associated researchers: André Fernando de Castro da Silva ; Vinicius Malatesta

Abstract

This work aims at improving the accuracy and robustness of the so-called spectral element methods for under-resolved simulations of transitional and turbulent incompressible flows. The study shall focus on the high-order method known as continuous Galerkin (CG) minding under-resolved DNS / implicit LES approaches. This numerical method is essentially a high-order extension of classical finite element methods, with CG being currently the primary representative of spectral element methods when in comes to incompressible flows. These methods have been gaining extensive popularity over the last three decades and are gradually finding their place into industry, showing advanced potential for high-fidelity analyses involving transition and turbulence. There are, however, aspects of accuracy (solution quality) and robustness (numerical stability) that should be improved to accelerate transition of these technologies from academia to industry. In under-resolved DNS / implicit LES approaches, the numerical dissipation of the adopted method acts in place of a subgrid-scale turbulence model (implicit modeling). Hence, aspects of accuracy and robustness will depend solely on the quantity and quality of the dissipation employed. The scientific challenge consists therefore in better understanding and quantifying the dissipation properties of each method, and also in developing numerical stabilization techniques to achieve an optimal balance between robustness and accuracy. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

MOURA, R. C.; FERNANDES, L. D.; SILVA, A. F. C.; MENGALDO, G.; SHERWIN, S. J.. Spectral/hp element methods' linear mechanism of (apparent) energy transfer in Fourier space: Insights into dispersion analysis for implicit LES. Journal of Computational Physics, v. 471, p. 9-pg., 2022-12-15. (20/10910-8)

MOURA, RODRIGO C.; CASSINELLI, ANDREA; DA SILVA, ANDRE F. C.; BURMAN, ERIK; SHERWIN, SPENCER J.. Gradient jump penalty stabilisation of spectral/hp element discretisation for under-resolved turbulence simulations. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, v. 388, JAN 1 2022. (20/10910-8)