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Energy, Enstrophy and Parameter Sensitivity for the Time Relaxation Model
Fran Pahlevani

Last modified: 2020-07-27


Fluid models were developed as an alternative to the Navier-Stokes equations to avoid computational complexity especially in case of turbulent flows. Model errors due to the variation of a model parameter become an immediate concern in different aspects. In this presentation, we discuss two such aspects as the conservation of energy and enstrophy, and the sensitivity to a model parameter for the so called Time Relaxation Model, TRM. This filter based stabilization model with an added relaxation term is considered a high order fluid model (see Refs. [1, 2, 3]). Energy and enstrophy are two essential quantities characterizing change in the structure of the flow in time and are used to test if a simulation of a fluid flow is properly performed. We show that the energy and enstrophy obtained from TRM tend to the corresponding quantities of Navier-Stokes Equation as the model parameters tend to zero. Our numerical experiments confirm the above conclusions.




[1]    W. Layton, M. Neda, Truncation of Scales by Time Relaxation, J. Math Anal. Appl. 325, pp. 788-807 (2007).

[2]    S. De, D. Hannasch, M. Neda and E. Nikonova, Numerical analysis and computations of a higher accuracy time relaxation fluid flow model, International Journal of Computer Mathematics, pp. 1-22 (2008).

[3]    M. Neda, F. Pahlevani and J. Waters, Sensitivity Analysis and Computations of the Time Relaxation Model, Journal of Advances in Applied Mathematics and Mechanics 7, pp. 89-115 (2015).



Fluid Models, Navier-Stokes Equations, Time Relaxation Model, Energy and Enstrophy, Sensitivity Analysis

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