Last modified: 2020-07-27

#### Abstract

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.

**References**

[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).