UC Irvine

The modeling of fluid flows at high Reynolds numbers using the Navier Stokes (NS) equations presents several numerical challenges. The non-linear convective terms in the NS-equations can lead to numerical instabilities and require careful consideration for the spatial discretization. In this dissertation, we investigate the use of the conservation law satisfying high order mimetic difference methods for solving the incompressible NS-equations in turbulent flow regimes. The skew-symmetric convective discretization terms are utilized to obtain structure preserving discretizations, in combination with pseudo symplectic temporal discretization schemes. The primary objective of this thesis is to investigate the application of the mimetic methods for the direct numerical simulations of the incompressible NS-equations in turbulent regimes.

A secondary objective of the thesis lies in developing a mimetic difference based machine learning framework to uncover the subgrid scale stress tensor terms. To this end, a mimetic data-driven machine learning framework is investigated with the Burgulence equation. a priori and a posteriori evaluations of the machine-learned turbulence model are compared with some of the popular large eddy simulation models such as the Smagorinsky. The promising results obtained from this study present several avenues for future research in this topic.