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Identifying invariant solutions of wall-bounded three-dimensional shear flows using robust adjoint-based variational techniques
- Publication Year :
- 2023
-
Abstract
- Invariant solutions of the Navier-Stokes equations play an important role in the spatiotemporally chaotic dynamics of turbulent shear flows. Despite the significance of these solutions, their identification remains a computational challenge, rendering many solutions inaccessible and thus hindering progress towards a dynamical description of turbulence in terms of invariant solutions. We compute equilibria of three-dimensional wall-bounded shear flows using an adjoint-based matrix-free variational approach. To address the challenge of computing pressure in the presence of solid walls, we develop a formulation that circumvents the explicit construction of pressure and instead employs the influence matrix method. Together with a data-driven convergence acceleration technique based on dynamic mode decomposition, this yields a practically feasible alternative to state-of-the-art Newton methods for converging equilibrium solutions. We compute multiple equilibria of plane Couette flow starting from inaccurate guesses extracted from a turbulent time series. The variational method outperforms Newton(-hookstep) iterations in successfully converging from poor initial guesses, suggesting a larger convergence radius.
- Subjects :
- Physics - Fluid Dynamics
Mathematics - Dynamical Systems
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2306.00165
- Document Type :
- Working Paper