A gradient-based framework for maximizing mixing in binary fluids

A computational framework based on nonlinear direct-adjoint looping is presented for optimizing mixing strategies for binary fluid systems. The governing equations are the nonlinear Navier–Stokes equations, augmented by an evolution equation for a passive scalar, which are solved by a spectral Fouri...

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Bibliographic Details
Published in:Journal of computational physics 2018-09, Vol.368, p.131-153
Main Authors: Eggl, M.F., Schmid, P.J.
Format: Article
Language:English
Subjects:
Adjoint method
Algorithms
Binary fluids
Computational fluid dynamics
Computational physics
Fluid dynamics
Mathematical analysis
Mixing
Navier-Stokes equations
Nonlinear equations
Optimization
Penalization
Stirrers
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Summary:A computational framework based on nonlinear direct-adjoint looping is presented for optimizing mixing strategies for binary fluid systems. The governing equations are the nonlinear Navier–Stokes equations, augmented by an evolution equation for a passive scalar, which are solved by a spectral Fourier-based method. The stirrers are embedded in the computational domain by a Brinkman-penalization technique, and shape and path gradients for the stirrers are computed from the adjoint solution. Four cases of increasing complexity are considered, which demonstrate the efficiency and effectiveness of the computational approach and algorithm. Significant improvements in mixing efficiency, within the externally imposed bounds, are achieved in all cases. •Successful embedding of penalized governing equations into an optimization procedure.•Explicit derivation of gradient-expressions for the penalization mask.•Benchmarks of the optimization platform with special emphasis on convergence behavior.•Demonstration of significant gain in mixing efficiency with control constraints.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2018.04.030