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arXiv · 2010.00621

Nonsmooth Exact Penalization Second-order Methods for incompressible Bingham flows

Sergio González-Andrade·Sofía López·Pedro Merino
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Abstract

We consider the exact penalization of the incompressibility condition $div(u)=0$ for the velocity field of a Bingham fluid in terms of the $L^1$-norm. This penalization procedure results in a nonsmooth optimization problem for which we propose an algorithm using generalized second-order information. Our method solves the resulting nonsmooth problem by considering the steepest descent direction and extra generalized second-order information associated to the nonsmooth term. This method has the advantage that the divergence-free property is enforced by the descent direction proposed by the method without the need of build-in divergence-free approximation schemes. The inexact penalization approach, given by the $L^2$-norm, is also considered in our discussion and comparison.

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Sergio González-Andrade, Sofía López, Pedro Merino. 2020-10-01. Nonsmooth Exact Penalization Second-order Methods for incompressible Bingham flows. https://arxiv.org/abs/2010.00621

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