A Convective Boundary Condition for the Navier-Stokes Equations: Existence Analysis and Numerical Implementations

Simon, John Sebastian H.; Notsu, Hirofumi

doi:10.48550/arxiv.2109.10025

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2022

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A popular one consists in using a do-nothing outlet condition (see e.g. [7,26,27,35,47,50]) which naturally comes from integration by parts when defining a weak formulation of the Navier-Stokes equations. However, since this outlet condition does not deal with re-entering flows, several papers use a non-smooth outlet boundary conditions for their numerical simulations (see e.g.…”

Section: Introductionmentioning

confidence: 99%

The Boussinesq System with Nonsmooth Boundary Conditions: Existence, Relaxation, and Topology Optimization

Vieira¹,

Cocquet

2022

SIAM J. Control Optim.

View full text Add to dashboard Cite

In this paper, we tackle a topology optimization problem which consists in finding the optimal shape of a solid located inside a fluid that minimizes a given cost function. The motion of the fluid is modeled thanks to the Boussinesq system which involves the unsteady Navier-Stokes equation coupled to a heat equation. In order to cover several models presented in the literature, we choose a non-smooth formulation for the outlet boundary conditions. This paper aims at proving existence of solutions to the resulting equations, along with the study of a relaxation scheme of the non-smooth conditions. A second part covers the topology optimization problem itself for which we proved the existence of optimal solutions and provides the definition of first order necessary optimality conditions.

show abstract