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This paper is concerned with the optimal shape design of the newtonian viscous incompressible fluids driven by the stationary nonhomogeneous Navier-Stokes equations. We use three approaches to derive the structures of shape gradients for…

Optimization and Control · Mathematics 2007-05-23 Zhiming Gao , Yichen Ma , Hongwei Zhuang

This paper is concerned with a numerical simulation of shape optimization in a two-dimensional viscous incompressible flow governed by Navier--Stokes equations with mixed boundary conditions containing the pressure. The minimization problem…

Optimization and Control · Mathematics 2007-05-23 Zhiming Gao , Yichen Ma

We consider the problem of finding optimal shapes of fluid domains. The fluid obeys the Navier--Stokes equations. Inside a holdall container we use a phase field approach using diffuse interfaces to describe the domain of free flow. We…

Optimization and Control · Mathematics 2014-05-15 Harald Garcke , Claudia Hecht , Michael Hinze , Christian Kahle

We investigate the behavior of dynamic shape design problems for fluid flow at large time horizon. In particular, we shall compare the shape solutions of a dynamic shape optimization problem with that of a stationary problem and show that…

Optimization and Control · Mathematics 2022-10-21 John Sebastian H. Simon

We consider shape and topology optimization for fluids which are governed by the Navier--Stokes equations. Shapes are modelled with the help of a phase field approach and the solid body is relaxed to be a porous medium. The phase field…

Optimization and Control · Mathematics 2015-04-27 Harald Garcke , Claudia Hecht , Michael Hinze , Christian Kahle , Kei Fong Lam

We study topology optimization governed by the incompressible Navier-Stokes flows using a phase field model. Novel stabilized semi-implicit schemes for the gradient flows of Allen-Cahn and Cahn-Hilliard types are proposed for solving the…

Numerical Analysis · Mathematics 2024-05-09 Jiajie Li , Shengfeng Zhu

We consider the shape optimization of an object in Navier--Stokes flow by employing a combined phase field and porous medium approach, along with additional perimeter regularization. By considering integral control and state constraints, we…

Optimization and Control · Mathematics 2018-12-04 Harald Garcke , Michael Hinze , Christian Kahle , Kei Fong Lam

This paper is concerned with a shape sensitivity analysis of a viscous incompressible fluid driven by Stokes equations with nonhomogeneous boundary condition. The structure of shape gradient with respect to the shape of the variable domain…

Optimization and Control · Mathematics 2007-05-23 Z. M. Gao , Y. C. Ma , H. W. Zhuang

We investigate a complex system involving multiple shapes to be optimized in a domain, taking into account geometric constraints on the shapes and uncertainty appearing in the physics. We connect the differential geometry of product shape…

Optimization and Control · Mathematics 2023-08-16 Caroline Geiersbach , Tim Suchan , Kathrin Welker

In this study, a shape optimization problem for the two-dimensional stationary Navier--Stokes equations with an artificial boundary condition is considered. The fluid is assumed to be flowing through a rectangular channel, and the…

Optimization and Control · Mathematics 2021-08-10 John Sebastian H. Simon , Hirofumi Notsu

In fluid physics, data-driven models to enhance or accelerate solution methods are becoming increasingly popular for many application domains, such as alternatives to turbulence closures, system surrogates, or for new physics discovery. In…

We investigate the long time behavior of solutions to a shape and topology optimization problem with respect to the time-dependent Navier--Stokes equations. The sought topology is represented by a stationary phase-field that represents a…

Optimization and Control · Mathematics 2026-05-04 Michael Hinze , Christian Kahle , John Sebastian H. Simon

In this paper, we study the role of boundary conditions on the optimal shape of a dyadic tree in which flows a Newtonian fluid. Our optimization problem consists in finding the shape of the tree that minimizes the viscous energy dissipated…

Analysis of PDEs · Mathematics 2010-12-13 Xavier Dubois De La Sablonière , Benjamin Mauroy , Yannick Privat

In this work, we study a boundary control problem for the evolutionary Navier-Stokes equations, under mixed boundary conditions, in two dimensions. The cost functional here considered is of quadratic type, depending on both state and…

Optimization and Control · Mathematics 2024-10-02 Telma Guerra , Irene Marín-Gayte , Jorge Tiago

We present a general numerical approach to shape optimization with state constraints for 2-dimensional geometries, without relaxing the constraints. To do this we reformulate the problem on a fixed reference domain using a conformal…

Optimization and Control · Mathematics 2014-12-16 Christian Leithäuser , René Pinnau , Robert Feßler

Shape optimization based on surface gradients and the Hadarmard-form is considered for a compressible viscous fluid. Special attention is given to the difference between the 'function composition' approach involving local shape derivatives…

Optimization and Control · Mathematics 2013-12-23 Matthias Sonntag , Stephan Schmidt , Nicolas R. Gauger

A new approach to model order reduction of the Navier-Stokes equations at high Reynolds number is proposed. Unlike traditional approaches, this method does not rely on empirical turbulence modeling or modification of the Navier-Stokes…

Fluid Dynamics · Physics 2013-09-11 Maciej Balajewicz , Earl Dowell , Bernd Noack

Computational design optimization in fluid dynamics usually requires to solve non-linear partial differential equations numerically. In this work, we explore a Bayesian optimization approach to minimize an object's drag coefficient in…

Computational Engineering, Finance, and Science · Computer Science 2017-12-12 Stephan Eismann , Stefan Bartzsch , Stefano Ermon

In this article we address flow problems that carry a multiscale character in time. In particular we consider the Navier-Stokes flow in a channel on a fast scale that influences the movement of the boundary which undergoes a deformation on…

Numerical Analysis · Mathematics 2020-08-11 Stefan Frei , Thomas Richter

We consider a test problem for Navier-Stokes solvers based on the flow around a cylinder that exhibits chaotic behavior, to examine the behavior of various numerical methods. We choose a range of Reynolds numbers for which the flow is…

Numerical Analysis · Mathematics 2024-08-19 Henry von Wahl , L. Ridgway Scott
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