Optimal Control of a Semidiscrete Cahn--Hilliard--Navier--Stokes System with Nonmatched Fluid Densities

DOI10.1137/15M1025128zbMath1368.49022arXiv1506.03591OpenAlexW2963062982WikidataQ115155125 ScholiaQ115155125MaRDI QIDQ5270334

Donat Wegner, Tobias Keil, Michael Hintermüller

Publication date: 23 June 2017

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.03591

zbMATH Keywords

optimal controlNavier-StokesCahn-HilliardYosida regularizationmathematical programming with equilibrium constraintssemidiscretization in timenonsmooth potentialslimiting C-stationaritynonmatched densities

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Optimality conditions and duality in mathematical programming (90C46) Liquid-gas two-phase flows, bubbly flows (76T10) Discrete approximations in optimal control (49M25) Unilateral problems for nonlinear elliptic equations and variational inequalities with nonlinear elliptic operators (35J87)

Related Items

Asymptotic limits and optimal control for the Cahn-Hilliard system with convection and dynamic boundary conditions ⋮ Optimal velocity control of a convective Cahn-Hilliard system with double obstacles and dynamic boundary conditions: a `deep quench' approach ⋮ Simulation and Control of a Nonsmooth Cahn–Hilliard Navier–Stokes System with Variable Fluid Densities ⋮ On a nonlocal Cahn-Hilliard/Navier-Stokes system with degenerate mobility and singular potential for incompressible fluids with different densities ⋮ Optimal boundary control of a nonstandard viscous Cahn-Hilliard system with dynamic boundary condition ⋮ Optimal distributed control of the Cahn-Hilliard-Brinkman system with regular potential ⋮ Optimal distributed control of two-dimensional nonlocal Cahn-Hilliard-Navier-Stokes systems with degenerate mobility and singular potential ⋮ Optimal control of time-discrete two-phase flow driven by a diffuse-interface model ⋮ Strong solutions to the density-dependent incompressible Cahn–Hilliard–Navier–Stokes system ⋮ A new global divergence free and pressure-robust HDG method for tangential boundary control of Stokes equations ⋮ Optimal distributed control of a generalized fractional Cahn-Hilliard system ⋮ Strong stationarity conditions for the optimal control of a Cahn-Hilliard-Navier-Stokes system ⋮ Optimal distributed control of two-dimensional Navier-Stokes-Cahn-Hilliard system with chemotaxis and singular potential ⋮ Nonlocal Phase Field Models of Viscous Cahn–Hilliard Type ⋮ Pontryagin maximum principle and second order optimality conditions for optimal control problems governed by 2D nonlocal Cahn-Hilliard-Navier-Stokes equations ⋮ Fully Adaptive and Integrated Numerical Methods for the Simulation and Control of Variable Density Multiphase Flows Governed by Diffuse Interface Models ⋮ Optimal control of geometric partial differential equations ⋮ A reduced order model for a stable embedded boundary parametrized Cahn-Hilliard phase-field system based on cut finite elements ⋮ Optimal Velocity Control of a Viscous Cahn--Hilliard System with Convection and Dynamic Boundary Conditions ⋮ Deep quench approximation and optimal control of general Cahn-Hilliard systems with fractional operators and double obstacle potentials ⋮ Optimal distributed control of a Cahn-Hilliard-Darcy system with mass sources ⋮ Optimal Actuator Design for Semilinear Systems ⋮ Optimal Control of Sliding Droplets Using the Contact Angle Distribution ⋮ Parallel generalized Lagrange-Newton method for fully coupled solution of PDE-constrained optimization problems with bound-constraints

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A boundary control problem for the viscous Cahn-Hilliard equation with dynamic boundary conditions
• Existence of weak solutions for a diffuse interface model for two-phase flows of incompressible fluids with different densities
• Several approaches for the derivation of stationarity conditions for elliptic MPECs with upper-level control constraints
• Asymptotic behavior of a Cahn-Hilliard-Navier-Stokes system in 2D
• A stable and linear time discretization for a thermodynamically consistent model for two-phase incompressible flow
• On a diffuse interface model for two-phase flows of viscous, incompressible fluids with matched densities
• On the Cahn-Hilliard equation
• Regularity and stability for the mathematical programming problem in Banach spaces
• Nonsmooth approach to optimization problems with equilibrium constraints. Theory, applications and numerical results
• Conservative multigrid methods for Cahn--Hilliard fluids.
• Numerical study of viscoelastic mixtures through a Cahn-Hilliard flow model
• Diffuse interface model for incompressible two-phase flows with large density ratios
• On the maximal monotonicity of subdifferential mappings
• Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity
• Optimal Distributed Control of a Nonlocal Cahn--Hilliard/Navier--Stokes System in Two Dimensions
• Distributed Optimal Control of the Cahn–Hilliard System Including the Case of a Double-Obstacle Homogeneous Free Energy Density
• THERMODYNAMICALLY CONSISTENT, FRAME INDIFFERENT DIFFUSE INTERFACE MODELS FOR INCOMPRESSIBLE TWO-PHASE FLOWS WITH DIFFERENT DENSITIES
• Optimal Boundary Control of a Viscous Cahn--Hilliard System with Dynamic Boundary Condition and Double Obstacle Potentials
• An adaptive finite-element Moreau–Yosida-based solver for a non-smooth Cahn–Hilliard problem
• Mathematical Programs with Complementarity Constraints in Function Space: C- and Strong Stationarity and a Path-Following Algorithm
• Feedback stabilization and optimal control for the Cahn-Hilliard equation
• On NEMYTSKIJ Operators inLp-Spaces of Abstract Functions
• Quasi–incompressible Cahn–Hilliard fluids and topological transitions
• An Introduction to Variational Inequalities and Their Applications
• 3. Distributed and boundary control problems for the semidiscrete Cahn–Hilliard/Navier–Stokes system with nonsmooth Ginzburg–Landau energies
• The Length of the Primal-Dual Path in Moreau--Yosida-Based Path-Following Methods for State Constrained Optimal Control
• Free Energy of a Nonuniform System. I. Interfacial Free Energy
• Development and Analysis of a Block-Preconditioner for the Phase-Field Crystal Equation
• Optimal Control of a Semidiscrete Cahn--Hilliard--Navier--Stokes System
• A theoretical and numerical model for the study of incompressible mixture flows