Related papers: Gradient-robustness in optimization subject to sta…
In this paper we discretize the incompressible Navier-Stokes equations in the framework of finite element exterior calculus. We make use of the Lamb identity to rewrite the equations into a vorticity-velocity-pressure form which fits into…
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…
The possibility that a discrete process can be fruitfully approximated by a continuous one, with the latter involving a differential system, is fascinating. Important theoretical insights, as well as significant computational efficiency…
This paper proposes novel gradient-flow schemes that yield convergence to the optimal point of a convex optimization problem within a \textit{fixed} time from any given initial condition for unconstrained optimization, constrained…
In this note, the importance of spectral properties of viscous flux discretization in solving compressible Navier-Stokes equations for turbulent flow simulations is discussed. We studied six different methods, divided into two different…
This article overviews how gradient flows, and discretizations thereof, are useful to design and analyze optimization and sampling algorithms. The interplay between optimization, sampling, and gradient flows is an active research area; our…
In this paper, we consider continuous-time stochastic optimal control problems where the cost is evaluated through a coherent risk measure. We provide an explicit gradient descent-ascent algorithm which applies to problems subject to…
In the present work, we investigate a numerical one-dimensional solver to the Navier-Stokes equation that retains all terms, including both pressure and dissipation. Solutions to simple examples that illustrate the actions of the nonlinear…
In this paper we study a distributed optimal control problem for a three-dimensional Navier-Stokes-$\alpha$ model. We prove the solvability of the optimal control problem, and derive first-order optimality conditions by using a Lagrange…
We consider error estimates for the fully discretized instationary Navier-Stokes problem. For the spatial approximation we use conforming inf-sup stable finite element methods in conjunction with grad-div and local projection stabilization…
This paper presents a novel robust trajectory optimization method for constrained nonlinear dynamical systems subject to unknown bounded disturbances. In particular, we seek optimal control policies that remain robustly feasible with…
Gradient Descent (GD) is a ubiquitous algorithm for finding the optimal solution to an optimization problem. For reduced computational complexity, the optimal solution $\mathrm{x^*}$ of the optimization problem must be attained in a minimum…
Systems of hydrodynamic type equations derived from the Navier-Stokes equations and the boundary layer equations are considered. A transformation of the Crocco type reducing the equation order for the longitudinal velocity component is…
Considering channel flow at Reynolds numbers below the linear stability threshold of the laminar profile as a generic example system showing a subcritical transition to turbulence connected with the existence of simple invariant solutions,…
Fluid flows are omnipresent in nature and engineering disciplines. The reliable computation of fluids has been a long-lasting challenge due to nonlinear interactions over multiple spatio-temporal scales. The compressible Navier-Stokes…
We consider policy gradient methods for stochastic optimal control problem in continuous time. In particular, we analyze the gradient flow for the control, viewed as a continuous time limit of the policy gradient method. We prove the global…
In the present study, the efficiency of preconditioners for solving linear systems associated with the discretized variable-density incompressible Navier-Stokes equations with semiimplicit second-order accuracy in time and spectral accuracy…
A stable numerical solution of the steady Stokes problem requires compatibility between the choice of velocity and pressure approximation that has traditionally proven problematic for meshless methods. In this work, we present a…
A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product…
Linearisation of the Navier-Stokes equations about the mean of a turbulent flow forms the foundation of popular models for energy amplification and coherent structures, including resolvent analysis. While the Navier-Stokes equations can be…