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We present a robust optimisation framework for computing invariant solutions of wall-bounded flows by recasting the Navier-Stokes equations as a variational problem as established in Ashtari and Schneider, JFM (2023). The approach minimises…
The optimal control of a globally unstable two-dimensional separated boundary layer over a bump is considered using augmented Lagrangian optimization procedures. The present strategy allows of controlling the flow from a fully developed…
We address the design and synthesis of optimal control strategies for high-dimensional stochastic dynamical systems. Such systems may be deterministic nonlinear systems evolving from random initial states, or systems driven by random…
We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…
The maximum-entropy sampling problem is a fundamental and challenging combinatorial-optimization problem, with application in spatial statistics. It asks to find a maximum-determinant order-$s$ principal submatrix of an order-$n$ covariance…
An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…
This paper concerns the numerical procedure for solving hybrid optimal control problems with sliding modes. The proposed procedure has several features which distinguishes it from the other procedures for the problem. First of all a sliding…
We present a simple and efficient variational finite difference method for simulating time-dependent Stokes flow in the presence of irregular free surfaces and moving solid boundaries. The method uses an embedded boundary approach on…
Optimal control under uncertainty is a prevailing challenge for many reasons. One of the critical difficulties lies in producing tractable solutions for the underlying stochastic optimization problem. We show how advanced approximate…
Typical topology optimization methods require complex iterative calculations, which cannot meet the requirements of fast computing applications. The neural network is studied to reduce the time of computing the optimization result, however,…
Optimal control of stochastic nonlinear dynamical systems is a major challenge in the domain of robot learning. Given the intractability of the global control problem, state-of-the-art algorithms focus on approximate sequential optimization…
The immersed boundary method is a numerical and mathematical formulation for solving fluid-structure interaction problems. It relies on solving fluid equations on an Eulerian fluid grid and interpolating the resulting velocity back onto…
Simulating the interaction of fluids with immersed moving solids is playing an important role for gaining a better quantitative understanding of how fluid dynamics is altered by the presence of obstacles and which forces are exerted on the…
The article discusses the gradient discretisation method (GDM) for distributed optimal control problems governed by diffusion equation with pure Neumann boundary condition. Using the GDM framework enables to develop an analysis that…
Uncertainty often plays an important role in dynamic flow problems. In this paper, we consider both, a stationary and a dynamic flow model with uncertain boundary data on networks. We introduce two different ways how to compute the…
In computational fluid dynamics, the demand for increasingly multidisciplinary reliable simulations, for both analysis and design optimization purposes, requires transformational advances in individual components of future solvers. At the…
The construction of weak solutions to compressible Navier-Stokes equations via a numerical method (including a rigorous proof of the convergence) is in a short supply, and so far, available only for one sole numerical scheme suggested in…
In this paper, we introduce a technique to enhance the computational efficiency of solution algorithms for high-dimensional discrete simulation-based optimization problems. The technique is based on innovative adaptive partitioning…
We present a modern stochastic control framework for dynamic optimization of river environment and ecology. We focus on a fisheries problem in Japan, and show several examples of simplified optimal control problems of stochastic…
We study a stochastic velocity tracking problem for the 2D-Navier-Stokes equations perturbed by a multiplicative Gaussian noise. From a physical point of view, the control acts through a boundary injection/suction device with uncertainty,…