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The paper is devoted to a free-time optimal control problem for sweeping processes. We develop a constructive finite-difference approximation procedure that allows us to establish necessary optimality conditions for discrete optimal…
The kinetics of interfaces in alloy solidification pose a classic free boundary problem. This paper introduces an approach that amalgamates the distinctive characteristics of sharp and diffuse interface models. The motion of the diffuse…
We present variational approximations of boundary value problems for curvature flow (curve shortening flow) and elastic flow (curve straightening flow) in two-dimensional Riemannian manifolds that are conformally flat. For the evolving open…
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…
Inspired by the recent realization of a 2D chiral fluid as an active monolayer droplet moving atop a 3D Stokesian fluid, we formulate mathematically its free-boundary dynamics. The surface droplet is described as a general 2D linear,…
We develop a framework for constructing mixed multiscale finite volume methods for elliptic equations with multiple scales arising from flows in porous media. Some of the methods developed using the framework are already known…
Real world networks are often subject to severe uncertainties which need to be addressed by any reliable prescriptive model. In the context of the maximum flow problem subject to arc failure, robust models have gained particular attention.…
The shape of liquid surface in a rotating frame depends on the angular velocity. In this experiment, a fluid in a rectangular container with a small width is placed on a rotating table. A smartphone fixed to the rotating frame…
We model a slip boundary condition at fluid-solid interface of an arbitrary geometry in smoothed particle hydrodynamics and smoothed dissipative particle dynamics simulations. Under an assumption of linear profile of the tangential velocity…
Free surface, axially symmetric shallow flow is analysed in both the centrifugal and centripetal directions. Referring to the inviscid steady flow over a flat plate characterised by a unique value of specific energy, the analytical sub- and…
Free surface and granular fluid mechanics problems combine the challenges of fluid dynamics with aspects of granular behaviour. This type of problem is particularly relevant in contexts such as the flow of sediments in rivers, the movement…
We study the time-averaged flow in a model of particles that randomly hop on a finite directed graph. In the limit as the number of particles and the time window go to infinity but the graph remains finite, the large-deviation rate…
Fluid flow applications can involve a number of coupled problems. One is the simulation of free-surface flows, which require the solution of a free-boundary problem. Within this problem, the governing equations of fluid flow are coupled…
In this work we will study the dynamics of a thin layer of a viscous fluid which is embedded in the interior of another viscous fluid. The resulting flow can be approximated by means of the solutions of a free boundary problem for the…
We consider steady nonlinear free surface flow past an arbitrary bottom topography in three dimensions, concentrating on the shape of the wave pattern that forms on the surface of the fluid. Assuming ideal fluid flow, the problem is…
In this paper, we present a novel approach to model the fluid/solid interaction forces in a direct solver of the Navier-Stokes equations based on the volume of fluid interface tracking method. The key ingredient of the model is the explicit…
We are concerned with a model describing the motion of two compressible, immiscible fluids with density-dependent viscosity in the whole $\mathbb R^3$. The phases of the flow may have different pressure and viscosity laws and are separated…
We report measurements of the hydrodynamic drag force acting on a smooth sphere falling down under gravity to a plane decorated with microscopic periodic grooves. Both surfaces are lyophilic, so that a liquid (silicone oil) invades the…
Nonlocal models provide exceptional simulation fidelity for a broad spectrum of scientific and engineering applications. However, wider deployment of nonlocal models is hindered by several modeling and numerical challenges. Among those, we…
The Active Flux scheme is a Finite Volume scheme with additional degrees of freedom. It makes use of a continuous reconstruction and does not require a Riemann solver. An evolution operator is used for the additional degrees of freedom on…