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A Finite-Volume based POD-Galerkin reduced order model is developed for fluid dynamics problems where the (time-dependent) boundary conditions are controlled using two different boundary control strategies: the lifting function method,…

In this paper we establish the convergence of a numerical scheme based, on the Finite Element Method, for a time-independent problem modelling the deformation of a linearly elastic elliptic membrane shell subjected to remaining confined in…

We derive entropy conserving and entropy dissipative overlapping domain formulations for systems of nonlinear hyperbolic equations in conservation form, such as would be approximated by overset mesh methods. The entropy conserving…

In this paper, we consider an open-loop, finite-time, optimal control problem of attaining a specific desired current profile during the ramp-up phase by finding the best open-loop actuator input trajectories. Average density, total power,…

Mediation analysis has been widely used to investigate how a treatment influences an outcome through intermediate variables, known as mediators. Analyzing a mediation mechanism typically requires assessing multiple model parameters that…

In this work, we investigate the dynamics of plasma blobs in the edge of magnetic confinement devices using a full-f gyrokinetic particle-in-cell code with X-point geometry. In simulations, the evolution of a seeded blob is followed as it…

We consider a 1 1/2degrees of freedom Hamiltonian dynamical system, which models the chaotic dynamics of charged test-particles in a turbulent electric field, across the confining magnetic field in controlled thermonuclear fusion devices.…

The optimum scheme for geometric phase measurement in EAST Tokamak is proposed in this paper. The theoretical values of geometric phase for the probe beams of EAST Polarimeter-Interferometer (POINT) system are calculated by path integration…

The goal of this paper is to understand from a mathematical point of view the magnetic confinement of plasmas for fusion. Following Fr\'enod and Sonnendr\"ucker \cite{FS2}, we first use two-scale convergence tools to derive a gyrokinetic…

The LBM is combined with the Volume Penalization (VP LBM) approach to simulate flows in the presence of obstacles. The single relaxation time LBM and the multiple relaxation time LBM are used. For cases where the fluid motion is enhanced by…

First-principles numerical simulations are used to describe a transport bifurcation in a differentially rotating tokamak plasma. Such a bifurcation is more probable in a region of zero magnetic shear than one of finite magnetic shear…

This manuscript describes an adjoint/reverse Monte Carlo method to calculate the flux of charged plasma particles to the wall of e.g. a tokamak. Two applications are described: a fusion product activation probe and a neutral beam injection…

This work presents a novel numerical investigation of the dynamics of free-boundary flows of viscoelastic liquid membranes. The governing equation describes the balance of linear momentum, in which the stresses include the viscoelastic…

We consider mixed-integer optimal control problems with combinatorial constraints that couple over time such as minimum dwell times. We analyze a lifting and decomposition approach into a mixed-integer optimal control problem without…

Real time control of many plasma parameters will be an essential aspect in the development of reliable high performance operation of Next Step Tokamaks. The main prerequisites for any feedback scheme are the precise real-time determination…

The properties of the boundary plasma in a tokamak are now recognized to play a key role in determining the achievable fusion power and the lifetimes of plasma-facing components. Accurate quantitative modeling and improved qualitative…

The magnetostatic field distribution in a nonlinear medium amounts to the unique minimizer of the magnetic coenergy over all fields that can be generated by the same current. This is a nonlinear saddlepoint problem whose numerical solution…

The classical level set method, which represents the boundary of the unknown geometry as the zero-level set of a function, has been shown to be very effective in solving shape optimization problems. The present work addresses the issue of…

The Immersed Boundary Method (IBM) is a popular numerical approach to impose boundary conditions without relying on body-fitted grids, thus reducing the costly effort of mesh generation. To obtain enhanced accuracy, IBM can be combined with…

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…