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The goal of this work is to develop a CFD methodology for solving reactive plasma flows. In particular this work focuses on the resolution of a post-shock relaxation problem.

plasma --- Discontinuous Galerkin Method --- reactive flows --- CFD --- Ingénierie, informatique & technologie > Ingénierie aérospatiale

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Since the beginning of the 20th century, research in low-temperature plasmas has grown into a major field of plasma science. In particular, confined plasmas are of great interest for a large range of technological applications: from domestic with lightning and plasma displays panels (PDPs), to electric space propulsion and, more recently, medicine. This vast domain of application gives rise to many numerical models whose specificities are adapted to current needs.

The main difficulty in plasma modelling is the very large mass disparity between electrons and the other species that compose the ionised gas. This intrinsic multiscale property makes the numerical problem very stiff. Paving the way to the need of high-resolution methods.

This work proposes the numerical simulation of a two-fluid low-temperature plasma with the use of high order Discontinuous Galerkin finite element Methods (DG-FEM). For this purpose, the coupled resolution of the electrons and ions transports equations with a Poisson's equation for the electrical potential is carried out through a fully implicit strategy. This choice permits to overcome the strict stability constraints coming from the electrons/ions mass disparity that affect explicit schemes.

Starting from the general Galerkin variational formulation, this coupled resolution of hyperbolic-elliptic equations is addressed with the implementation of specific strategies: An entropy-consistent Roe numerical flux is developed alongside incomplete internal penalty methods being applied only to the electrostatic system. An extension to the classical formulation of the implicit ESDIRK scheme is provided. Indeed, the inertia terms associate to the potential is deactivated by the introduction of a Boolean parameter which is equal to 1 for all the parameters excepts for the potential. As a result, this modification of the implicit method permits to treat the Poisson's equation alongside the fluid equations during the Newton iterator, enhancing then its convergence. An automatic evaluation of the Jacobian matrix using first-order central difference is also described with a specific treatment made onto the linearisation of the ionisation contributions. All of these strategies were implemented in the ForDGe solver, an immersed boundary Cartesian DG-FEM solver developed at the University of Liege.

Tested on two practical cases, namely: the two-stream periodic perturbation and the sheath problem, the current fully-coupled implicit DG-FEM solver is able to tackle accurately the physics of low-temperature collisionless plasma. In the case of the two-stream instability, the current implicit solver demonstrated its increased stability with resolution using time step that is more than two orders of magnitude bigger than the electron plasma frequency, one of the most stringent stability constraints for plasma flows. Non-linear behaviour of the solution is encountered when dealing with longer simulation. This can be addressed to a lack of consistency of the Roe flux at low-Mach regime.

For the plasma sheath problem, the current solver allows us to reach a steady state solution that is in very good agreement with state of the art solution, but also gives a good representation of the physics of the sheath. The steady state is achieved with the simple use of time integration, at the cost of considerable computational effort.

plasma, --- Discontinuous Galerkin --- multifluid formulation --- potential equation --- low-temperature plasma --- implicit time integration --- two-fluid model --- Ingénierie, informatique & technologie > Ingénierie aérospatiale

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Microwave imaging techniques allow for the development of systems that are able to inspect, identify, and characterize in a noninvasive fashion under different scenarios, ranging from biomedical to subsurface diagnostics as well as from surveillance and security applications to nondestructive evaluation. Such great opportunities, though, are actually severely limited by difficulties arising from the solution of the underlying inverse scattering problem. As a result, ongoing research efforts in this area are devoted to developing inversion strategies and experimental apparatus so that they are as reliable and accurate as possible with respect to reconstruction capabilities and resolution performance, respectively. The intent of this Special Issue is to present the experiences of leading scientists in the electromagnetic inverse scattering community, as well as to serve as an assessment tool for people who are new to the area of microwave imaging and electromagnetic inverse scattering problems.

joint sparsity --- magnetic resonance imaging --- near-field measurements --- rank minimization --- compressed sensing --- array diagnosis --- microwave plasma diagnostics --- radar-based breast imaging --- image-based approach --- contraction integral equation for inversion (CIE-I) --- nonlinear optimization --- contrast-source inversion --- electromagnetic inverse scattering problems --- nonlinear problem --- tomography --- RCS estimation --- inverse problems --- discontinuous Galerkin method (DGM) --- microwave imaging profilometry --- electrical-property tomography --- breast imaging --- antenna array --- finite-difference methods --- adjoint inversion methods --- Bayesian compressive sensing (BCS) --- orthogonality sampling method --- inverse scattering --- linear sampling method --- breast cancer --- contrast source inversion (CSI) --- imaging --- electromagnetic inverse scattering --- antenna testing --- stopping criteria --- 3D --- microwave imaging --- Kolmogorov-Smirnov (K-S) test --- inverse obstacles problem --- 5G communication --- inverse source problem

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The use of scientific computing tools is currently customary for solving problems at several complexity levels in Applied Sciences. The great need for reliable software in the scientific community conveys a continuous stimulus to develop new and better performing numerical methods that are able to grasp the particular features of the problem at hand. This has been the case for many different settings of numerical analysis, and this Special Issue aims at covering some important developments in various areas of application.

structured matrices --- numerical methods --- time fractional differential equations --- hierarchical splines --- finite difference methods --- null-space --- highly oscillatory problems --- stochastic Volterra integral equations --- displacement rank --- constrained Hamiltonian problems --- hyperbolic partial differential equations --- higher-order finite element methods --- continuous geometric average --- spectral (eigenvalue) and singular value distributions --- generalized locally Toeplitz sequences --- Volterra integro–differential equations --- B-spline --- discontinuous Galerkin methods --- adaptive methods --- Cholesky factorization --- energy-conserving methods --- order --- collocation method --- Poisson problems --- time harmonic Maxwell’s equations and magnetostatic problems --- tree --- multistep methods --- stochastic differential equations --- optimal basis --- finite difference method --- elementary differential --- gradient system --- curl–curl operator --- conservative problems --- line integral methods --- stochastic multistep methods --- Hamiltonian Boundary Value Methods --- limited memory --- boundary element method --- convergence --- analytical solution --- preconditioners --- asymptotic stability --- collocation methods --- histogram specification --- local refinement --- Runge–Kutta --- edge-preserving smoothing --- numerical analysis --- THB-splines --- BS methods --- barrier options --- stump --- shock waves and discontinuities --- mean-square stability --- Volterra integral equations --- high order discontinuous Galerkin finite element schemes --- B-splines --- vectorization and parallelization --- initial value problems --- one-step methods --- scientific computing --- fractional derivative --- linear systems --- Hamiltonian problems --- low rank completion --- ordinary differential equations --- mixed-index problems --- edge-histogram --- Hamiltonian PDEs --- matrix ODEs --- HBVMs --- floating strike Asian options --- Hermite–Obreshkov methods --- generalized Schur algorithm --- Galerkin method --- symplecticity --- high performance computing --- isogeometric analysis --- discretization of systems of differential equations

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Currently, the use of computational fluid dynamics (CFD) solutions is considered as the state-of-the-art in the modeling of unsteady nonlinear flow physics and offers an early and improved understanding of air vehicle aerodynamics and stability and control characteristics. This Special Issue covers recent computational efforts on simulation of aerospace vehicles including fighter aircraft, rotorcraft, propeller driven vehicles, unmanned vehicle, projectiles, and air drop configurations. The complex flow physics of these configurations pose significant challenges in CFD modeling. Some of these challenges include prediction of vortical flows and shock waves, rapid maneuvering aircraft with fast moving control surfaces, and interactions between propellers and wing, fluid and structure, boundary layer and shock waves. Additional topic of interest in this Special Issue is the use of CFD tools in aircraft design and flight mechanics. The problem with these applications is the computational cost involved, particularly if this is viewed as a brute-force calculation of vehicle’s aerodynamics through its flight envelope. To make progress in routinely using of CFD in aircraft design, methods based on sampling, model updating and system identification should be considered.

numerical methods --- modeling --- aerodynamics --- Taylor–Green vortex --- slender-body --- neural networks --- shock-channel --- wind gust responses --- installed propeller --- bifurcation --- RANS --- wake --- multi-directional --- bluff body --- MDO --- variable fidelity --- computational fluid dynamics (CFD) --- high angles of attack --- aeroelasticity --- computational fluid dynamics --- wind tunnel --- Godunov method --- flow control --- unsteady aerodynamic characteristics --- overset grid approach --- convolution integral --- MUSCL --- DDES --- dynamic Smagorinsky subgrid-scale model --- CPACS --- flutter --- reduced-order model --- meshing --- vortex generators --- hybrid reduced-order model --- microfluidics --- Riemann solver --- characteristics-based scheme --- CFD --- wing–propeller aerodynamic interaction --- kinetic energy dissipation --- Euler --- formation --- square cylinder --- multi-fidelity --- turbulence model --- subsonic --- large eddy simulation --- after-body --- flow distortion --- VLM --- numerical dissipation --- hypersonic --- modified equation analysis --- fluid mechanics --- reduced order aerodynamic model --- p-factor --- URANS --- flexible wings --- chemistry --- detection --- microelectromechanical systems (MEMS) --- angle of attack --- sharp-edge gust --- truncation error --- aerodynamic performance --- quasi-analytical --- gasdynamics --- discontinuous Galerkin finite element method (DG–FEM) --- geometry --- S-duct diffuser