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Shin Nishimura - One of the best experts on this subject based on the ideXlab platform.

  • Momentum Balance and radial electric fields in axisymmetric and nonaxisymmetric toroidal plasmas
    Plasma Physics and Controlled Fusion, 2011
    Co-Authors: Hideo Sugama, Tomo-hiko Watanabe, Masanori Nunami, Shin Nishimura
    Abstract:

    We have investigated the influence of symmetry properties of toroidal magnetic configurations on the mechanisms used for determining the radial electric field such as the Momentum Balance and the ambipolar particle transport. Both neoclassical and anomalous transport of particles, heat and Momentum in axisymmetric and nonaxisymmetric toroidal systems are taken into account. Generally, in nonaxisymmetric systems, the radial electric field is determined by the neoclassical ambipolarity condition. For axisymmetric systems with up–down symmetry and quasisymmetric systems with stellarator symmetry, it is shown using a novel parity transformation that the particle fluxes are automatically ambipolar up to and the determination of the radial electric field Es requires solving the Momentum Balance Equations, where δ denotes the ratio of the thermal gyroradius to the characteristic equilibrium scale length. In axisymmetric systems with large E × B flows on the order of the ion thermal velocity vTi, the radial fluxes of particles, heat and toroidal Momentum are dependent on Es and its radial derivative while the time evolution of the Es profile is governed by the toroidal Momentum Balance Equation. In nonaxisymmetric systems, E × B flows of are not generally allowed even in the presence of quasisymmetry because the nonzero radial current is produced by the large flow term in the equilibrium force Balance for which the Boozer and Hamada coordinates cannot be constructed.

  • Observation of Edge Reynolds Stress Increase Preceding an L-H Transition in Compact Helical System
    Plasma and Fusion Research, 2010
    Co-Authors: Yoshihiko Nagashima, Kenichi Nagaoka, Kimitaka Itoh, Akihide Fujisawa, Mitsutaka Isobe, Tsuyoshi Akiyama, Chihiro Suzuki, Shin Nishimura, Yasuo Yoshimura, Keisuke Matsuoka
    Abstract:

    An increase in turbulent Reynolds stress preceding an L-H transition in the Compact Helical System (CHS) was observed. A positive increase in the Reynolds stress is associated with a negative jump in the floating potential. The relationship of signs is consistent with the Momentum Balance Equation. Therefore, this observation supports the hypothesis that the Reynolds stress plays an important role in triggering the L-H transition in CHS plasmas.

P.c. Stangeby - One of the best experts on this subject based on the ideXlab platform.

  • Particle and parallel Momentum Balance Equations with inclusion of drifts, for modelling strong- to weakly-collisional edge plasmas
    Nuclear Fusion, 2006
    Co-Authors: A. V. Chankin, P.c. Stangeby
    Abstract:

    A system of plasma particle and parallel Momentum Balance Equations is derived appropriate for understanding the role of drifts in the edge and for edge modelling, particularly in the scrape-off layer (SOL) of tokamaks, stellarators and other magnetic confinement devices. The formulation allows for strong collisionality?but also covers the case of weak collisionality and strong drifts, a combination often encountered in the SOL. The most important terms are identified by assessing the magnitude of characteristic velocities and fluxes for the plasma edge region. Explanations of the physical nature of each term are provided. A number of terms that are sometimes not included in edge modelling has been included in the parallel Momentum Balance Equation after detailed analysis of the parallel component of the gradient of the total pressure-stress tensor. This includes terms related to curvature and divergence of the field lines, as well as further contributions coming from viscous forces related mainly to the ion centrifugal drift. All these terms are shown to be roughly of the same order of magnitude as convective Momentum fluxes related to drifts and therefore should be included in the Momentum Balance Equation.

Jean-claude LatchÉ - One of the best experts on this subject based on the ideXlab platform.

  • A Marker-and-Cell scheme for viscoelastic flows on nonuniform grids
    2020
    Co-Authors: Omar Mokhtari, Yohan Davit, Jean-claude LatchÉ, Romain De Loubens, Michel Quintard
    Abstract:

    In this paper, we develop a numerical scheme for the solution of the coupled Stokes and Navier-Stokes Equations with constitutive Equations describing the flow of viscoelastic fluids. The space discretization is based on the so-called Marker-And-Cell (MAC) scheme. The time discretization uses a fractional-step algorithm where the solution of the Navier-Stokes Equations is first obtained by a projection method and then the transport-reaction Equation for the conformation tensor is solved by a finite-volume scheme. In order to obtain consistency, the space discretization of the divergence of the elastic part of the stress tensor in the Momentum Balance Equation is derived using a weak form of the MAC scheme. For stability and accuracy reasons, the solution of the transport-reaction Equation for the conformation tensor is split into pure convection steps, with a change of variable from c to log(c), and a reaction step, which consists in solving one ODE per cell via an Euler scheme with local sub-cycling. Numerical computations for the Stokes flow of an Oldroyd-B fluid in the lid-driven cavity at We=1 confirm the scheme efficiency.

  • A Convergent Staggered Scheme for the Variable Density Incompressible Navier-Stokes Equations
    Mathematics of Computation, 2017
    Co-Authors: Jean-claude LatchÉ, Khaled Saleh
    Abstract:

    In this paper, we analyze a scheme for the time-dependent variable density Navier-Stokes Equations. The algorithm is implicit in time, and the space approximation is based on a low-order staggered non-conforming finite element, the so-called Rannacher-Turek element. The convection term in the Momentum Balance Equation is discretized by a finite volume technique, in such a way that a solution obeys a discrete kinetic energy Balance, and the mass Balance is approximated by an upwind finite volume method. We first show that the scheme preserves the stability properties of the continuous problem (L ∞-estimate for the density, L ∞ (L 2)-and L 2 (H 1)-estimates for the velocity), which yields, by a topological degree technique, the existence of a solution. Then, invoking compactness arguments and passing to the limit in the scheme, we prove that any sequence of solutions (obtained with a sequence of discretizations the space and time step of which tend to zero) converges up to the extraction of a subsequence to a weak solution of the continuous problem.

  • Stability of a Crank-Nicolson Pressure Correction Scheme Based on Staggered Discretizations
    International Journal for Numerical Methods in Fluids, 2013
    Co-Authors: Franck Boyer, Fanny Dardalhon, Céline Lapuerta, Jean-claude LatchÉ
    Abstract:

    In the context of Large Eddy Simulation of turbulent flows, the control of kinetic energy seems to be an essential requirement for the numerical scheme. Designing such an algorithm, ie as less dissipative as possible while being simple, for the resolution of variable density Navier-Stokes Equations is the aim of the present work.The developed numerical scheme, based on a pressure correction technique, uses a Crank-Nicolson time discretization and a staggered space discretization relying on the Rannacher-Turek finite element. For the inertia term in the Momentum Balance Equation, we propose a finite volume discretization, for which we derive a discrete analogue of the continuous kinetic energy local conservation identity. Contrary to what was obtained for the backward Euler discretization, the dissipation defect term associated to the Crank-Nicolson scheme is second order in time. This behaviour is evidenced by numerical simulations.

  • Discretization of the viscous dissipation term with the MAC scheme
    2011
    Co-Authors: Fabrice Babik, Raphaele Herbin, Walid Kheriji, Jean-claude LatchÉ
    Abstract:

    We propose a discretization for the MAC scheme of the viscous dissipation term τ (u) : ∇u (where τ (u) stands for the shear stress tensor associated to the velocity field u), which is suitable for the approximation of this term in a conservation Equation for a scalar variable. This discretization enjoys the property that the integral over the computational domain Ω of the (discrete) dissipation term is equal to what is obtained when taking the inner product of the (discrete) Momentum Balance Equation by u and integrating over Ω. As a consequence, it may be used as an ingredient to obtain an unconditionally stable scheme for the compressible Navier-Stokes Equations. It is also shown, in some model cases, to ensure the strong convergence in L1 of the dissipation term.

M. Z. Tokar - One of the best experts on this subject based on the ideXlab platform.

  • Numerical solution of Momentum Balance Equations for plasmas with two ion species
    Journal of Computational Physics, 2011
    Co-Authors: M. Z. Tokar
    Abstract:

    In plasmas bounded by material surfaces the Bohm criterion has to be satisfied at the entrance of the Debye sheath near the surface. With a single ion species this constraint prescribes a boundary condition for the Momentum Balance Equation governing the ion mass velocity. If, however, several ion species are present a generalization of the Bohm criterion does not provide enough number of boundary conditions. Additional ''intermediate'' conditions follow from the requirement that spatial derivatives of the ion velocities are finite everywhere within the plasma volume. The amount of such independent conditions is sufficient to determine, in an iterative way, also the position in the plasma where they have to be imposed. A numerical approach to find unique regular solutions of fluid motion Equations, satisfying the generalized Bohm criterion at the plasma boundary, is elaborated and realized for the case of two ion species.

Nelson Studart - One of the best experts on this subject based on the ideXlab platform.

  • Magnetoresistance of nondegenerate quantum electron channels formed on the surface of superfluid helium
    Physical Review B, 2004
    Co-Authors: Yu. P. Monarkha, Sviatoslav S. Sokolov, Guo-qiang Hai, Nelson Studart
    Abstract:

    Transport properties of quasi-one-dimensional nondegenerate quantum wires formed on the surface of liquid helium in the presence of a normal magnetic field are studied using the Momentum Balance Equation method and the memory function formalism. The interaction with both kinds of scatterers available (vapor atoms and capillary wave quanta) is considered. We show that unlike classical wires, quantum nondegenerate channels exhibit strong magnetoresistance which increases with lowering the temperature.