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Force Terms (force + term)
Selected AbstractsAn Euler system source term that develops prototype Z-pinch implosions intended for the evaluation of shock-hydro methodsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2009J. W. Banks Abstract In this paper, a phenomenological model for a magnetic drive source term for the momentum and total energy equations of the Euler system is described. This body force term is designed to produce a Z-pinch like implosion that can be used in the development and evaluation of shock-hydrodynamics algorithms that are intended to be used in Z-pinch simulations. The model uses a J × B Lorentz force, motivated by a 0-D analysis of a thin shell (or liner implosion), as a source term in the equations and allows for arbitrary current drives to be simulated. An extension that would include the multi-physics aspects of a proposed combined radiation hydrodynamics (rad-hydro) capability is also discussed. The specific class of prototype problems that are developed is intended to illustrate aspects of liner implosions into a near vacuum and with idealized pre-fill plasma effects. In this work, a high-resolution flux-corrected-transport method implemented on structured overlapping meshes is used to demonstrate the application of such a model to these idealized shock-hydrodynamic studies. The presented results include an asymptotic solution based on a limiting-case thin-shell analytical approximation in both (x, y) and (r, z). Additionally, a set of more realistic implosion problems that include density profiles approximating plasma pre-fill and a set of perturbed liner geometries that excite a hydro-magnetic like Rayleigh,Taylor instability in the implosion dynamics are demonstrated. Finally, as a demonstration of including and evaluating multiphysics effects in the Euler system, a simple radiation model is included and self-convergence results for two types of (r, z) implosions are presented. Copyright © 2008 John Wiley & Sons, Ltd. [source] The Milne problem for the linear Fokker,Planck operator with a force termMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 5 2003Brigitte Lucquin-Desreux Abstract This paper deals with the mathematical analysis of the linear stationary Fokker,Planck equation in a half-space (also called ,Milne' problem), in presence of an external electrostatic force field. We prove existence, uniqueness and asymptotic properties of the solution. Copyright © 2003 John Wiley & Sons, Ltd. [source] Ginzburg-Landau vortex dynamics driven by an applied boundary currentCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 12 2010Ian Tice In this paper we study the time-dependent Ginzburg-Landau equations on a smooth, bounded domain , , ,2, subject to an electrical current applied on the boundary. The dynamics with an applied current are nondissipative, but via the identification of a special structure in an interaction energy, we are able to derive a precise upper bound for the energy growth. We then turn to the study of the dynamics of the vortices of the solutions in the limit , , 0. We first consider the original time scale in which the vortices do not move and the solutions undergo a "phase relaxation." Then we study an accelerated time scale in which the vortices move according to a derived dynamical law. In the dynamical law, we identify a novel Lorentz force term induced by the applied boundary current. © 2010 Wiley Periodicals, Inc. [source] On the design of energy,momentum integration schemes for arbitrary continuum formulations.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2004Applications to classical, chaotic motion of shells Abstract The construction of energy,momentum methods depends heavily on three kinds of non-linearities: (1) the geometric (non-linearity of the strain,displacement relation), (2) the material (non-linearity of the elastic constitutive law), and (3) the one exhibited in displacement-dependent loading. In previous works, the authors have developed a general method which is valid for any kind of geometric non-linearity. In this paper, we extend the method and combine it with a treatment of material non-linearity as well as that exhibited in force terms. In addition, the dynamical formulation is presented in a general finite element framework where enhanced strains are incorporated as well. The non-linearity of the constitutive law necessitates a new treatment of the enhanced strains in order to retain the energy conservation property. Use is made of the logarithmic strain tensor which allows for a highly non-linear material law, while preserving the advantage of considering non-linear vibrations of classical metallic structures. Various examples and applications to classical and non-classical vibrations and non-linear motion of shells are presented, including (1) chaotic motion of arches, cylinders and caps using a linear constitutive law and (2) large overall motion and non-linear vibration of shells using non-linear constitutive law. Copyright © 2004 John Wiley & Sons, Ltd. [source] Large eddy simulation of turbulent flows in complex and moving rigid geometries using the immersed boundary methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2005Mayank Tyagi Abstract A large eddy simulation (LES) methodology for turbulent flows in complex rigid geometries is developed using the immersed boundary method (IBM). In the IBM body force terms are added to the momentum equations to represent a complex rigid geometry on a fixed Cartesian mesh. IBM combines the efficiency inherent in using a fixed Cartesian grid and the ease of tracking the immersed boundary at a set of moving Lagrangian points. Specific implementation strategies for the IBM are described in this paper. A two-sided forcing scheme is presented and shown to work well for moving rigid boundary problems. Turbulence and flow unsteadiness are addressed by LES using higher order numerical schemes with an accurate and robust subgrid scale (SGS) stress model. The combined LES,IBM methodology is computationally cost-effective for turbulent flows in moving geometries with prescribed surface trajectories. Several example problems are solved to illustrate the capability of the IBM and LES methodologies. The IBM is validated for the laminar flow past a heated cylinder in a channel and the combined LES,IBM methodology is validated for turbulent film-cooling flows involving heat transfer. In both cases predictions are in good agreement with measurements. LES,IBM is then used to study turbulent fluid mixing inside the complex geometry of a trapped vortex combustor. Finally, to demonstrate the full potential of LES,IBM, a complex moving geometry problem of stator,rotor interaction is solved. Copyright © 2005 John Wiley & Sons, Ltd. [source] A semi-implicit method conserving mass and potential vorticity for the shallow water equations on the sphereINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8-9 2005Luca Bonaventura Abstract A semi-implicit discretization for the shallow water equations is discussed, which uses triangular Delaunay cells on the sphere as control volumes and conserves mass and potential vorticity. The geopotential gradient, the Coriolis force terms and the divergence of the velocity field are discretized implicitly, while an explicit time discretization is used for the non-linear advection terms. The results obtained with a preliminary implementation on some idealized test cases are presented, showing that the main features of large scale atmospheric flows are well represented by the proposed method. Copyright © 2004 John Wiley & Sons, Ltd. [source] Stretching operational life of trickle-bed filters by liquid-induced pulse flowAICHE JOURNAL, Issue 7 2005Ion Iliuta Abstract When dilute liquid suspensions contaminated with fine solids are treated in catalytic trickle-bed reactors, bed plugging develops and increases the resistance to two-phase flow until ultimate unit shutdown for bed substitution with pristine catalyst. The release of deposited fines, or the inhibition of fines deposition over some regions of the collector, is expected to alleviate the plugging if liquid flow shock or periodic operation policies are implemented. Current physical models linking gas,liquid phase flow to space,time evolution of fines deposition and release are unable to depict this new type of filtration in trickle beds. This work attempts to fill in this gap by developing a dynamic multiphase flow deep-bed filtration model. The model incorporates the physical effects of porosity and effective specific surface area changes as a result of fines deposition/release, gas and suspension inertial effects, and coupling effects between the filtration parameters and the interfacial momentum exchange force terms. The release of the fine particles from the collector surface was assumed to be induced by the colloidal forces in the case of Brownian particles or by the hydrodynamic forces in the case of non-Brownian particles. An important finding of the work was that for noncolloidal fines both induced pulsing and liquid flow shock operations conferred substantial improvements (measured in terms of reduction in specific deposit and pressure drop) in the mitigation of plugging in trickle-bed reactors. However, because of the highest critical shear stress for fines in the colloidal range, induced pulsing did not substantiate any practically useful effect. © 2005 American Institute of Chemical Engineers AIChE J, 2005 [source] | |||||||||||||