A new algorithm based on spectral element discretization and non-oscillatory ideas is developed for the solution of hyperbolic partial differential equations. A conservative formulation is proposed based on cell avera...
A new algorithm based on spectral element discretization and non-oscillatory ideas is developed for the solution of hyperbolic partial differential equations. A conservative formulation is proposed based on cell averaging and reconstruction procedures, that employs a staggered grid of Gauss-Chebyshev and Gauss-Lobatto Chebyshev discretizations. The non-oscillatory reconstruction procedure is based on ideas similar to those proposed by Cai et al. (Math. Comput. 52, 389 (1989)) but employs a modified technique which is more robust and simpler in terms of determining the location and strength of a discontinuity. It is demonstrated through model problems of linear advection, inviscid Burgers equation, and one-dimensional Euler system that the proposed algorithm leads to stable, non-oscillatory accurate results. Exponential accuracy away from the discontinuity is realized for the inviscid Burgers equation example.
Results of a numerical study of the dynamics of a collection of disks colliding inelastically in a periodic two-dimensional enclosure are presented. The properties of this system, which is perhaps the simplest model f...
详细信息
Numerical simulation is used to model ion etching in trilayer lithography. The simulations are capable of capturing the evolution of the boundary between two materials as well as the physically observed phonemena reac...
Numerical simulation is used to model ion etching in trilayer lithography. The simulations are capable of capturing the evolution of the boundary between two materials as well as the physically observed phonemena reactive ion etching lag and undercutting. Numerical results are compared with experimental data and a good agreement is found except close to the material interface where the slope of the surface is large. This error is attributed to a purely energy dependent yield used in the simulations.
The flow in a channel with its lower wall mounted with streamwise V-shaped riblets is simulated using a highly efficient spectral-element-Fourier method. The range of Reynolds numbers investigated is 500 to 4000, whic...
The wakes of bluff objects and in particular of circular cylinders are known to undergo a ‘fast ’ transition, from a laminar two-dimensional state a t Reynolds number 200 to a turbulent state a t Reynolds number 400...
The wakes of bluff objects and in particular of circular cylinders are known to undergo a ‘fast ’ transition, from a laminar two-dimensional state a t Reynolds number 200 to a turbulent state a t Reynolds number 400. The process has been documented in several eXperimental mvestigations, but the underlying physical mechanisms have remained largely unknown so far. In this paper, the transition process is investigated numerically, through direct simulation of the NavierStokes equations at representative Reynolds numbers, up to 500. A high-order timeaccurate, miXed spectral/spectral element technique is used. It is shown that the wake first becomes three-dimensional, as a result of a secondary instability of the two-dimensional vorteX street. This secondary instability appears at a Reynolds number close to 200. For slightly supercritical Reynolds numbers, a harmonic state develops, in which the flow oscillates at its fundamental frequency (Strouhal number) around a spanwise modulated time-average flow. In the near wake the modulation wavelength of the time-average flow is half of the spanwise wavelength of the perturbation flow, consistently with linear instability theory. The vorteX filaments have a spanwise wavy shape in the near wake, and form rib-like structures further downstream. At higher Reynolds numbers the three-dimensional flow oscillation undergoes a period-doubling bifurcation, in which the flow alternates between two different states. Phase-space analysis of the flow shows that the basic limit cycle has branched into two connected limit cycles. In physical space the period doubling appears as the shedding of two distinct types of vorteX filaments. Further increases of the Reynolds number result in a cascade of period-doubling bifurcations, which create a chaotic state in the flow at a Reynolds number of about 500. The flow is characterized by broadband power spectra, and the appearance intermittent phenomena. It is concluded that the wake undergoes transit
In this article we present a new formulation for coupling spectral element discretizations to finite difference and finite element discretizations addressing flow problems in very complicated geometries. A general ite...
详细信息
The response of transport measures (Nusselt number, drag and lift force) for two- and three-dimensional flow past a heated cylinder reaching a chaotic state is investigated numerically using a spectral element discret...
The response of transport measures (Nusselt number, drag and lift force) for two- and three-dimensional flow past a heated cylinder reaching a chaotic state is investigated numerically using a spectral element discretization at a Reynolds number Re = 500. The undisturbed two-dimensional flow remains periodic at this Reynolds number, unless a suitable forcing is applied on the naturally produced system. Three-dimensional simulations establish that three-dimensionality sets in at Re almost-equal-to 200. Successive supercritical states are established through a series of period-doublings, before a chaotic state is reached at a Re almost-equal-to 500. For the two-dimensional forced flow, all transport measures oscillate aperiodically in time and undergo a "crisis," i.e., a sudden and dramatic increase in their amplitude. The corresponding three-dimensional, naturally produced chaotic state corresponds to a less drastic change of the transport quantities with both rms and mean values lower than their two-dimensional counterparts.
It has been observed, in earlier computations of bifurcation diagrams for dissipative partial differential equations, that the use of certain explicit approximate inertial forms can give rise to numerical artifacts su...
详细信息
S. Kida, M. Takaoka, F. Hussain; Corrigendum:‘‘Reconnection of two vortex rings’’ [Phys. Fluids A 1, 630 (1989)]Comments, Physics of Fluids A: Fluid Dynamics, V
S. Kida, M. Takaoka, F. Hussain; Corrigendum:‘‘Reconnection of two vortex rings’’ [Phys. Fluids A 1, 630 (1989)]Comments, Physics of Fluids A: Fluid Dynamics, V
暂无评论