Comparison between theoretical predictions and direct numerical simulation results for a decaying turbulent suspension

2004 ◽  
Vol 69 (5) ◽  
Author(s):  
G. Ooms ◽  
C. Poelma
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Theoretical Predictions ◽  
Simulation Results

BIFURCATIONS OF PERIODIC ORBITS IN A JOSEPHSON EQUATION WITH A PHASE SHIFT

2002 ◽  
Vol 12 (07) ◽  
pp. 1515-1530 ◽  
Author(s):  
ZHUJUN JING ◽  
HONGJUN CAO
Keyword(s):  
Numerical Simulation ◽  
Phase Shift ◽  
Periodic Orbits ◽  
Averaging Method ◽  
Melnikov Function ◽  
Second Order ◽  
Constant Current ◽  
Small Perturbations ◽  
Theoretical Predictions ◽  
Simulation Results

The Josephson equation with constant current and sinusoidal forcings and a phase shift is investigated in detail: the existence and the bifurcations of harmonics and subharmonics under small perturbations are given, by using the second-order averaging method and Melnikov function; the influence on bifurcations of periodic or subharmonics as the phase shift varies is considered; some numerical simulation results are reported in order to prove our theoretical predictions.

Direct Numerical Simulation of Forced Convective Heat Transfer From a Heated Rotating Sphere in Laminar Flows

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Zhi-Gang Feng
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Direct Numerical Simulation ◽  
Density Function ◽  
Heat Diffusion ◽  
Rotating Sphere ◽  
Nusselt Numbers ◽  
Flow Reynolds Number ◽  
The Mean ◽  
Simulation Results

The laminar forced convection of a heated rotating sphere in air has been studied using a three-dimensional immersed boundary based direct numerical simulation method. A regular Eulerian grid is used to solve the modified momentum and energy equations for the entire flow region simultaneously. In the region that is occupied by the rotating sphere, a moving Lagrangian grid is used, which tracks the rotational motion of the particle. A force density function or an energy density function is introduced to represent the momentum interaction or thermal interaction between the sphere and fluid. This numerical method is validated by comparing simulation results with analytical solutions of heat diffusion problem and other published experimental data. The flow structures and the mean Nusselt numbers for flow Reynolds number ranging from 0 to 1000 are obtained. We compared our simulation results of the mean Nusselt numbers with the correlations from the literature and found a good agreement for flow Reynolds number greater than 500; however, a significant discrepancy arises at flow Reynolds number below 500. This leads us to develop a new equation that correlates the mean Nusselt number of a heated rotating sphere for flows of 0≤Re≤500.

scholarly journals A New Explicit Magnus Expansion for Nonlinear Stochastic Differential Equations

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 183
Author(s):  
Xiaoling Wang ◽  
Xiaofei Guan ◽  
Pei Yin
Keyword(s):  
Differential Equation ◽  
Numerical Simulation ◽  
Stochastic Equation ◽  
Iterative Technique ◽  
Magnus Expansion ◽  
Nonlinear Stochastic Differential Equations ◽  
Drift Term ◽  
Theoretical Predictions ◽  
Simulation Results ◽  
The One

In this paper, based on the iterative technique, a new explicit Magnus expansion is proposed for the nonlinear stochastic equation d y = A ( t , y ) y d t + B ( t , y ) y ∘ d W . One of the most important features of the explicit Magnus method is that it can preserve the positivity of the solution for the above stochastic differential equation. We study the explicit Magnus method in which the drift term only satisfies the one-sided Lipschitz condition, and discuss the numerical truncated algorithms. Numerical simulation results are also given to support the theoretical predictions.

scholarly journals A wave driver theory for vortical waves propagating across junctions with application to those between rigid and compliant walls

2009 ◽  
Vol 625 ◽  
pp. 1-46 ◽  
Author(s):  
P. K. SEN ◽  
P. W. CARPENTER ◽  
S. HEGDE ◽  
C. DAVIES
Keyword(s):  
Numerical Simulation ◽  
Kinetic Energy ◽  
Direct Numerical Simulation ◽  
Outgoing Wave ◽  
Energy Integral ◽  
Incoming Wave ◽  
Cutoff Frequencies ◽  
New Concepts ◽  
Compliant Walls ◽  
Simulation Results

A theory is described for propagation of vortical waves across alternate rigid and compliant panels. The structure in the fluid side at the junction of panels is a highly vortical narrow viscous structure which is idealized as a wave driver. The wave driver is modelled as a ‘half source cum half sink’. The incoming wave terminates into this structure and the outgoing wave emanates from it. The model is described by half Fourier–Laplace transforms respectively for the upstream and downstream sides of the junction. The cases below cutoff and above cutoff frequencies are studied. The theory completely reproduces the direct numerical simulation results of Davies & Carpenter (J. Fluid Mech., vol. 335, 1997, p. 361). Particularly, the jumps across the junction in the kinetic energy integral, the vorticity integral and other related quantities as obtained in the work of Davies & Carpenter are completely reproduced. Also, some important new concepts emerge, notable amongst which is the concept of the pseudo group velocity.

scholarly journals Transition models from the quenched to ignited states for flows of inertial particles suspended in a simple sheared viscous fluid

2012 ◽  
Vol 711 ◽  
pp. 147-160 ◽  
Author(s):  
J.-F. Parmentier ◽  
O. Simonin
Keyword(s):  
Numerical Simulation ◽  
Viscous Fluid ◽  
Inertial Particles ◽  
Precise Calculation ◽  
Theoretical Predictions ◽  
Dense Flows ◽  
Transition Models ◽  
Simulation Results ◽  
Anisotropy Coefficients ◽  
Good Agreement

AbstractA review of existing theories for flows of inertial particles suspended in an unbounded sheared viscous fluid is presented first. A comparison between theoretical predictions and numerical simulation results is made for Stokes numbers from $1$ to $10$ in dilute and dense flows. Both particle agitation and anisotropy coefficients are examined, showing that neither of them is able to give satisfactory results in dense flows. A more precise calculation of collisional contributions to the balance law of the particle stress tensor is presented. Results of the corresponding theory are in very good agreement with numerical simulations both in dilute and dense flows.

scholarly journals Response of a stratified boundary layer on a tilted wall to surface undulations

2014 ◽  
Vol 751 ◽  
pp. 663-684 ◽  
Author(s):  
Pierre-Yves Passaggia ◽  
Patrice Meunier ◽  
Stéphane Le Dizès
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Direct Numerical Simulation ◽  
Spatial Structure ◽  
Transverse Velocity ◽  
Critical Layer ◽  
Velocity Response ◽  
Viscous Solution ◽  
Simulation Results ◽  
Good Agreement

AbstractThe structure of a stratified boundary layer over a tilted bottom with a small streamwise undulation is studied theoretically and numerically. We show that the tilt of the boundary can induce strong density variations and wall-transverse velocities in the critical layer when the frequency of the forcing by the topography $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}kU(z_c)$ is equal to the transverse Brunt–Väisälä frequency $N \sin \alpha $ ($N$ being the vertical Brunt–Väisälä frequency). The viscous solution in the critical layer, obtained and compared with direct numerical simulation results, is in good agreement for both the scaling and the spatial structure. The amplitude of the transverse velocity response is also shown to exhibit quasi-resonance peaks when the stratification strength is varied.

Transverse depinning threshold revealed by non linear Hall effect of Wigner solid in a disorder field

2002 ◽  
Vol 12 (9) ◽  
pp. 329-329
Author(s):  
F. I.B. Williams ◽  
F. Perruchot ◽  
B. Etienne ◽  
C. J. Mellor ◽  
R. Gaal ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Hall Effect ◽  
Lorentz Force ◽  
Solid Phase ◽  
Wigner Solid ◽  
Non Linear ◽  
Theoretical Predictions ◽  
Simulation Results ◽  
Current Lines

Both electrons and holes at a GaAs/GaAlAs heterojunction show a non linear Hall effect as a function of current in the magnetically induced Wigner solid phase. Arguing that this arises from a threshold Lorentz force transverse to the current lines, this threshold is found to be proportional to the longitudinal depinning threshold and about 10% of its value. This is to be compared with theoretical predictions by Giamarchi and LeDoussal and with numerical simulation results (Moon, Scalettar and Zimanyi).

Cylindrical bubble dynamics: Exact and direct numerical simulation results

2008 ◽  
Vol 20 (4) ◽  
pp. 040903 ◽  
Author(s):  
Can F. Delale ◽  
Gretar Tryggvason ◽  
Selman Nas
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Bubble Dynamics ◽  
Simulation Results

Intrusions propagating into linearly stratified ambients

2018 ◽  
Vol 844 ◽  
pp. 956-969 ◽  
Author(s):  
M. A. Khodkar ◽  
K. El Allam ◽  
E. Meiburg
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Propagation Velocity ◽  
Constant Velocity ◽  
Two Dimensional ◽  
Computational Data ◽  
Simulation Results ◽  
Modelling Approach ◽  
Non Equilibrium

Equilibrium and non-equilibrium intrusions released from long, full-depth locks and advancing into linearly stratified ambients are investigated via a vorticity-based modelling approach, for the constant-velocity slumping phase. Non-equilibrium intrusions give rise to an upstream-propagating wave, which we model as a bore. Predictions by the vorticity model agree closely with two-dimensional direct numerical simulation results and earlier experimental and computational data regarding front velocities, current thicknesses as well as the height and propagation velocity of the bore.

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