Towards a Three-Dimensional Parallel, Adaptive, Multilevel Solver for the Solution of Nonlinear, Time-Dependent, Phase-Change Problems

2009 ◽  
pp. 251-274
Author(s):  
J.R. Green ◽  
P.K. Jimack ◽  
A.M. Mullis ◽  
J. Rosam
Keyword(s):  
Phase Change ◽  
Three Dimensional ◽  
Time Dependent ◽  
Multilevel Solver

scholarly journals A Code for Simulating Heat Transfer in Turbulent Channel Flow

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 756
Author(s):  
Federico Lluesma-Rodríguez ◽  
Francisco Álcantara-Ávila ◽  
María Jezabel Pérez-Quiles ◽  
Sergio Hoyas
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Turbulent Channel Flow ◽  
Passive Scalar ◽  
Direct Numerical Simulations ◽  
Time Dependent ◽  
Navier Stokes ◽  
Thermal Flow ◽  
Navier Stokes Equations

One numerical method was designed to solve the time-dependent, three-dimensional, incompressible Navier–Stokes equations in turbulent thermal channel flows. Its originality lies in the use of several well-known methods to discretize the problem and its parallel nature. Vorticy-Laplacian of velocity formulation has been used, so pressure has been removed from the system. Heat is modeled as a passive scalar. Any other quantity modeled as passive scalar can be very easily studied, including several of them at the same time. These methods have been successfully used for extensive direct numerical simulations of passive thermal flow for several boundary conditions.

Flow Mixing Enhancement from Balloon Pulsations in an Intravenous Oxygenator

2004 ◽  
Vol 127 (3) ◽  
pp. 400-415 ◽  
Author(s):  
Amador M. Guzmán ◽  
Rodrigo A. Escobar ◽  
Cristina H. Amon
Keyword(s):  
Numerical Simulations ◽  
Oxygen Transfer ◽  
Fiber Bundle ◽  
Transfer Rate ◽  
Oxygen Transfer Rate ◽  
Three Dimensional ◽  
Time Dependent ◽  
Fiber Placement ◽  
Flow Mixing ◽  
Dependent Flow

Computational investigations of flow mixing and oxygen transfer characteristics in an intravenous membrane oxygenator (IMO) are performed by direct numerical simulations of the conservation of mass, momentum, and species equations. Three-dimensional computational models are developed to investigate flow-mixing and oxygen-transfer characteristics for stationary and pulsating balloons, using the spectral element method. For a stationary balloon, the effect of the fiber placement within the fiber bundle and the number of fiber rings is investigated. In a pulsating balloon, the flow mixing characteristics are determined and the oxygen transfer rate is evaluated. For a stationary balloon, numerical simulations show two well-defined flow patterns that depend on the region of the IMO device. Successive increases of the Reynolds number raise the longitudinal velocity without creating secondary flow. This characteristic is not affected by staggered or non-staggered fiber placement within the fiber bundle. For a pulsating balloon, the flow mixing is enhanced by generating a three-dimensional time-dependent flow characterized by oscillatory radial, pulsatile longitudinal, and both oscillatory and random tangential velocities. This three-dimensional flow increases the flow mixing due to an active time-dependent secondary flow, particularly around the fibers. Analytical models show the fiber bundle placement effect on the pressure gradient and flow pattern. The oxygen transport from the fiber surface to the mean flow is due to a dominant radial diffusion mechanism, for the stationary balloon. The oxygen transfer rate reaches an asymptotic behavior at relatively low Reynolds numbers. For a pulsating balloon, the time-dependent oxygen-concentration field resembles the oscillatory and wavy nature of the time-dependent flow. Sherwood number evaluations demonstrate that balloon pulsations enhance the oxygen transfer rate, even for smaller flow rates.

The two-sided lid-driven cavity: experiments on stationary and time-dependent flows

2002 ◽  
Vol 450 ◽  
pp. 67-95 ◽  
Author(s):  
CH. BLOHM ◽  
H. C. KUHLMANN
Keyword(s):  
Three Dimensional ◽  
Standing Waves ◽  
Reynolds Numbers ◽  
Time Dependent ◽  
Flow State ◽  
Incompressible Fluid Flow ◽  
Velocity Measurements ◽  
Driven Cavity ◽  
Rectangular Container ◽  
Hot Film

The incompressible fluid flow in a rectangular container driven by two facing sidewalls which move steadily in anti-parallel directions is investigated experimentally for Reynolds numbers up to 1200. The moving sidewalls are realized by two rotating cylinders of large radii tightly closing the cavity. The distance between the moving walls relative to the height of the cavity (aspect ratio) is Γ = 1.96. Laser-Doppler and hot-film techniques are employed to measure steady and time-dependent vortex flows. Beyond a first threshold robust, steady, three-dimensional cells bifurcate supercritically out of the basic flow state. Through a further instability the cellular flow becomes unstable to oscillations in the form of standing waves with the same wavelength as the underlying cellular flow. If both sidewalls move with the same velocity (symmetrical driving), the oscillatory instability is found to be tricritical. The dependence on two sidewall Reynolds numbers of the ranges of existence of steady and oscillatory cellular flows is explored. Flow symmetries and quantitative velocity measurements are presented for representative cases.

Upstream motions in stratified flow

1988 ◽  
Vol 187 ◽  
pp. 487-506 ◽  
Author(s):  
I. P. Castro ◽  
W. H. Snyder
Keyword(s):  
Body Height ◽  
Three Dimensional ◽  
Time Dependent ◽  
Experimental Measurements ◽  
Two Dimensional ◽  
Towing Tank ◽  
First Order ◽  
Density Perturbations ◽  
Small Obstacle ◽  
Obstacle Height

In this paper experimental measurements of the time-dependent velocity and density perturbations upstream of obstacles towed through linearly stratified fluid are presented. Attention is concentrated on two-dimensional obstacles which generate turbulent separated wakes at Froude numbers, based on velocity and body height, of less than 0.5. The form of the upstream columnar modes is shown to be largely that of first-order unattenuating disturbances, which have little resemblance to the perturbations described by small-obstacle-height theories. For two-dimensional obstacles the disturbances are similar to those found by Wei, Kao & Pao (1975) and it is shown that provided a suitable obstacle drag coefficient is specified, the lowest-order modes (at least) are quantitatively consistent with the results of the Oseen inviscid model.Discussion of some results of similar measurements upstream of three-dimensional obstacles, the importance of towing tank endwalls and the relevance of the Foster & Saffman (1970) theory for the limit of zero Froude number is also included.

Three-Dimensional Computations of Transport and Growth for Crystal Growth Systems

2000 ◽  
Author(s):  
Jeffrey J. Derby ◽  
Andrew Yeckel
Keyword(s):  
Finite Element ◽  
Crystal Growth ◽  
Finite Element Methods ◽  
Three Dimensional ◽  
Bulk Crystal ◽  
Time Dependent ◽  
Engineering Systems ◽  
Bulk Crystal Growth ◽  
Strongly Nonlinear ◽  
Parallel Supercomputers

Abstract Modern finite element methods implemented on parallel supercomputers promise to allow the study of three-dimensional, time-dependent continuum phenomena in many engineering systems. This paper shows several examples of the fruitful application of these approaches to bulk crystal growth systems, where strongly nonlinear coupled phenomena are important.

Energy and Momentum Eigenspectrum of the Hulthén-screened Cosine Kratzer Potential Using Proper Quantization Rule and SUSYQM Method

2021 ◽  
Author(s):  
Kaushal R Purohit ◽  
Rajendrasinh H PARMAR ◽  
Ajay Kumar Rai
Keyword(s):  
Quantum Mechanics ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Numerical Data ◽  
Time Dependent ◽  
Quantization Rule ◽  
Approximation Approach ◽  
Momentum Spectra ◽  
Energy And Momentum ◽  
Three Dimensional Space

Abstract Using the Qiang-Dong proper quantization rule (PQR) and the supersymmetric quantum mechanics approach, we obtained the eigenspectrum of the energy and momentum for time independent and time dependent Hulthen-screened cosine Kratzer potentials. For the suggested time independent Hulthen-screened cosine Kratzer potential, we solved the Schrodinger equation in D dimensions (HSCKP). The Feinberg-Horodecki equation for time-dependent Hulthen-screened cosine Kratzer potential was also solved (tHSCKP). To address the inverse square term in the time independent and time dependent equations, we employed the Greene-Aldrich approximation approach. We were able to extract time independent and time dependent potentials, as well as their accompanying energy and momentum spectra. In three-dimensional space, we estimated the rotational vibrational (RV) energy spectrum for many homodimers ($H_2, I_2, O_2$) and heterodimers ($MnH, ScN, LiH, HCl$). We also used the recently introduced formula approach to obtain the relevant eigen function. We also calculated momentum spectra for the dimers $MnH$ and $ScN$. The method is compared to prior methodologies for accuracy and validity using numerical data for heterodimer $LiH, HCl$ and homodimer $I_2, O_2,H_2$. The calculated energy and momentum spectra are tabulated and analysed.

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