This book makes a clear presentation of the traditional topics included in a course of undergraduate parallel programming. As explained by the authors, it was developed from their own experience in classrooms, introducing their students to parallel programming. It can be used almost directly to teach basic parallel programming.

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Parallel programming: techniques and applications using networked workstations and parallel computers. Barry Wilkinson, C. Michael Allen

A fast pressure-correction method for incompressible two-fluid flows

A methodology termed the “filtered density function” (FDF) is developed and implemented for large eddy simulation (LES) of chemically reacting turbulent flows. In this methodology, the effects of the unresolved scalar fluctuations are taken into account by considering the probability density function (PDF) of subgrid scale (SGS) scalar quantities. A transport equation is derived for the FDF in which the effect of chemical reactions appears in a closed form. The influences of scalar mixing and convection within the subgrid are modeled. The FDF transport equation is solved numerically via a Lagrangian Monte Carlo scheme in which the solutions of the equivalent stochastic differential equations (SDEs) are obtained. These solutions preserve the Ito-Gikhman nature of the SDEs. The consistency of the FDF approach, the convergence of its Monte Carlo solution and the performance of the closures employed in the FDF transport equation are assessed by comparisons with results obtained by direct numerical simulation (DNS) and by conventional LES procedures in which the first two SGS scalar moments are obtained by a finite difference method (LES-FD). These comparative assessments are conducted by implementations of all three schemes (FDF, DNS and LES-FD) in a temporally developing mixing layer and a spatially developing planar jet under both non-reacting and reacting conditions. In non-reacting flows, the Monte Carlo solution of the FDF yields results similar to those via LES-FD. The advantage of the FDF is demonstrated by its use in reacting flows. In the absence of a closure for the SGS scalar fluctuations, the LES-FD results are significantly different from those based on DNS. The FDF results show a much closer agreement with filtered DNS results. © 1998 American Institute of Physics.

Filtered density function for large eddy simulation of turbulent reacting flows

A comprehensive survey of the literature in the area of numerical heat transfer (NHT) published between 2000 and 2009 has been conducted Due to the immenseness of the literature volume, the survey

Literature Survey of Numerical Heat Transfer (2000–2009): Part II

A quasi-DNS of the partially premixed turbulent Sydney flame in configuration FJ200-5GP-Lr75-57 has been conducted using detailed molecular diffusion for multi-component mixtures and complex reaction mechanisms. In order to study flame dynamics like regime transition in this flame for the development of new combustion models and to directly compare the quasi-DNS to different LES models, the simulation results are compiled into a data base. Because the simulation was performed with OpenFOAM, we demonstrate the quasi-DNS capabilities of OpenFOAM by performing canonical test cases. They attest that OpenFOAM’s cubic discretization has lower numerical diffusion compared to classical central difference schemes and can reach higher than second order convergence rate in some cases. The quasi-DNS of the Sydney flame is conducted with a self-developed reacting flow solver which is able to accurately compute molecular diffusion coefficients from kinetic gas theory and employs a fast implementation for detailed reaction mechanisms. The computational mesh is shown to be able to resolve the flow as well as the flame front sufficiently for the quasi-DNS. Comparisons with experimental data also show that the simulation can quantitatively reproduce measured time-mean and time-RMS statistics.

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Quasi-DNS Dataset of a Piloted Flame with Inhomogeneous Inlet Conditions

Scalable Tools for Generating Synthetic Isotropic Turbulence with Arbitrary Spectra

Taylor’s incompressible and rotational profile is extended to a porous cylinder with arbitrary headwall injection. This profile, often referred to as Culick’s mean flow, is now generalized to permit the imposition of reactive headwall conditions. Starting with Euler’s steady equations, the solution that we derive is approximate, being exact only at the sidewall, the centerline, or for similarity-conforming inlet profiles. Furthermore, the approximation is quasiviscous, being observant of the no slip requirement at the sidewall. Based on numerical experiments under inviscid flow conditions, the closed-form approximation that we obtain appears to be well suited to describe the bulk flow field in basic models of solid and hybrid rockets where uniform sidewall injection is imposed at the propellant surface. For similarity-nonconforming profiles, the approximation becomes more accurate as we move away from the headwall. Results are verified using computational fluid dynamics for several headwall injection patterns.

The Taylor-Culick profile with arbitrary headwall injection

The Uintah Software framework was developed to provide an environment for solving fluid-structure interaction problems on structured adaptive grids on large-scale, long-running, data-intensive problems. Uintah uses a combination of fluid-flow solvers and particle-based methods for solids together with a novel asynchronous task-based approach with fully automated load balancing. As Uintah is often used to solve incompressible flow problems in combustion applications it is important to have a scalable linear solver. While there are many such solvers available, the scalability of those codes varies greatly. The hypre software offers a range of solvers and preconditioners for different types of grids. The weak scalability of Uintah and hypre is addressed for particular examples of both packages when applied to a number of incompressible flow problems. After careful software engineering to reduce startup costs, much better than expected weak scalability is seen for up to 100K cores on NSFs Kraken architecture and up to 260K cpu cores, on DOEs new Titan machine. The scalability is found to depend in a crtitical way on the choice of algorithm used by hypre for a realistic application problem.

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Large scale parallel solution of incompressible flow problems using Uintah and hypre

The Taylor–Culick solution for a porous cylinder is often used to describe the bulk gas motion in idealized representations of solid rocket motors. However, other approximate solutions may be found that satisfy the same fundamental constraints. In this vein, steeper or smoother profiles may be observed in either experimental or numerical tests, particularly in the presence of intense levels of acoustic energy. In this study, we use the Lagrangian optimization principle to arrive at multiple solutions that can help to explain the practically observed motions. We then search for the extreme states that display either the least or the most kinetic energy. These are derived and found to be dependent on the chamber’s aspect ratio. By assuming a slender case, simple expressions are retrieved from which both the rotational Taylor–Culick and the irrotational Hart– McClure solutions are recovered as special cases. At the outset, a new family of flow approximations is derived extending from purely potential to highly rotational fields. These are constructed, verified and catalogued based on their kinetic energies. To help understand the tendency of a motion to shift energy states, a second law analysis is performed and used to rank these solutions based on their entropy content. Interestingly, the Taylor–Culick profile is found to represent an equilibrium state entailing the most energy and entropy among those starting from the rest. A formal extension of Kelvin’s minimum energy theorem to an open region is then pursued, followed by a direct implementation to the problem at hand. Three other flow motions with open boundaries are examined to further exemplify the application of Kelvin’s extended criteria. Our efforts illustrate the overarching harmony that exists between Lagrange’s minimization principle and Kelvin’s minimum energy theorem; both converge on the potential solution as the least kinetic energy bearer even when the velocity at the open barrier is finite.

On the Lagrangian optimization of wall-injected flows: from the Hart–McClure potential to the Taylor–Culick rotational motion

In this paper, Taylor's incompressible and rotational flow in a porous channel with surface mass addition is extended to account for arbitrary headwall injection. Our analysis considers Euler's steady-state equations from which an approximate solution is derived. The resulting mean flow representation satisfies the vanishing axial velocity condition at the blowing walls and is confirmed through comparisons with inviscid finite volume numerical simulations. For a given class of symmetric headwall injection profiles, our solutions are exact at the sidewall and along the midsection plane, where the error in the approximations vanishes identically. The case of uniform injection stands as an exception due to its discontinuity at the sidewall. All solutions become increasingly more accurate in the downstream direction. They hence enable us to approximate the bulk flowfield in both hybrid and solid rockets with variable headwall injection.

Tony Saad

Papers

Scalable Tools for Generating Synthetic Isotropic Turbulence with Arbitrary Spectra

The Taylor-Culick profile with arbitrary headwall injection

Large scale parallel solution of incompressible flow problems using Uintah and hypre

On the Lagrangian optimization of wall-injected flows: from the Hart–McClure potential to the Taylor–Culick rotational motion

Rotational Flowfields in Porous Channels with Arbitrary Headwall Injection