Scaling finite difference methods in large eddy simulation of jet engine noise to the petascale: numerical methods and their efficient and automated implementation

Reduction of jet engine noise has recently become a new arena of competition between aircraft manufacturers. As a relatively new field of research in computational fluid dynamics (CFD), computational aeroacoustics (CAA) prediction of jet engine noise based on large eddy simulation (LES) is a robust and accurate tool that complements the existing theoretical and experimental approaches. In order to satisfy the stringent requirements of CAA on numerical accuracy, finite difference methods in LES-based jet engine noise prediction rely on the implicitly formulated compact spatial partial differentiation and spatial filtering schemes, a crucial component of which is an embedded solver for tridiagonal linear systems spatially oriented along the three coordinate directions of the computational space. Traditionally, researchers and engineers in CAA have employed manually crafted implementations of solvers including the transposition method, the multiblock method and the Schur complement method. Algorithmically, these solvers force a trade-off between numerical accuracy and parallel scalability. Programmingwise, implementing them for each of the three coordinate directions is tediously repetitive and error-prone. ^ In this study, we attempt to tackle both of these two challenges faced by researchers and engineers. We first describe an accurate and scalable tridiagonal linear system solver as a specialization of the truncated SPIKE algorithm and strategies for efficient implementation of the compact spatial partial differentiation and spatial filtering schemes. We then elaborate on two programming models tailored for composing regular grid-based numerical applications including finite difference-based LES of jet engine noise, one based on generalized elemental subroutines and the other based on functional array programming, and the accompanying code optimization and generation methodologies. Through empirical experiments, we demonstrate that truncated SPIKE-based spatial partial differentiation and spatial filtering deliver the theoretically promised optimal scalability in weak scaling conditions and can be implemented using the two programming models with performance on par with handwritten code while significantly reducing the required programming effort

A Computational Analysis of the Aerodynamics and Aeroacoustics of Jets with Fluid Injection

A detailed numerical analysis of fluidic injection as a tool to reduce noise emission is presented here. The noise reduction strategy, developed at the Pennsylvania State University, is based on injectors that blow air into the diverging section of the nozzle to emulate the effect of interior corrugation on the jet plume. The advantage is that the injection can be activated during takeoff and turned o_ during other phases of flight so that performance is not affected. Numerical simulations are performed on a military-style nozzle based on the GE F400-series engines, with a design Mach number of 1:65, for over-expanded jet conditions. The effectiveness of the fluidic injection as noise reduction technique is analyzed for heated and unheated jets. A high-order Large Eddy Simulation (LES) solver, developed originally at Purdue University, is used to analyze the flow-field and the acoustic field. New initial conditions and new boundary conditions are introduced. A set of Reynolds Averaged Navier-Stokes (RANS) simulations is used to set up the initial and boundary conditions for the LES runs. The numerical results are compared and validated with the outcome of experiments and RANS simulations performed at the Pennsylvania State University. The characteristics of unheated and heated jets are presented and compared. The higher temperatures do not modify the shock-cell structures, while they affect the jet development and the acoustic signature. The fluidic injection shows the potential of breaking down the shock-cells into smaller structures with lower strength, directly reducing the intensity of broadband shock associated noise. Moreover, the injectors are found to affect the development of the larger turbulent structures that generate the peak noise. For the cases tested the injectors reduce the peak noise by more than 1:5 dB for the unheated jet and by 3 dB for the heated jet, on the azimuthal plane in between two lines of injectors. The direction of maximum sound propagation moves from about 30_ to about 50_ as the jet gets heated. An analysis of the thrust changes due to activating the injectors is also presented for the heated and unheated jet conditions. The specific thrust is reduced by about 3% when the injectors are used

A conservative overlap method for multi-block parallelization of compact finite-volume schemes

A conservative approach for MPI-based parallelization of tridiagonal compact schemes is developed in the context of multi-block finite-volume methods. For each block, an enlarged linear system is solved by overlapping a certain number of neighbour cells from adjacent sub-domains. The values at block-to-block boundary faces are evaluated by a high-order centered approximation formula. Unlike previous methods, conservation is retained by properly re-computing the common interface value between two neighbouring blocks. Numerical tests show that parallelization artifacts decrease significantly as the number of overlapping cells is increased, at some expense of parallel efficiency. A reasonable trade-off between accuracy and performances is discussed in the paper with reference to both the spectral properties of the method and the results of fully turbulent numerical simulations.Peer ReviewedPostprint (published version

Development of a high-order parallel solver for direct and large eddy simulations of turbulent flows

Turbulence is inherent in fluid dynamics, in that laminar flows are rather the exception than the rule, hence the longstanding interest in the subject, both within the academic community and the industrial R&D laboratories. Since 1883, much progress has been made, and statistics applied to turbulence have provided understanding of the scaling laws which are peculiar to several model flows, whereas experiments have given insight on the structure of real-world flows, but, soon enough, numerical approaches to the matter have become the most promising ones, since they lay the ground for the solution of high Reynolds number unsteady Navier-Stokes equations by means of computer systems. Nevertheless, despite the exponential rise in computational capability over the last few decades, the more computer technology advances, the higher the Reynolds number sought for test-cases of industrial interest: there is a natural tendency to perform simulations as large as possible, a habit that leaves no room for wasting resources. Indeed, as the scale separation grows with Re, the reduction of wall clock times for a high-fidelity solution of desired accuracy becomes increasingly important. To achieve this task, a CFD solver should rely on the use of appropriate physical models, consistent numerical methods to discretize the equations, accurate non-dissipative numerical schemes, efficient algorithms to solve the numerics, and fast routines implementing those algorithms. Two archetypal approaches to CFD are direct and large-eddy simulation (DNS and LES respectively), which profoundly differ in several aspects but are both “eddy-resolving” methods, meant to resolve the structures of the flow-field with the highest possible accuracy and putting in as little spurious dissipation as possible. These two requirements of accurate resolution of scales, and energy conservation, should be addressed by any numerical method, since they are essential to many real-world fluid flows of industrial interest. As a consequence, high order numerical schemes, and compact schemes among them, have received much consideration, since they address both goals, at the cost of a lower ease of application of the boundary condition, and a higher computational cost. The latter problem is tackled with parallel computing, which also allows to take advantage of the currently available computer power at the best possible extent. The research activity conducted by the present author has concerned the development, from scratch, of a three-dimensional, unsteady, incompressible Navier-Stokes parallel solver, which uses an advanced algorithm for the process-wise solution of the linear systems arising from the application of high order compact finite difference schemes, and hinges upon a three-dimensional decomposition of the cartesian computational space. The code is written in modern Fortran 2003 — plus a few features which are unique to the 2008 standard — and is parallelized through the use of MPI 3.1 standard’s advanced routines, as implemented by the OpenMPI library project. The coding was carried out with the objective of creating an original CFD high-order parallel solver which is maintainable and extendable, of course within a well-defined range of possibilities. With this main priority being outlined, particular attention was paid to several key concepts: modularity and readability of the source code and, in turn, its reusability; ease of implementation of virtually any new explicit or implicit finite difference scheme; modern programming style and avoidance of deprecated old legacy Fortran constructs and features, so that the world wide web is a reliable and active means to the quick solution of coding problems arising from the implementation of new modules in the code; last but not least, thorough comments, especially in critical sections of the code, explaining motives and possible expected weak links. Design, production, and documentation of a program from scratch is almost never complete. This is certainly true for the present effort. The method and the code are verified against the full three-dimensional Lid-Driven Cavity and Taylor-Green Vortex flows. The latter test is used also for the assessment of scalability and parallel efficiency

Numerical simulation of multiphase jet fragmentation using Smoothed Particle Hydrodynamics

This thesis is devoted to the study of multiphase jet fragmentation using Smoothed Particle Hydrodynamics (SPH). The theoretical aspects of three hydrodynamic instabilities, namely the Kelvin-Helmholtz instability (KHI), Rayleigh-Taylor instability (RTI), and Rayleigh Plateau instability (RPI) are reviewed. The linear growth rate of the combined KHI and RTI are derived by means of linear perturbation in chapter 2. The linear growth rate of the multiphase RPI is presented in chapter 7. An overview of the Smoothed Particle Hydrodynamics is given in chapter 3. A pseudo-consistent SPH scheme is presented for the simulation of multiphase flow problems. Additionally, two interface stabilisation models are presented: quasi-buoyancy model and gas-repulsion model. When used in combination with the pseudo-consistent SPH scheme, these models are found to be superior than those presented in the weakly-compressible SPH literature and allows for the simulations for density ratio up to three-magnitudes. The development of an idealised KHI and a KHI subjected to constant gravitational acceleration (stratified shear instability) is examined in chapter 5. The extracted linear growth rate are compared with the theoretical growth rate presented both in the literature and in chapter 2 for the purpose of validation. The development of a single- and multi-mode RTI are studied by means of SPH in chapter 6. Chapter 7 presents the results for the three-dimensional RPI occurring between two fluids. Based on the knowledge acquired in chapter 5-7, the multiphase jet fragmentation driven by the previously mentioned hydrodynamic instabilities are presented in chapter 8. Finally, the major research findings and recommendations are summarised in chapter 9

Numerical simulation of multiphase jet fragmentation using Smoothed Particle Hydrodynamics

This thesis is devoted to the study of multiphase jet fragmentation using Smoothed Particle Hydrodynamics (SPH). The theoretical aspects of three hydrodynamic instabilities, namely the Kelvin-Helmholtz instability (KHI), Rayleigh-Taylor instability (RTI), and Rayleigh Plateau instability (RPI) are reviewed. The linear growth rate of the combined KHI and RTI are derived by means of linear perturbation in chapter 2. The linear growth rate of the multiphase RPI is presented in chapter 7. An overview of the Smoothed Particle Hydrodynamics is given in chapter 3. A pseudo-consistent SPH scheme is presented for the simulation of multiphase flow problems. Additionally, two interface stabilisation models are presented: quasi-buoyancy model and gas-repulsion model. When used in combination with the pseudo-consistent SPH scheme, these models are found to be superior than those presented in the weakly-compressible SPH literature and allows for the simulations for density ratio up to three-magnitudes. The development of an idealised KHI and a KHI subjected to constant gravitational acceleration (stratified shear instability) is examined in chapter 5. The extracted linear growth rate are compared with the theoretical growth rate presented both in the literature and in chapter 2 for the purpose of validation. The development of a single- and multi-mode RTI are studied by means of SPH in chapter 6. Chapter 7 presents the results for the three-dimensional RPI occurring between two fluids. Based on the knowledge acquired in chapter 5-7, the multiphase jet fragmentation driven by the previously mentioned hydrodynamic instabilities are presented in chapter 8. Finally, the major research findings and recommendations are summarised in chapter 9

XSEDE: eXtreme Science and Engineering Discovery Environment Third Quarter 2012 Report

The Extreme Science and Engineering Discovery Environment (XSEDE) is the most advanced, powerful, and robust collection of integrated digital resources and services in the world. It is an integrated cyberinfrastructure ecosystem with singular interfaces for allocations, support, and other key services that researchers can use to interactively share computing resources, data, and expertise.This a report of project activities and highlights from the third quarter of 2012.National Science Foundation, OCI-105357

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal