Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

Numerical Initial Value Problems in Ordinary Differential Equations

Viscous flow computations with the method of lattice Boltzmann equation

Complex fluid physics can be modeled using an extended kinetic (Boltzmann) equation in a more efficient way than using the continuum Navier-Stokes equations. Here, we explain this method for modeling fluid turbulence and show its effectiveness with the use of a computationally efficient implementation in terms of a discrete or "lattice" Boltzmann equation.

http://science.sciencemag.org/content/sci/301/5633/633.full.pdf

Extended Boltzmann kinetic equation for turbulent flows.

https://www.colonius.caltech.edu/pdfs/ColoniusLele2004.pdf

Computational aeroacoustics: progress on nonlinear problems of sound generation

An efficient, two-dimensional implementation of the ffowcs williams and hawkings equation

An acoustic analysis based on the Ffowcs Williams and Hawkings equation was performed for a high-lift system. As input, the acoustic analysis used un- steady flow data obtained from a highly resolved, time-dependent, Reynolds-averaged Navier-Stokes calculation. The analysis strongly suggests that vor- tex shedding from the trailing edge of the slat results in a high-amplitude, high-frequency acoustic signal, similar to that which was observed in a correspond- ing experimental study of the high-lift system.

/pdf/computational-aeroacoustic-analysis-of-slat-trailing-edge-1zpdviw1os.pdf

Computational Aeroacoustic Analysis of Slat Trailing-Edge Flow

The NASA goal of reducing external aircraft noise by 10 dB in the near-term presents the acoustics community with an enormous challenge. This report identifies technologies with the greatest potential to reduce airframe noise. Acoustic and aerodynamic effects will be discussed, along with the likelihood of industry accepting and implementing the different technologies. We investigate the lower bound, defined as noise generated by an aircraft modified with a virtual retrofit capable of eliminating all noise associated with the high lift system and landing gear. However, the airframe noise of an aircraft in this 'clean' configuration would only be about 8 dB quieter on approach than current civil transports. To achieve the NASA goal of 10 dB noise reduction will require that additional noise sources be addressed. Research shows that energy in the turbulent boundary layer of a wing is scattered as it crosses trailing edge. Noise generated by scattering is the dominant noise mechanism on an aircraft flying in the clean configuration. Eliminating scattering would require changes to much of the aircraft, and practical reduction devices have yet to receive serious attention. Evidence suggests that to meet NASA goals in civil aviation noise reduction, we need to employ emerging technologies and improve landing procedures; modified landing patterns and zoning restrictions could help alleviate aircraft noise in communities close to airports.

/pdf/the-airframe-noise-reduction-challenge-1s7vikq1kc.pdf

The Airframe Noise Reduction Challenge

This paper presents a comparison between two implementations of the Ffowcs Williams and Hawkings equation for airframe noise applications. Airframe systems are generally moving at constant speed and not rotating, so these conditions are used in the current investigation. Efficient and easily implemented forms of the equations applicable to subsonic, rectilinear motion of all acoustic sources are used. The assumptions allow the derivation of a simple form of the equations in the frequency-domain, and the time-domain method uses the restrictions on the motion to reduce the work required to find the emission time. The comparison between the frequency domain method and the retarded time formulation reveals some of the advantages of the different approaches. Both methods are still capable of predicting the far-field noise from nonlinear near-field flow quantities. Because of the large input data sets and potentially large numbers of observer positions of interest in three-dimensional problems, both codes utilize the message passing interface to divide the problem among different processors. Example problems are used to demonstrate the usefulness and efficiency of the two schemes.

/pdf/a-comparison-of-ffowcs-williams-hawkings-solvers-for-2c4be7gw1u.pdf

A comparison of ffowcs williams-hawkings solvers for airframe noise applications

Recent experience in the application of an optimized, second-order, backward-difference (BDF2OPT) temporal scheme is reported. The primary focus of the work is on obtaining accurate solutions of the unsteady Reynolds-averaged Navier-Stokes equations over long periods of time for aerodynamic problems of interest. The baseline flow solver under consideration uses a particular BDF2OPT temporal scheme with a dual-timestepping algorithm for advancing the flow solutions in time. Numerical difficulties are encountered with this scheme when the flow code is run for a large number of time steps, a behavior not seen with the standard secondorder, backward-difference, temporal scheme. Based on a stability analysis, slight modifications to the BDF2OPT scheme are suggested. The performance and accuracy of this modified scheme is assessed by comparing the computational results with other numerical schemes and experimental data.

/pdf/re-evaluation-of-an-optimized-second-order-backward-2eze7y2g7z.pdf

David P. Lockard

Papers

An efficient, two-dimensional implementation of the ffowcs williams and hawkings equation

Computational Aeroacoustic Analysis of Slat Trailing-Edge Flow

The Airframe Noise Reduction Challenge

A comparison of ffowcs williams-hawkings solvers for airframe noise applications

Re-evaluation of an Optimized Second Order Backward Difference (BDF2OPT) Scheme for Unsteady Flow Applications