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Solutions of the benchmark problems by the dispersion-relation-preserving schemeThe 7-point stencil Dispersion-Relation-Preserving scheme of Tam and Webb is used to solve all the six categories of the CAA benchmark problems. The purpose is to show that the scheme is capable of solving linear, as well as nonlinear aeroacoustics problems accurately. Nonlinearities, inevitably, lead to the generation of spurious short wave length numerical waves. Often, these spurious waves would overwhelm the entire numerical solution. In this work, the spurious waves are removed by the addition of artificial selective damping terms to the discretized equations. Category 3 problems are for testing radiation and outflow boundary conditions. In solving these problems, the radiation and outflow boundary conditions of Tam and Webb are used. These conditions are derived from the asymptotic solutions of the linearized Euler equations. Category 4 problems involved solid walls. Here, the wall boundary conditions for high-order schemes of Tam and Dong are employed. These conditions require the use of one ghost value per boundary point per physical boundary condition. In the second problem of this category, the governing equations, when written in cylindrical coordinates, are singular along the axis of the radial coordinate. The proper boundary conditions at the axis are derived by applying the limiting process of r approaches 0 to the governing equations. The Category 5 problem deals with the numerical noise issue. In the present approach, the time-independent mean flow solution is computed first. Once the residual drops to the machine noise level, the incident sound wave is turned on gradually. The solution is marched in time until a time-periodic state is reached. No exact solution is known for the Category 6 problem. Because of this, the problem is formulated in two totally different ways, first as a scattering problem then as a direct simulation problem. There is good agreement between the two numerical solutions. This offers confidence in the computed results. Both formulations are solved as initial value problems. As such, no Kutta condition is required at the trailing edge of the airfoil.
Document ID
19950023724
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Authors
Tam, Christopher K. W.
(Florida State Univ. Tallahassee, FL, United States)
Shen, H.
(Florida State Univ. Tallahassee, FL, United States)
Kurbatskii, K. A.
(Florida State Univ. Tallahassee, FL, United States)
Auriault, L.
(Florida State Univ. Tallahassee, FL, United States)
Date Acquired
September 6, 2013
Publication Date
May 1, 1995
Publication Information
Publication: NASA. Langley Research Center, ICASE(LaRC Workshop on Benchmark Problems in Computational Aeroacoustics (CAA) p 149-171 (SEE N95-30133 10-71)
Subject Category
Numerical Analysis
Accession Number
95N30145
Funding Number(s)
CONTRACT_GRANT: NAG3-1267
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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