Aeroacoustic Predictions Using High-Order Shock-Capturing Schemes

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Feb 22, 2014 (3 years and 8 months ago)

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Aeroacoustic Predictions Using High
-
Order Shock
-
Capturing Schemes


John A. Ekaterinaris


FORTH/IACM, PO Box 1527

71110 Heraklion, Crete, GREECE

e
-
mail:
ekaterin@iacm.forth.gr



ABSTRACT


High
-
order accurate,
finite
-
difference methods used in CFD are applied to
aeroacoustics. These methods are suitable for aeroacoustic predictions of complex
flows in curvilinear coordinates. Furthermore, the proposed methods are applicable
for the prediction of sound generation

from both subsonic, compressible flows and
flows with discontinuities. The accuracy of the proposed methods is evaluated for test
problems.


Background


For the computation of flows with shocks, methods designed to regularize the
numerical solution have b
een studied since the early attempts of von Neumann and
Richtmyer who used finite
-
difference techniques combined with the so
-
called
artificial viscosity or numerical dissipation. Use of numerical dissipation in the finite
difference and finite volume conte
xt found widespread application in computational
fluid dynamics (CFD) of compressible aerodynamic flows. The main difficulty in the
application of these methods in aeroacoustics predictions, direct numerical
simulations (DNS) and large
-
eddy simulations (LE
S) of compressible flows is the
control of numerical dissipation necessary to capture discontinuities that occur in such
flows. In previous numerical investigations [1] [2], it was found that the numerical
dissipation of high
-
order, shock
-
capturing schemes

can lead to significant damping of
turbulence fluctuations [1] and masks the effects of the subgrid

scale (SGS) models.
For these cases, a local application of the shock
-
capturing scheme was found
absolutely necessary in order to minimize numerical dissip
ation. In the study of Ref.
[1], for example, this requirement was achieved by means of the application of an
essentially non
-
oscillatory (ENO) scheme only in the shock
-
normal direction and over
a few mesh points around the mean shock position. Unfortunate
ly, in most cases, the
shock position is unknown and one needs to introduce a sensor to detect possible
discontinuities. On the other hand, high
-
order, finite
-
difference schemes with explicit
filtering for numerical stability [3], [4] were found sufficient
ly accurate for the
computation of flows without discontinuities and the convection of vortical and
aeroacoustice disturbances.


Explicit filters for high
-
order schemes that have improved computational
efficiency compared to ENO or weighted ENO (WENO) meth
ods have been derived
by Engquist et al. [5]. This method can be easily implemented into existing codes
because the filter step is essentially independent of the basic differencing scheme and
is applied as post processing. In the same way, Yee et al. [6] s
howed that the
dissipative part of a shock
-
capturing scheme could be applied after each time step to
regularize the numerical solution and acts like a filter. Moreover, to meet the
requirement of a local application of the numerical dissipation the amplitu
de of the
dissipation is evaluated with a sensor derived from the artificial compression method
(ACM) of Harten [7]. The numerical test in Ref. [6] used total variation diminishing
(TVD) schemes for the nonlinear filter. The possibility of using high
-
order

nonlinear
filters based on ENO reconstruction and evaluation of the accuracy over TVD
-
base
filters has been demonstrated in [8].


Explicit filters [3], WENO schemes, and extension of
high
-
order WENO
schemes for filtering of high
-
order centered schemes of
Ref. [6] is investigated for
aeroacoustic simulations in flows with and without discontinuities. Application of
these methods for sound level emission from transitional and turbulent compressible
flow through direct numerical simulation is possible.








References


[1]

Lee, S., Lele, S. K., and Moin, P., “Interaction of Isotropic Turbulence with
Shock Waves: Effect of Shock Strength,”
J. Fluid Mechanics
, Vol. 340, 1997,
p. 225.


[2]

Garnier, E., Mossi, M., Sagaut, P., Comte, P., and Deville, M., “On th
e Use of
Shock
-
Capturing Schemes for Large
-
Eddy Simulations,”
J. Comput. Phys
.
Vol. 153, 1999, p. 273.


[3]

Gaitonde, D. V. and Visbal, M. R., “Pade
-
Type High
-
Order Boundary Filters
for the Navier
-
Stokes Equations,”
AIAA Journal
, Vol. 38, No. 11, 2000, pp.

2103
-
2112.


[4]

Rizzetta, D. P., Visbal, M. R., and Gaitonde, D. P., “Large
-
Eddy Simulation of
Supersonic Compression Ramp Flow by High
-
Order Method,”
AIAA Journal
,
Vol. 39, No. 12, 2001, pp. 2283
-
2292.


[5]

Engquist, B. Loetstedt, P. and Sjoergreen, B.,
“Nonlinear Filters fpr Efficient
Shock Computation,”

Math. Comput
., Vol 52, 1989, p. 232.


[6]

Yee, H. C., Sandham, N. D. and Djomehri, M. J. “Low
-
Dissipative High
-
Order Shock
-
Capturing Methods Using Characteristic
-
Based Filters,”
J.
Comp.
Phys.
, Vol. 150,

1999, p. 199.


[7]

Harten, A., “The Artificial Compression Method for Computation of Shocks
and Contact Discontinuities, III Self
-
Adjusting Hybrid Schemes,”
Math.
Comput
., Vol 32, 1978, p. 363


[8]

Garnier, E. , Sagaut, and Deville, M., “A Class of Explic
it ENO Filters with
Application to Unsteady Flows”
J. Comput. Phys
. Vol. 170, 2001, p. 184.