Aeroacoustic Predictions Using High-Order Shock-Capturing Schemes


22 févr. 2014 (il y a 8 années et 10 jours)

325 vue(s)

Aeroacoustic Predictions Using High
Order Shock
Capturing Schemes

John A. Ekaterinaris


71110 Heraklion, Crete, GREECE



order accurate,
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


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
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

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

Explicit filters [3], WENO schemes, and extension of
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.



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.


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


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.



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


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

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


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

1999, p. 199.


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


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.