J. Casper et Mh. Carpenter, COMPUTATIONAL CONSIDERATIONS FOR THE SIMULATION OF SHOCK-INDUCED SOUND, SIAM journal on scientific computing, 19(3), 1998, pp. 813-828
The numerical study of aeroacoustic problems places stringent demands
on the choice of a computational algorithm because it requires the abi
lity to propagate disturbances of small amplitude and short wavelength
. The demands are particularly high when shock waves are involved beca
use the chosen algorithm must also resolve discontinuities in the solu
tion. The extent to which a high-order accurate shock-capturing method
can be relied upon for aeroacoustics applications that involve the in
teraction of shocks with other waves has not been previously quantifie
d. Such a study is initiated in this work. A fourth-order accurate ess
entially nonoscillatory (ENO) method is used to investigate the soluti
ons of inviscid, compressible flows with shocks. The design order of a
ccuracy is achieved in the smooth regions of a steady-state, quasi-one
-dimensional test case. However, in an unsteady test case, only first-
order results are obtained downstream of a sound-shock interaction. Th
e difficulty in obtaining a globally high-order accurate solution in s
uch a case with a shock-capturing method is demonstrated through the s
tudy of a simplified, linear model problem. Some of the difficult issu
es and ramifications for aeroacoustic simulations of flows with shocks
that are raised by these results are discussed.