{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,24]],"date-time":"2026-08-24T03:23:30Z","timestamp":1787541810717,"version":"build-2736575974"},"reference-count":20,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[1998,1]]},"abstract":"<jats:p>The numerical study of aeroacoustic problems places stringent demands on the choice of a computational algorithm because it requires the ability to propagate disturbances of small amplitude and short wavelength. The demands are particularly high when shock waves are involved because the chosen algorithm must also resolve discontinuities in the solution. The extent to which a high-order accurate shock-capturing method can be relied upon for aeroacoustics applications that involve the interaction of shocks with other waves has not been previously quantified. Such a study is initiated in this work. A fourth-order accurate essentially nonoscillatory (ENO) method is used to investigate the solutions of inviscid, compressible flows with shocks. The design order of accuracy 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. The difficulty in obtaining a globally high-order accurate solution in such a case with a shock-capturing method is demonstrated through the study of a simplified, linear model problem. Some of the difficult issues and ramifications for aeroacoustic simulations of flows with shocks that are raised by these results are discussed.<\/jats:p>","DOI":"10.1137\/s1064827595294101","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"813-828","source":"Crossref","is-referenced-by-count":95,"title":["Computational Considerations for the Simulation of Shock-Induced Sound"],"prefix":"10.1137","volume":"19","author":[{"given":"Jay","family":"Casper","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mark H.","family":"Carpenter","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1994.1008"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(92)90324-R"},{"key":"R3","unstructured":"A. Harten and S. Chakravarthy,\n                      Multi\u2010Dimensional ENO Schemes for General Geometries\n                      , NASA Contractor report 187637, ICASE report 91\u201076, 1991."},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(87)90031-3"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(88)90177-5"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1989-0955749-2"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1993.1041"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1994.1171"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1007\/BF01065582"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1007\/BF01065581"},{"key":"R11","doi-asserted-by":"crossref","unstructured":"H. Atkins,\n                      High\u2010Order ENO Methods for the Unsteady Navier\u2010Stokes Equations\n                      , AIAA 91\u20101557, Washington, DC, 1991.","DOI":"10.2514\/6.1991-1557"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.2514\/3.12240"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.2514\/3.12203"},{"key":"R14","doi-asserted-by":"crossref","unstructured":"J. Casper and K. R. Meadows,\n                      Using High\u2010Order Accurate Essentially Non\u2010Oscillatory Schemes for Aeroacoustic Applications\n                      , AIAA 95\u20100163, Washington, DC, 1995.","DOI":"10.2514\/6.1995-163"},{"key":"R15","doi-asserted-by":"crossref","unstructured":"M. H. Carpenter, H. L. Atkins, and D. J. Singh,\n                      Characteristic and Finite\u2010Wave Shock\u2010Fitting Boundary Conditions for Chebyshev Methods\n                      , in Transition, Turbulence, and Combustion, Vol. II, M. Y. Hussaini, T. B. Gatski, and T. L. Jackson, eds., Kluwer Academic Publishers, Norwell, MA, 1994.","DOI":"10.1007\/978-94-011-1034-1_29"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160300602"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160310403"},{"key":"R18","unstructured":"C. W. Shu,\n                      Numerical Solutions of Conservation Laws\n                      , Ph.D. Dissertation, University of California, Los Angeles, CA, 1986."},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7825(90)90014-D"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(89)90226-X"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1064827595294101","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:26:21Z","timestamp":1787333181000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1064827595294101"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,1]]},"references-count":20,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1998,1]]}},"alternative-id":["10.1137\/S1064827595294101"],"URL":"https:\/\/doi.org\/10.1137\/s1064827595294101","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,1]]}}}