{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:30:42Z","timestamp":1787337042084,"version":"build-2736575974"},"reference-count":24,"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":[[2001,1]]},"abstract":"The numerical simulation of physical problems modeled by systems of conservation laws is difficult due to the presence of discontinuities in the solution. High-order shock capturing schemes combine sharp numerical profiles at discontinuities with a highly accurate approximation in smooth regions, but usually their computational cost is quite large.<\/jats:p>\n Following the idea of A. Harten [Comm. Pure Appl. Math., 48 (1995), pp. 1305--1342] and Bihari and Harten [SIAM J. Sci. Comput., 18 (1997), pp. 315--354], we present in this paper a method to reduce the execution time of such simulations. It is based on a point value multiresolution transform that is used to detect regions with singularities. In these regions, an expensive high-resolution shock capturing scheme is applied to compute the numerical flux at cell interfaces. In smooth regions a cheap polynomial interpolation is used to deduce the value of the numerical divergence from values previously obtained on lower resolution scales.<\/jats:p>\n This method is applied to solve the two-dimensional compressible Euler equations for two classical configurations. The results are analyzed in terms of quality and efficiency.<\/jats:p>","DOI":"10.1137\/s1064827599363988","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"805-823","source":"Crossref","is-referenced-by-count":53,"title":["Point Value Multiscale Algorithms for 2D Compressible Flows"],"prefix":"10.1137","volume":"23","author":[{"given":"Guillaume","family":"Chiavassa","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rosa","family":"Donat","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"R. Abgrall,\n Multiresolution in unstructured meshes: Application to CFD\n , in Numerical Methods for Fluid Dynamics, Vol. 5, K. W. Morton and M. J. Baines, eds., Oxford Sci. Publ. OxfordUniversityPress, New York, 1995, pp. 271\u2013276.","DOI":"10.1093\/oso\/9780198514800.003.0019"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1521-4001(199901)79:1<3::AID-ZAMM3>3.0.CO;2-1"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142996308770"},{"key":"R4","doi-asserted-by":"crossref","unstructured":"G. Ben\u2010Dor,\n Shock Wave Reflection Phenomena\n , Springer\u2010Verlag, New York, 1992.","DOI":"10.1007\/978-1-4757-4279-4"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827594278848"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1007\/s211-001-8009-3"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1995.1164"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1996.0078"},{"key":"R9","doi-asserted-by":"crossref","unstructured":"Rosa Donat, Antonio Marquina, Computing strong shocks in ultrarelativistic flows: a robust alternative, Internat. Ser. Numer. Math., Vol. 129, Birkh\u00e4user, Basel, 1999, 243\u20132511717194","DOI":"10.1007\/978-3-0348-8720-5_27"},{"key":"R10","unstructured":"Jos\u00e9 Ib\u00e1\u00f1ez, Numerical relativistic hydrodynamics, Lecture Notes in Phys., Vol. 423, Springer, Berlin, 1993, 149\u201318394j:76084"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1998.6129"},{"key":"R12","unstructured":"R. Fedkiw, B. Merriman, R. Donat, and S. Osher,\n The Penultimate Scheme for Systems of Conservation Laws: Finite Difference ENO with Marquina\u2019s Flux Splitting\n , UCLA CAM Report 96\u201018, UCLA, Los Angeles, CA, 1996."},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1016\/0168-9274(93)90117-A"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160481201"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1137\/0733060"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1998.6165"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1016\/S0764-4442(99)80278-X"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1137\/0915054"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1086\/303842"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1002\/fld.1650180603"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(89)90222-2"},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1995.1063"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1137\/S0036141095289051"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(84)90142-6"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1064827599363988","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:42:11Z","timestamp":1787334131000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1064827599363988"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2001,1]]},"references-count":24,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2001,1]]}},"alternative-id":["10.1137\/S1064827599363988"],"URL":"https:\/\/doi.org\/10.1137\/s1064827599363988","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2001,1]]}}}