{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,24]],"date-time":"2026-08-24T09:19:30Z","timestamp":1787563170420,"version":"build-2736575974"},"reference-count":26,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2000,1]]},"abstract":"<jats:p>We present a new third-order central scheme for approximating solutions of systems of conservation laws in one and two space dimensions. In the spirit of Godunov-type schemes, our method is based on reconstructing a piecewise-polynomial interpolant from cell-averages which is then advanced exactly in time.<\/jats:p>\n                  <jats:p>In the reconstruction step, we introduce a new third-order, compact, central weighted essentially nonoscillatory (CWENO) reconstruction, which is written as a convex combination of interpolants based on different stencils. The heart of the matter is that one of these interpolants is taken as a suitable quadratic polynomial, and the weights of the convex combination are set as to obtain third-order accuracy in smooth regions. The embedded mechanism in the WENO-like schemes guarantees that in regions with discontinuities or large gradients, there is an automatic switch to a one-sided second-order reconstruction, which prevents the creation of spurious oscillations.<\/jats:p>\n                  <jats:p>In the one-dimensional case, our new third-order reconstruction is based on an extremely compact three-point stencil. Analogous compactness is retained in more space dimensions. The accuracy, robustness, and high-resolution properties of our scheme are demonstrated in a variety of one- and two-dimensional problems.<\/jats:p>","DOI":"10.1137\/s1064827599359461","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"656-672","source":"Crossref","is-referenced-by-count":321,"title":["Compact Central WENO Schemes for Multidimensional Conservation Laws"],"prefix":"10.1137","volume":"22","author":[{"given":"Doron","family":"Levy","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gabriella","family":"Puppo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Giovanni","family":"Russo","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","unstructured":"P. Arminjon, D. Stanescu, and M.\u2010C. Viallon,\n                      A two\u2010dimensional finite volume extension of the Lax\u2010Friedrichs and Nessyahu\u2010Tadmor schemes for compressible flow\n                      , in Proceedings of the 6th International Symposium on Computational Fluid Dynamics, Vol. IV, M. Hafez and K. Oshima, eds., Lake Tahoe, NV, 1995, pp. 7\u201314."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827597324998"},{"key":"R3","doi-asserted-by":"crossref","unstructured":"Franca Bianco, Gabriella Puppo, Giovanni Russo, High order central schemes for hyperbolic systems of conservation laws, Internat. Ser. Numer. 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