{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T20:10:06Z","timestamp":1784664606010,"version":"3.55.0"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"2-3","license":[{"start":{"date-parts":[[2007,11,8]],"date-time":"2007-11-08T00:00:00Z","timestamp":1194480000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2008,6]]},"DOI":"10.1007\/s10915-007-9166-4","type":"journal-article","created":{"date-parts":[[2007,11,7]],"date-time":"2007-11-07T09:45:15Z","timestamp":1194428715000},"page":"350-371","source":"Crossref","is-referenced-by-count":228,"title":["An Unconditionally Stable MacCormack Method"],"prefix":"10.1007","volume":"35","author":[{"given":"Andrew","family":"Selle","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ronald","family":"Fedkiw","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"ByungMoon","family":"Kim","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yingjie","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jarek","family":"Rossignac","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2007,11,8]]},"reference":[{"key":"9166_CR1","volume-title":"Computational Fluid Dynamics: The Basics With Applications","author":"J.D. Anderson","year":"1995","unstructured":"Anderson, J.D.: Computational Fluid Dynamics: The Basics With Applications. McGraw-Hill, New York (1995)"},{"key":"9166_CR2","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1002\/cpa.3160050303","volume":"5","author":"R. Courant","year":"1952","unstructured":"Courant, R., Issacson, E., Rees, M.: On the solution of nonlinear hyperbolic differential equations by finite differences. Commun. Pure Appl. Math. 5, 243\u2013255 (1952)","journal-title":"Commun. Pure Appl. Math."},{"issue":"1","key":"9166_CR3","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1016\/S0021-9991(03)00276-6","volume":"190","author":"T. Dupont","year":"2003","unstructured":"Dupont, T., Liu, Y.: Back and forth error compensation and correction methods for removing errors induced by uneven gradients of the level set function. J. Comput. Phys. 190(1), 311\u2013324 (2003)","journal-title":"J. Comput. Phys."},{"key":"9166_CR4","doi-asserted-by":"crossref","first-page":"647","DOI":"10.1090\/S0025-5718-06-01898-9","volume":"76","author":"T. Dupont","year":"2007","unstructured":"Dupont, T., Liu, Y.: Back and forth error compensation and correction methods for semi-Lagrangian schemes with application to level set interface computations. Math. Comp. 76, 647\u2013668 (2007)","journal-title":"Math. Comp."},{"key":"9166_CR5","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1006\/jcph.2002.7166","volume":"183","author":"D. Enright","year":"2002","unstructured":"Enright, D., Fedkiw, R., Ferziger, J., Mitchell, I.: A hybrid particle level set method for improved interface capturing. J. Comput. Phys. 183, 83\u2013116 (2002)","journal-title":"J. Comput. Phys."},{"key":"9166_CR6","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1016\/j.compstruc.2004.04.024","volume":"83","author":"D. Enright","year":"2005","unstructured":"Enright, D., Losasso, F., Fedkiw, R.: A fast and accurate semi-Lagrangian particle level set method. Comput. Struct. 83, 479\u2013490 (2005)","journal-title":"Comput. Struct."},{"issue":"3","key":"9166_CR7","doi-asserted-by":"crossref","first-page":"736","DOI":"10.1145\/566654.566645","volume":"21","author":"D. Enright","year":"2002","unstructured":"Enright, D., Marschner, S., Fedkiw, R.: Animation and rendering of complex water surfaces. ACM Trans. Graph. (SIGGRAPH Proc.) 21(3), 736\u2013744 (2002)","journal-title":"ACM Trans. Graph. (SIGGRAPH Proc.)"},{"key":"9166_CR8","doi-asserted-by":"crossref","unstructured":"Enright, D., Nguyen, D., Gibou, F., Fedkiw, R.: Using the particle level set method and a second order accurate pressure boundary condition for free surface flows. In: Proc. 4th ASME-JSME Joint Fluids Eng. Conf., no. FEDSM2003\u201345144. ASME (2003)","DOI":"10.1115\/FEDSM2003-45144"},{"key":"9166_CR9","doi-asserted-by":"crossref","unstructured":"Fedkiw, R., Stam, J., Jensen, H.: Visual simulation of smoke. In: Proc. of ACM SIGGRAPH 2001, pp. 15\u201322 (2001)","DOI":"10.1145\/383259.383260"},{"issue":"12","key":"9166_CR10","doi-asserted-by":"crossref","first-page":"2879","DOI":"10.2514\/1.18235","volume":"44","author":"M. Herrmann","year":"2006","unstructured":"Herrmann, M., Blanquart, G.: Flux corrected finite volume scheme for preserving scalar boundedness in reacting large-eddy simulations. AIAA J. 44(12), 2879\u20132886 (2006)","journal-title":"AIAA J."},{"issue":"3","key":"9166_CR11","doi-asserted-by":"crossref","first-page":"805","DOI":"10.1145\/1141911.1141959","volume":"25","author":"G. Irving","year":"2006","unstructured":"Irving, G., Guendelman, E., Losasso, F., Fedkiw, R.: Efficient simulation of large bodies of water by coupling two and three dimensional techniques. ACM Trans. Graph. (SIGGRAPH Proc.) 25(3), 805\u2013811 (2006)","journal-title":"ACM Trans. Graph. (SIGGRAPH Proc.)"},{"key":"9166_CR12","doi-asserted-by":"crossref","first-page":"2126","DOI":"10.1137\/S106482759732455X","volume":"21","author":"G.-S. Jiang","year":"2000","unstructured":"Jiang, G.-S., Peng, D.: Weighted ENO schemes for Hamilton-Jacobi equations. SIAM J. Sci. Comput. 21, 2126\u20132143 (2000)","journal-title":"SIAM J. Sci. Comput."},{"key":"9166_CR13","unstructured":"Kim, B.-M., Liu, Y., Llamas, I., Rossignac, J.: Using BFECC for fluid simulation. In: Eurographics Workshop on Natural Phenomena (2005)"},{"issue":"1","key":"9166_CR14","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1109\/TVCG.2007.3","volume":"13","author":"B.-M. Kim","year":"2007","unstructured":"Kim, B.-M., Liu, Y., Llamas, I., Rossignac, J.: Advections with significantly reduced dissipation and diffusion. IEEE Trans. Vis. Comput. Graph. 13(1), 135\u2013144 (2007)","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"9166_CR15","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1002\/cpa.3160140324","volume":"14","author":"P.D. Lax","year":"1961","unstructured":"Lax, P.D.: On the stability of difference approximations to solutions of hyperbolic equations with variable coefficients. Commun. Pure Appl. Math. 14, 497\u2013520 (1961)","journal-title":"Commun. Pure Appl. Math."},{"key":"9166_CR16","doi-asserted-by":"crossref","first-page":"995","DOI":"10.1016\/j.compfluid.2005.01.006","volume":"35","author":"F. Losasso","year":"2006","unstructured":"Losasso, F., Fedkiw, R., Osher, S.: Spatially adaptive techniques for level set methods and incompressible flow. Comput. Fluids 35, 995\u20131010 (2006)","journal-title":"Comput. Fluids"},{"key":"9166_CR17","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1145\/1015706.1015745","volume":"23","author":"F. Losasso","year":"2004","unstructured":"Losasso, F., Gibou, F., Fedkiw, R.: Simulating water and smoke with an octree data structure. ACM Trans. Graph. (SIGGRAPH Proc.) 23, 457\u2013462 (2004)","journal-title":"ACM Trans. Graph. (SIGGRAPH Proc.)"},{"key":"9166_CR18","doi-asserted-by":"crossref","unstructured":"MacCormack, R.: The effect of viscosity in hypervelocity impact cratering. In: AIAA Hypervelocity Impact Conference, 1969. AIAA paper, pp. 69\u2013354 (1969)","DOI":"10.2514\/6.1969-354"},{"key":"9166_CR19","doi-asserted-by":"crossref","first-page":"912","DOI":"10.1016\/j.jcp.2006.07.019","volume":"219","author":"C. Min","year":"2006","unstructured":"Min, C., Gibou, F.: A second order accurate projection method for the incompressible Navier-Stokes equation on non-graded adaptive grids. J. Comput. Phys. 219, 912\u2013929 (2006)","journal-title":"J. Comput. Phys."},{"key":"9166_CR20","volume-title":"Level Set Methods and Dynamic Implicit Surfaces","author":"S. Osher","year":"2002","unstructured":"Osher, S., Fedkiw, R.: Level Set Methods and Dynamic Implicit Surfaces. Springer, New York (2002)"},{"key":"9166_CR21","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1016\/0021-9991(88)90002-2","volume":"79","author":"S. Osher","year":"1988","unstructured":"Osher, S., Sethian, J.: Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79, 12\u201349 (1988)","journal-title":"J. Comput. Phys."},{"issue":"3","key":"9166_CR22","doi-asserted-by":"crossref","first-page":"910","DOI":"10.1145\/1073204.1073282","volume":"24","author":"A. Selle","year":"2005","unstructured":"Selle, A., Rasmussen, N., Fedkiw, R.: A vortex particle method for smoke, water and explosions. ACM Trans. Graph. (SIGGRAPH Proc.) 24(3), 910\u2013914 (2005)","journal-title":"ACM Trans. Graph. (SIGGRAPH Proc.)"},{"key":"9166_CR23","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1016\/0021-9991(88)90177-5","volume":"77","author":"C.-W. Shu","year":"1988","unstructured":"Shu, C.-W., Osher, S.: Efficient implementation of essentially non-oscillatory shock capturing schemes. J. Comput. Phys. 77, 439\u2013471 (1988)","journal-title":"J. Comput. Phys."},{"key":"9166_CR24","doi-asserted-by":"crossref","unstructured":"Stam, J.: Stable fluids. In: Proc. of SIGGRAPH 99, pp. 121\u2013128 (1999)","DOI":"10.1145\/311535.311548"},{"key":"9166_CR25","doi-asserted-by":"crossref","first-page":"2206","DOI":"10.1175\/1520-0493(1991)119<2206:SLISFA>2.0.CO;2","volume":"119","author":"A. Staniforth","year":"1991","unstructured":"Staniforth, A., Cote, J.: Semi-Lagrangian integration schemes for atmospheric models: A review. Mon. Weather Rev. 119, 2206\u20132223 (1991)","journal-title":"Mon. Weather Rev."},{"issue":"8","key":"9166_CR26","doi-asserted-by":"crossref","first-page":"2738","DOI":"10.1063\/1.868164","volume":"6","author":"J. Steinhoff","year":"1994","unstructured":"Steinhoff, J., Underhill, D.: Modification of the Euler equations for \u201cvorticity confinement\u201d: Application to the computation of interacting vortex rings. Phys. Fluids 6(8), 2738\u20132744 (1994)","journal-title":"Phys. Fluids"},{"key":"9166_CR27","doi-asserted-by":"crossref","first-page":"616","DOI":"10.1006\/jcph.1999.6205","volume":"151","author":"J. Strain","year":"1999","unstructured":"Strain, J.: Tree methods for moving interfaces. J. Comput. Phys. 151, 616\u2013648 (1999)","journal-title":"J. Comput. Phys."},{"key":"9166_CR28","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1006\/jcph.1994.1155","volume":"114","author":"M. Sussman","year":"1994","unstructured":"Sussman, M., Smereka, P., Osher, S.: A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114, 146\u2013159 (1994)","journal-title":"J. Comput. Phys."},{"issue":"9","key":"9166_CR29","doi-asserted-by":"crossref","first-page":"1241","DOI":"10.2514\/3.61457","volume":"14","author":"R.F. Warming","year":"1976","unstructured":"Warming, R.F., Beam, R.M.: Upwind second-order difference schemes and applications in aerodynamic flows. AIAA J. 14(9), 1241\u20131249 (1976)","journal-title":"AIAA J."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-007-9166-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-007-9166-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-007-9166-4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T04:41:29Z","timestamp":1559450489000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-007-9166-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,11,8]]},"references-count":29,"journal-issue":{"issue":"2-3","published-print":{"date-parts":[[2008,6]]}},"alternative-id":["9166"],"URL":"https:\/\/doi.org\/10.1007\/s10915-007-9166-4","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,11,8]]}}}