{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:33:43Z","timestamp":1787337223078,"version":"build-2736575974"},"reference-count":47,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2010,1]]},"abstract":"<jats:p>A hybrid of the front tracking (FT) and the level set (LS) methods is introduced, combining advantages and removing drawbacks of both methods. The kinematics of the interface is treated in a Lagrangian (FT) manner, by tracking markers placed at the interface. The markers are not connected\u2014instead, the interface topology is resolved in an Eulerian (LS) framework, by wrapping a signed distance function around Lagrangian markers each time the markers move. For accuracy and efficiency, we have developed a high-order \u201canchoring\u201d algorithm and an implicit PDE-based redistancing. We have demonstrated that the method is 3rd-order accurate in space, near the markers, and therefore 1st-order convergent in curvature; this is in contrast to traditional PDE-based reinitialization algorithms, which tend to slightly relocate the zero level set and can be shown to be nonconvergent in curvature. The implicit pseudo-time discretization of the redistancing equation is implemented within the Jacobian-free Newton\u2013Krylov (JFNK) framework combined with ILU(k) preconditioning. Due to the LS localization, the bandwidth of the Jacobian matrix is nearly constant, and the ILU preconditioning scales as $\\sim N\\log(\\sqrt{N})$ in two dimensions, which implies efficiency and good scalability of the overall algorithm. We have demonstrated that the steady-state solutions in pseudo-time can be achieved very efficiently, with $\\approx10$ iterations ($\\mathrm{CFL}\\approx10^4$), in contrast to the explicit redistancing which requires hundreds of iterations with $\\mathrm{CFL}\\leq1$.<\/jats:p>","DOI":"10.1137\/080727439","type":"journal-article","created":{"date-parts":[[2010,2,5]],"date-time":"2010-02-05T18:13:52Z","timestamp":1265393632000},"page":"320-348","source":"Crossref","is-referenced-by-count":10,"title":["Marker Redistancing\/Level Set Method for High-Fidelity Implicit Interface Tracking"],"prefix":"10.1137","volume":"32","author":[{"given":"Robert","family":"Nourgaliev","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Samet","family":"Kadioglu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vincent","family":"Mousseau","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2010,2,5]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2002.7059"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-005-4649-7"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2007.12.018"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(86)90101-4"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1993.1092"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/S106482750037617X"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(67)90037-X"},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2002.7166"},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1999.6236"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2005.08.004"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827595293600"},{"key":"R12","doi-asserted-by":"crossref","unstructured":"J. Helmsen, E.G. Puckett, P. Colella, and M. Dorr,\n                      Two new methods for simulating photolithography development in 3D\n                      , in Proceedings of the SPIE, Vol. 2726, 1996, pp. 253\u2013261.","DOI":"10.1117\/12.240959"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2005.04.013"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(81)90145-5"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1137\/S106482759732455X"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1996.0130"},{"key":"R17","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142996304796"},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2003.08.010"},{"key":"R19","doi-asserted-by":"crossref","unstructured":"V. Mihalef, D. Metaxas, and M. Sussman,\n                      Textured liquids based on the marker level set\n                      , in EUROGRAPHICS, D. Cohen-Orr and P. Slavik, eds., Vol. 26, The Eurographics Association and Blackwell Publishing, Oxford, UK, 2007.","DOI":"10.1111\/j.1467-8659.2007.01068.x"},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijmultiphaseflow.2004.03.010"},{"key":"R21","unstructured":"R.R. Nourgaliev, D. Knoll, V. Mousseau, and R. Berry,\n                      Direct numerical simulation of boiling multiphase flows: State-of-the-art, modeling, algorithmic and computer needs\n                      , in Joint International Topical Meeting on Mathematics & Computation and Supercomputing in Nuclear Applications (M&C + SNA 2007, Monterey, CA), American Nuclear Society, LaGrange Park, IL, 2007."},{"key":"R22","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2007.12.008"},{"key":"R23","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2006.10.031"},{"key":"R24","doi-asserted-by":"crossref","unstructured":"R.R. Nourgaliev, T.G. Theofanous, H. Park, V. Mousseau, and D. Knoll,\n                      Direct numerical simulation of interfacial flows: Implicit sharp-interface method (I-SIM)\n                      , in 46th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, 2008, AIAA-2008-1453.","DOI":"10.2514\/6.2008-1453"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijmultiphaseflow.2005.08.003"},{"key":"R26","doi-asserted-by":"crossref","unstructured":"S. Osher and R. Fedkiw,\n                      Level Set Methods and Dynamic Implicit Surfaces\n                      , Springer-Verlag, New York, Berlin, Heidelberg, 2003.","DOI":"10.1007\/b98879"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(88)90002-2"},{"key":"R28","unstructured":"H. Park, R.R. Nourgaliev, R.C. Martineau, and D.A. Knoll,\n                      Jacobian free-Newton Krylov discontinuous Galerkin method and physics-based preconditioner for nuclear reactor simulations\n                      , in International Conference on Reactor Physics, Nuclear Power: A Sustainable Resource, Interlaken, Switzerland, 2008."},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1999.6345"},{"key":"R30","unstructured":"W.H. Press, S.A. Teukilsky, W.T. Vetterling, and B.P. Flannery,\n                      Numerical Recipes in C\n                      , 2nd ed., Cambridge University Press, Cambridge, UK, 1999."},{"key":"R31","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2002.7190"},{"key":"R32","doi-asserted-by":"crossref","unstructured":"W.J. Rider and D.B. Kothe,\n                      Stretching and tearing interface tracking methods\n                      , in 12th AIAA CFD Conference, San Diego, 1995, AIAA-95-1717.","DOI":"10.2514\/6.1995-1717"},{"key":"R33","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1998.5906"},{"key":"R34","doi-asserted-by":"crossref","unstructured":"Y. Saad,\n                      Iterative Methods for Sparse Linear Systems\n                      , 2nd ed., SIAM, Philadelphia, 2003.","DOI":"10.1137\/1.9780898718003"},{"key":"R35","doi-asserted-by":"publisher","DOI":"10.1137\/0907058"},{"key":"R36","unstructured":"J.A. Sethian,\n                      Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Material Science\n                      , Cambridge University Press, Cambridge, UK, 1999."},{"key":"R37","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2002.7086"},{"key":"R38","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(88)90177-5"},{"key":"R39","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1998.6106"},{"key":"R40","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827596298245"},{"key":"R41","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2000.6537"},{"key":"R42","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1994.1155"},{"key":"R43","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2006.06.020"},{"key":"R44","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112007008853"},{"key":"R45","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2000.6635"},{"key":"R46","doi-asserted-by":"publisher","DOI":"10.1109\/9.412624"},{"key":"R47","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(92)90307-K"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/080727439","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:50:36Z","timestamp":1787334636000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/080727439"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1]]},"references-count":47,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2010,1]]}},"alternative-id":["10.1137\/080727439"],"URL":"https:\/\/doi.org\/10.1137\/080727439","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,1]]}}}