{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T14:58:57Z","timestamp":1767193137287,"version":"3.37.3"},"reference-count":68,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2023,10,11]],"date-time":"2023-10-11T00:00:00Z","timestamp":1696982400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,10,11]],"date-time":"2023-10-11T00:00:00Z","timestamp":1696982400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["GRK 2160\/1 - 270852890","GRK 2160\/1 - 270852890"],"award-info":[{"award-number":["GRK 2160\/1 - 270852890","GRK 2160\/1 - 270852890"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"name":"High Performance Computing Center Stuttgart","award":["hpcmphas\/44084","hpcmphas\/44084","EXC 2075 - 390740016"],"award-info":[{"award-number":["hpcmphas\/44084","hpcmphas\/44084","EXC 2075 - 390740016"]}]},{"DOI":"10.13039\/501100009534","name":"Universit\u00e4t Stuttgart","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100009534","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2023,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We present an hp-adaptive discretization for a sharp interface model with a level-set ghost-fluid method to simulate compressible multiphase flows. The scheme applies an efficient p-adaptive discontinuous Galerkin (DG) operator in regions of smooth flow. Shocks and the phase interface are captured by a Finite Volume (FV) scheme on a h-refined element-local sub-grid. The resulting hp-adaptive scheme thus combines both the high order accuracy of the DG method and the robustness of the FV scheme by using p-adaptation in smooth areas and h-refinement at discontinuities, respectively. For the level-set based interface tracking, a similar hybrid DG\/FV operator is employed. Both p-refinement and FV shock and interface capturing are performed at runtime and controlled by an indicator, which is based on the modal decay of the solution polynomials. In parallel simulations, the hp-adaptive discretization together with the costly interface tracking algorithm cause a significant imbalance in the processor workloads. To ensure parallel efficiency, we propose a dynamic load balancing scheme that determines the workload distribution by element-local wall time measurements and redistributes elements along a space filling curve. The parallelization strategy is supported by strong scaling tests using up to 8192 cores. The framework is applied to established benchmarks problems for inviscid, compressible multiphase flows. The results demonstrate that the hybrid adaptive discretization can efficiently and accurately handle complex multiphase flow problems involving pronounced interface deformations and merging interface contours.\n<\/jats:p>","DOI":"10.1007\/s10915-023-02363-7","type":"journal-article","created":{"date-parts":[[2023,10,11]],"date-time":"2023-10-11T12:02:49Z","timestamp":1697025769000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["An Efficient hp-Adaptive Strategy for a Level-Set Ghost-Fluid Method"],"prefix":"10.1007","volume":"97","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9371-2132","authenticated-orcid":false,"given":"Pascal","family":"Mossier","sequence":"first","affiliation":[]},{"given":"Daniel","family":"Appel","sequence":"additional","affiliation":[]},{"given":"Andrea D.","family":"Beck","sequence":"additional","affiliation":[]},{"given":"Claus-Dieter","family":"Munz","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,10,11]]},"reference":[{"issue":"1","key":"2363_CR1","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1146\/annurev.fluid.30.1.139","volume":"30","author":"DM Anderson","year":"1998","unstructured":"Anderson, D.M., McFadden, G.B., Wheeler, A.A.: Diffuse-interface methods in fluid mechanics. Annu. Rev. Fluid Mech. 30(1), 139\u2013165 (1998). https:\/\/doi.org\/10.1146\/annurev.fluid.30.1.139","journal-title":"Annu. Rev. Fluid Mech."},{"key":"2363_CR2","unstructured":"Appel, D., J\u00f6ns, S., Keim, J., M\u00fcller, C., Zeifang, J., Munz, C.D.: A narrow band-based dynamic load balancing scheme for the level-set ghost-fluid method. In: High Performance Computing in Science and Engineering\u201921 (in press) (2021)"},{"issue":"6","key":"2363_CR3","doi-asserted-by":"publisher","first-page":"861","DOI":"10.1016\/0301-9322(86)90033-9","volume":"12","author":"M Baer","year":"1986","unstructured":"Baer, M., Nunziato, J.: A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials. Int. J. Multiph. Flow 12(6), 861\u2013889 (1986). https:\/\/doi.org\/10.1016\/0301-9322(86)90033-9","journal-title":"Int. J. Multiph. Flow"},{"key":"2363_CR4","volume-title":"Performance Improvements for Large Scale Simulations Using the Discontinuous Galerkin Framework FLEXI","author":"M Blind","year":"2022","unstructured":"Blind, M., Kopper, P., Kempf, D., Kurz, M., Schwarz, A., Beck, A., Munz, C.D.: Performance Improvements for Large Scale Simulations Using the Discontinuous Galerkin Framework FLEXI. Springer, Cham (2022)"},{"key":"2363_CR5","unstructured":"Bolemann, T.: Towards industrialization of high-order discontinuous Galerkin methods for turbulent flows. Ph.D. thesis, University of Stuttgart (2018)"},{"issue":"255","key":"2363_CR6","doi-asserted-by":"publisher","first-page":"1103","DOI":"10.1090\/S0025-5718-06-01851-5","volume":"75","author":"M Castro","year":"2006","unstructured":"Castro, M., Gallardo, J., Par\u00e9s, C.: High order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products. Applications to shallow-water systems. Math. Comput. 75(255), 1103\u20131134 (2006)","journal-title":"Math. Comput."},{"key":"2363_CR7","doi-asserted-by":"publisher","first-page":"114","DOI":"10.1007\/s10915-007-9177-1","volume":"35","author":"A Ch\u00e9n\u00e9","year":"2008","unstructured":"Ch\u00e9n\u00e9, A., Min, C., ou, F.: Second-order accurate computation of curvatures in a level set framework using novel high-order reinitialization schemes. J. Sci. Comput. 35, 114\u2013131 (2008). https:\/\/doi.org\/10.1007\/s10915-007-9177-1","journal-title":"J. Sci. Comput."},{"issue":"1","key":"2363_CR8","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1007\/BF02434010","volume":"35","author":"JP Cocchi","year":"1996","unstructured":"Cocchi, J.P., Saurel, R., Loraud, J.C.: Treatment of interface problems with Godunov-type schemes. Shock Waves 35(1), 347\u2013357 (1996). https:\/\/doi.org\/10.1007\/BF02434010","journal-title":"Shock Waves"},{"key":"2363_CR9","doi-asserted-by":"publisher","unstructured":"Cockburn, B., Karniadakis, G., Shu, C.W.: Discontinuous Galerkin Methods: Theory, Computation and Application, vol.\u00a011. Springer, Berlin (2000). https:\/\/doi.org\/10.1007\/978-3-642-59721-3","DOI":"10.1007\/978-3-642-59721-3"},{"issue":"1","key":"2363_CR10","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1007\/bf01448839","volume":"100","author":"R Courant","year":"1928","unstructured":"Courant, R., Friedrichs, K., Lewy, H.: \u00dcber die partiellen Differenzengleichungen der mathematischen Physik. Math. Ann. 100(1), 32\u201374 (1928). https:\/\/doi.org\/10.1007\/bf01448839","journal-title":"Math. Ann."},{"key":"2363_CR11","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1016\/j.jcp.2015.01.021","volume":"285","author":"F Denner","year":"2015","unstructured":"Denner, F., van Wachem, B.G.: Numerical time-step restrictions as a result of capillary waves. J. Comput. Phys. 285, 24\u201340 (2015). https:\/\/doi.org\/10.1016\/j.jcp.2015.01.021","journal-title":"J. Comput. Phys."},{"issue":"1","key":"2363_CR12","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1177\/1094342010391989","volume":"25","author":"J Dongarra","year":"2011","unstructured":"Dongarra, J., Beckman, P., et al.: The international exascale software project roadmap. Int. J. High Perform. Comput. Appl. 25(1), 3\u201360 (2011). https:\/\/doi.org\/10.1177\/1094342010391989","journal-title":"Int. J. High Perform. Comput. Appl."},{"key":"2363_CR13","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1016\/j.jcp.2016.05.002","volume":"319","author":"M Dumbser","year":"2016","unstructured":"Dumbser, M., Loub\u00e8re, R.: A simple robust and accurate a posteriori sub-cell finite volume limiter for the discontinuous Galerkin method on unstructured meshes. J. Comput. Phys. 319, 163\u2013199 (2016). https:\/\/doi.org\/10.1016\/j.jcp.2016.05.002","journal-title":"J. Comput. Phys."},{"issue":"1","key":"2363_CR14","doi-asserted-by":"publisher","first-page":"204","DOI":"10.1016\/j.jcp.2007.04.004","volume":"226","author":"M Dumbser","year":"2007","unstructured":"Dumbser, M., K\u00e4ser, M., Titarev, V.A., Toro, E.F.: Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems. J. Comput. Phys. 226(1), 204\u2013243 (2007). https:\/\/doi.org\/10.1016\/j.jcp.2007.04.004","journal-title":"J. Comput. Phys."},{"key":"2363_CR15","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/j.jcp.2014.08.009","volume":"278","author":"M Dumbser","year":"2014","unstructured":"Dumbser, M., Zanotti, O., Loub\u00e8re, R., Diot, S.: A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws. J. Comput. Phys. 278, 47\u201375 (2014). https:\/\/doi.org\/10.1016\/j.jcp.2014.08.009","journal-title":"J. Comput. Phys."},{"issue":"6","key":"2363_CR16","doi-asserted-by":"publisher","first-page":"A2564","DOI":"10.1137\/17M1111036","volume":"39","author":"M Dumbser","year":"2017","unstructured":"Dumbser, M., Boscheri, W., Semplice, M., Russo, G.: Central weighted ENO schemes for hyperbolic conservation laws on fixed and moving unstructured meshes. SIAM J. Sci. Comput. 39(6), A2564\u2013A2591 (2017). https:\/\/doi.org\/10.1137\/17M1111036","journal-title":"SIAM J. Sci. Comput."},{"issue":"2","key":"2363_CR17","doi-asserted-by":"publisher","first-page":"294","DOI":"10.1137\/0725021","volume":"25","author":"B Einfeldt","year":"1988","unstructured":"Einfeldt, B.: On Godunov-type methods for gas dynamics. SIAM J. Numer. Anal. 25(2), 294\u2013318 (1988). https:\/\/doi.org\/10.1137\/0725021","journal-title":"SIAM J. Numer. Anal."},{"key":"2363_CR18","unstructured":"Fechter, S.: Compressible multi-phase simulation at extreme conditions using a discontinuous Galerkin scheme. Ph.D. thesis, University of Stuttgart (2015)"},{"key":"2363_CR19","doi-asserted-by":"publisher","first-page":"112","DOI":"10.1016\/j.compfluid.2013.01.024","volume":"75","author":"S Fechter","year":"2013","unstructured":"Fechter, S., Jaegle, F., Schleper, V.: Exact and approximate Riemann solvers at phase boundaries. Comput. Fluids 75, 112\u2013126 (2013). https:\/\/doi.org\/10.1016\/j.compfluid.2013.01.024","journal-title":"Comput. Fluids"},{"key":"2363_CR20","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1016\/j.jcp.2017.02.001","volume":"336","author":"S Fechter","year":"2017","unstructured":"Fechter, S., Munz, C.D., Rohde, C., Zeiler, C.: A sharp interface method for compressible liquid\u2013vapor flow with phase transition and surface tension. J. Comput. Phys. 336, 347\u2013374 (2017). https:\/\/doi.org\/10.1016\/j.jcp.2017.02.001","journal-title":"J. Comput. Phys."},{"key":"2363_CR21","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1016\/j.compfluid.2017.03.026","volume":"169","author":"S Fechter","year":"2018","unstructured":"Fechter, S., Munz, C.D., Rohde, C., Zeiler, C.: Approximate Riemann solver for compressible liquid vapor flow with phase transition and surface tension. Comput. Fluids 169, 169\u2013185 (2018). https:\/\/doi.org\/10.1016\/j.compfluid.2017.03.026","journal-title":"Comput. Fluids"},{"issue":"2","key":"2363_CR22","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1006\/jcph.1999.6236","volume":"152","author":"RP Fedkiw","year":"1999","unstructured":"Fedkiw, R.P., Aslam, T., Merriman, B., Osher, S.: A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method). J. Comput. Phys. 152(2), 457\u2013492 (1999). https:\/\/doi.org\/10.1006\/jcph.1999.6236","journal-title":"J. Comput. Phys."},{"key":"2363_CR23","doi-asserted-by":"publisher","DOI":"10.1007\/s00193-019-00896-1","author":"F F\u00f6ll","year":"2019","unstructured":"F\u00f6ll, F., Hitz, T., M\u00fcller, C., Munz, C.D., Dumbser, M.: On the use of tabulated equations of state for multi-phase simulations in the homogeneous equilibrium limit. Shock Waves (2019). https:\/\/doi.org\/10.1007\/s00193-019-00896-1","journal-title":"Shock Waves"},{"key":"2363_CR24","doi-asserted-by":"publisher","first-page":"825","DOI":"10.1017\/jfm.2017.403","volume":"825","author":"X Gaoming","year":"2017","unstructured":"Gaoming, X., Wang, B.: Numerical study of a planar shock interacting with a cylindrical water column embedded with an air cavity. J. Fluid Mech. 825, 825\u2013852 (2017). https:\/\/doi.org\/10.1017\/jfm.2017.403","journal-title":"J. Fluid Mech."},{"key":"2363_CR25","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1016\/j.jcp.2017.10.006","volume":"353","author":"F Gibou","year":"2018","unstructured":"Gibou, F., Fedkiw, R., Osher, S.: A review of level-set methods and some recent applications. J. Comput. Phys. 353, 82\u2013109 (2018). https:\/\/doi.org\/10.1016\/j.jcp.2017.10.006","journal-title":"J. Comput. Phys."},{"key":"2363_CR26","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1007\/s00193-018-0809-1","volume":"29","author":"E Goncalves","year":"2019","unstructured":"Goncalves, E., Hoarau, Y., Zeidan, D.: Simulation of shock-induced bubble collapse using a four-equation model. Shock Waves 29, 221\u2013234 (2019). https:\/\/doi.org\/10.1007\/s00193-018-0809-1","journal-title":"Shock Waves"},{"issue":"25\u201328","key":"2363_CR27","doi-asserted-by":"publisher","first-page":"3406","DOI":"10.1016\/j.cma.2005.06.020","volume":"195","author":"J Grooss","year":"2006","unstructured":"Grooss, J., Hesthaven, J.: A level set discontinuous Galerkin method for free surface flows. Comput. Methods Appl. Mech. Eng. 195(25\u201328), 3406\u20133429 (2006). https:\/\/doi.org\/10.1016\/j.cma.2005.06.020","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"2363_CR28","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1016\/j.jcp.2013.12.061","volume":"262","author":"L Han","year":"2014","unstructured":"Han, L., Hu, X., Adams, N.: Adaptive multi-resolution method for compressible multi-phase flows with sharp interface model and pyramid data structure. J. Comput. Phys. 262, 131\u2013152 (2014). https:\/\/doi.org\/10.1016\/j.jcp.2013.12.061","journal-title":"J. Comput. Phys."},{"key":"2363_CR29","first-page":"1","volume-title":"\u00dcber die stetige Abbildung einer Linie auf ein Fl\u00e4chenst\u00fcck\"","author":"D Hilbert","year":"1935","unstructured":"Hilbert, D.: \u00dcber die stetige Abbildung einer Linie auf ein Fl\u00e4chenst\u00fcck\", pp. 1\u20132. Springer, Berlin (1935)"},{"key":"2363_CR30","doi-asserted-by":"crossref","unstructured":"Hindenlang, F.: Mesh curving techniques for high order parallel simulations on unstructured meshes. Ph.D. thesis, Universit\u00e4t Stuttgart (2014)","DOI":"10.1007\/978-3-319-12886-3_8"},{"issue":"2","key":"2363_CR31","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1016\/j.jcp.2006.04.001","volume":"219","author":"X Hu","year":"2006","unstructured":"Hu, X., Khoo, B., Adams, N., Huang, F.: A conservative interface method for compressible flows. J. Comput. Phys. 219(2), 553\u2013578 (2006). https:\/\/doi.org\/10.1016\/j.jcp.2006.04.001","journal-title":"J. Comput. Phys."},{"key":"2363_CR32","doi-asserted-by":"publisher","first-page":"1614","DOI":"10.1002\/fld.2654","volume":"69","author":"A Huerta","year":"2012","unstructured":"Huerta, A., Casoni, E., Peraire, J.: A simple shock-capturing technique for high-order discontinuous Galerkin methods. Int. J. Numer. Methods Fluids 69, 1614\u20131632 (2012). https:\/\/doi.org\/10.1002\/fld.2654","journal-title":"Int. J. Numer. Methods Fluids"},{"issue":"6","key":"2363_CR33","doi-asserted-by":"publisher","first-page":"2126","DOI":"10.1137\/s106482759732455x","volume":"21","author":"GS Jiang","year":"2000","unstructured":"Jiang, G.S., Peng, D.: Weighted ENO schemes for Hamilton\u2013Jacobi equations. SIAM J. Sci. Comput. 21(6), 2126\u20132143 (2000). https:\/\/doi.org\/10.1137\/s106482759732455x","journal-title":"SIAM J. Sci. Comput."},{"key":"2363_CR34","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2022.127624","volume":"440","author":"S J\u00f6ns","year":"2023","unstructured":"J\u00f6ns, S., Munz, C.D.: Riemann solvers for phase transition in a compressible sharp-interface method. Appl. Math. Comput. 440, 127624 (2023). https:\/\/doi.org\/10.1016\/j.amc.2022.127624","journal-title":"Appl. Math. Comput."},{"key":"2363_CR35","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1007\/978-3-030-72850-2_7","volume-title":"Recent Advances in Numerical Methods for Hyperbolic PDE Systems","author":"S J\u00f6ns","year":"2021","unstructured":"J\u00f6ns, S., M\u00fcller, C., Zeifang, J., Munz, C.D.: Recent advances and complex applications of the compressible ghost-fluid method. In: Mu\u00f1oz-Ruiz, M.L., Par\u00e9s, C., Russo, G. (eds.) Recent Advances in Numerical Methods for Hyperbolic PDE Systems, pp. 155\u2013176. Springer, Cham (2021)"},{"key":"2363_CR36","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijmultiphaseflow.2020.103409","volume":"132","author":"J Kaiser","year":"2020","unstructured":"Kaiser, J., Winter, J., Adami, S., Adams, N.: Investigation of interface deformation dynamics during high-Weber number cylindrical droplet breakup. Int. J. Multiph. Flow 132, 103409 (2020). https:\/\/doi.org\/10.1016\/j.ijmultiphaseflow.2020.103409","journal-title":"Int. J. Multiph. Flow"},{"issue":"1","key":"2363_CR37","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1016\/S0168-9274(02)00138-1","volume":"44","author":"CA Kennedy","year":"2003","unstructured":"Kennedy, C.A., Carpenter, M.H.: Additive Runge\u2013Kutta schemes for convection-diffusion-reaction equations. Appl. Numer. Math. 44(1), 139\u2013181 (2003). https:\/\/doi.org\/10.1016\/S0168-9274(02)00138-1","journal-title":"Appl. Numer. Math."},{"key":"2363_CR38","doi-asserted-by":"crossref","unstructured":"Kopriva, D.A.: Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers. Springer Publishing Company, Incorporated (2009)","DOI":"10.1007\/978-90-481-2261-5"},{"key":"2363_CR39","doi-asserted-by":"publisher","first-page":"186","DOI":"10.1016\/j.camwa.2020.05.004","volume":"81","author":"N Krais","year":"2020","unstructured":"Krais, N., Beck, A., Bolemann, T., Frank, H., Flad, D., Gassner, G., Hindenlang, F., Hoffmann, M., Kuhn, T., Sonntag, M., Munz, C.D.: Flexi: A high order discontinuous Galerkin framework for hyperbolic-parabolic conservation laws. Comput. Math. Appl. 81, 186\u2013219 (2020). https:\/\/doi.org\/10.1016\/j.camwa.2020.05.004","journal-title":"Comput. Math. Appl."},{"key":"2363_CR40","doi-asserted-by":"publisher","first-page":"575","DOI":"10.1016\/j.future.2017.04.042","volume":"82","author":"M Lieber","year":"2018","unstructured":"Lieber, M., Nagel, W.E.: Highly scalable SFC-based dynamic load balancing and its application to atmospheric modeling. Futur. Gener. Comput. Syst. 82, 575\u2013590 (2018). https:\/\/doi.org\/10.1016\/j.future.2017.04.042","journal-title":"Futur. Gener. Comput. Syst."},{"key":"2363_CR41","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1007\/978-3-663-13975-1_34","volume-title":"Proceedings of the Eighth GAMM-Conference on Numerical Methods in Fluid Mechanics","author":"C Mavriplis","year":"1990","unstructured":"Mavriplis, C.: A posteriori error estimators for adaptive spectral element techniques. In: Wesseling, P. (ed.) Proceedings of the Eighth GAMM-Conference on Numerical Methods in Fluid Mechanics, pp. 333\u2013342. Vieweg+Teubner Verlag, Wiesbaden (1990)"},{"key":"2363_CR42","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1007\/s00193-014-0546-z","volume":"25","author":"JC Meng","year":"2015","unstructured":"Meng, J.C., Colonius, T.: Numerical simulations of the early stages of high-speed droplet breakup. Shock Waves 25, 399\u2013414 (2015)","journal-title":"Shock Waves"},{"issue":"06","key":"2363_CR43","doi-asserted-by":"publisher","first-page":"1089","DOI":"10.1051\/m2an:2007048","volume":"41","author":"C Merkle","year":"2007","unstructured":"Merkle, C., Rohde, C.: The sharp-interface approach for fluids with phase change: Riemann problems and ghost fluid techniques. ESAIM Math. Model. Numer. Anal. 41(06), 1089\u20131123 (2007). https:\/\/doi.org\/10.1051\/m2an:2007048","journal-title":"ESAIM Math. Model. Numer. Anal."},{"key":"2363_CR44","unstructured":"Message Passing Interface Forum: MPI: A Message-Passing Interface Standard (2021). https:\/\/www.mpi-forum.org\/"},{"issue":"3","key":"2363_CR45","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1016\/j.ijthermalsci.2003.09.002","volume":"43","author":"OL M\u00e9tayer","year":"2004","unstructured":"M\u00e9tayer, O.L., Massoni, J., Saurel, R.: \u00c9laboration des lois d\u2019\u00e9tat d\u2019un liquide et de sa vapeur pour les mod\u00e8les d\u2019\u00e9coulements diphasiques. Int. J. Therm. Sci. 43(3), 265\u2013276 (2004). https:\/\/doi.org\/10.1016\/j.ijthermalsci.2003.09.002","journal-title":"Int. J. Therm. Sci."},{"issue":"1","key":"2363_CR46","doi-asserted-by":"publisher","first-page":"1573","DOI":"10.1007\/s10915-022-01770-6","volume":"91","author":"P Mossier","year":"2022","unstructured":"Mossier, P., Munz, C.D., Beck, A.: A p-adaptive discontinuous Galerkin method with hp-shock capturing. J. Sci. Comput. 91(1), 1573\u20137691 (2022). https:\/\/doi.org\/10.1007\/s10915-022-01770-6","journal-title":"J. Sci. Comput."},{"key":"2363_CR47","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1007\/978-3-030-33338-6_2","volume-title":"Droplet Interactions and Spray Processes","author":"C M\u00fcller","year":"2020","unstructured":"M\u00fcller, C., Hitz, T., J\u00f6ns, S., Zeifang, J., Chiocchetti, S., Munz, C.D.: Improvement of the level-set ghost-fluid method for the compressible Euler equations. In: Lamanna, G., Tonini, S., Cossali, G.E., Weigand, B. (eds.) Droplet Interactions and Spray Processes, pp. 17\u201329. Springer, Cham (2020)"},{"key":"2363_CR48","doi-asserted-by":"publisher","first-page":"232","DOI":"10.1063\/1.1699639","volume":"21","author":"JV Neumann","year":"1950","unstructured":"Neumann, J.V., Richtmyer, R.D.: A method for the numerical calculation of hydrodynamic shocks. J. Appl. Phys. 21, 232\u2013237 (1950)","journal-title":"J. Appl. Phys."},{"issue":"2","key":"2363_CR49","doi-asserted-by":"publisher","first-page":"500","DOI":"10.1016\/j.jcp.2005.08.028","volume":"213","author":"RR Nourgaliev","year":"2006","unstructured":"Nourgaliev, R.R., Dinh, T.N., Theofanous, T.G.: Adaptive characteristics-based matching for compressible multifluid dynamics. J. Comput. Phys. 213(2), 500\u2013529 (2006). https:\/\/doi.org\/10.1016\/j.jcp.2005.08.028","journal-title":"J. Comput. Phys."},{"issue":"2","key":"2363_CR50","doi-asserted-by":"publisher","first-page":"410","DOI":"10.1006\/jcph.1999.6345","volume":"155","author":"D Peng","year":"1998","unstructured":"Peng, D., Merriman, B., Osher, S., Zhao, H., Kang, M.: A PDE-based fast local level set method 1. J. Comput. Phys. 155(2), 410\u2013438 (1998)","journal-title":"J. Comput. Phys."},{"key":"2363_CR51","doi-asserted-by":"publisher","unstructured":"Persson, P.O.: Shock capturing for high-order discontinuous Galerkin simulation of transient flow problems. In: 21st AIAA Computational Fluid Dynamics Conference. American Institute of Aeronautics and Astronautics (2013). https:\/\/doi.org\/10.2514\/6.2013-3061","DOI":"10.2514\/6.2013-3061"},{"key":"2363_CR52","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2021.110765","volume":"449","author":"PO Persson","year":"2022","unstructured":"Persson, P.O., Stamm, B.: A discontinuous Galerkin method for shock capturing using a mixed high-order and sub-grid low-order approximation space. J. Comput. Phys. 449, 110765 (2022). https:\/\/doi.org\/10.1016\/j.jcp.2021.110765","journal-title":"J. Comput. Phys."},{"issue":"8","key":"2363_CR53","doi-asserted-by":"publisher","first-page":"974","DOI":"10.1016\/j.jpdc.2004.05.003","volume":"64","author":"A P\u0131nar","year":"2004","unstructured":"P\u0131nar, A., Aykanat, C.: Fast optimal load balancing algorithms for 1d partitioning. J. Parallel Distrib. Comput. 64(8), 974\u2013996 (2004)","journal-title":"J. Parallel Distrib. Comput."},{"issue":"4","key":"2363_CR54","doi-asserted-by":"publisher","first-page":"1591","DOI":"10.1073\/pnas.93.4.1591","volume":"93","author":"JA Sethian","year":"1996","unstructured":"Sethian, J.A.: A fast marching level set method for monotonically advancing fronts. Proc. Natl. Acad. Sci. 93(4), 1591\u20131595 (1996). https:\/\/doi.org\/10.1073\/pnas.93.4.1591","journal-title":"Proc. Natl. Acad. Sci."},{"key":"2363_CR55","doi-asserted-by":"publisher","unstructured":"Sonntag, M., Munz, C.D.: Shock capturing for discontinuous Galerkin methods using finite volume subcells. In: Finite Volumes for Complex Applications VII, vol. 78, pp. 945\u2013953 (2014). https:\/\/doi.org\/10.1007\/978-3-319-05591-6_96","DOI":"10.1007\/978-3-319-05591-6_96"},{"key":"2363_CR56","doi-asserted-by":"publisher","first-page":"1262","DOI":"10.1007\/s10915-016-0287-5","volume":"70","author":"M Sonntag","year":"2017","unstructured":"Sonntag, M., Munz, C.D.: Efficient parallelization of a shock capturing for discontinuous Galerkin methods using finite volume sub-cells. J. Sci. Comput. 70, 1262\u20131289 (2017). https:\/\/doi.org\/10.1007\/s10915-016-0287-5","journal-title":"J. Sci. Comput."},{"key":"2363_CR57","doi-asserted-by":"publisher","DOI":"10.1063\/1.4948274","volume":"28","author":"S Sundarapandian","year":"2016","unstructured":"Sundarapandian, S., Liverts, M., Tillmark, N., Apazidis, N.: Plane shock wave interaction with a cylindrical water column. Phys. Fluids 28, 056102 (2016). https:\/\/doi.org\/10.1063\/1.4948274","journal-title":"Phys. Fluids"},{"issue":"1","key":"2363_CR58","doi-asserted-by":"publisher","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(1), 146\u2013159 (1994). https:\/\/doi.org\/10.1006\/jcph.1994.1155","journal-title":"J. Comput. Phys."},{"issue":"4","key":"2363_CR59","doi-asserted-by":"publisher","first-page":"516","DOI":"10.1115\/1.1777234","volume":"126","author":"TG Theofanous","year":"2004","unstructured":"Theofanous, T.G., Li, G.J., Dinh, T.N.: Aerobreakup in rarefied supersonic gas flows. J. Fluids Eng. 126(4), 516\u2013527 (2004). https:\/\/doi.org\/10.1115\/1.1777234","journal-title":"J. Fluids Eng."},{"issue":"1","key":"2363_CR60","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1007\/bf01414629","volume":"4","author":"EF Toro","year":"1994","unstructured":"Toro, E.F., Spruce, M., Speares, W.: Restoration of the contact surface in the HLL-Riemann solver. Shock Waves 4(1), 25\u201334 (1994). https:\/\/doi.org\/10.1007\/bf01414629","journal-title":"Shock Waves"},{"issue":"2","key":"2363_CR61","doi-asserted-by":"publisher","first-page":"673","DOI":"10.1137\/s0036142901396533","volume":"41","author":"YHR Tsai","year":"2003","unstructured":"Tsai, Y.H.R., Cheng, L.T., Osher, S., Zhao, H.K.: Fast sweeping algorithms for a class of Hamilton\u2013Jacobi equations. SIAM J. Numer. Anal. 41(2), 673\u2013694 (2003). https:\/\/doi.org\/10.1137\/s0036142901396533","journal-title":"SIAM J. Numer. Anal."},{"issue":"4","key":"2363_CR62","doi-asserted-by":"publisher","first-page":"1585","DOI":"10.1016\/j.jcp.2010.11.023","volume":"230","author":"P Tsoutsanis","year":"2011","unstructured":"Tsoutsanis, P., Titarev, V., Drikakis, D.: WENO schemes on arbitrary mixed-element unstructured meshes in three space dimensions. J. Comput. Phys. 230(4), 1585\u20131601 (2011). https:\/\/doi.org\/10.1016\/j.jcp.2010.11.023","journal-title":"J. Comput. Phys."},{"key":"2363_CR63","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-021-01673-y","author":"P Tsoutsanis","year":"2021","unstructured":"Tsoutsanis, P., Adebayo, E., Merino, A., Arjona, A., Skote, M.: CWENO finite-volume interface capturing schemes for multicomponent flows using unstructured meshes. J. Sci. Comput. (2021). https:\/\/doi.org\/10.1007\/s10915-021-01673-y","journal-title":"J. Sci. Comput."},{"issue":"1","key":"2363_CR64","doi-asserted-by":"publisher","first-page":"48","DOI":"10.1016\/0021-9991(80)90033-9","volume":"35","author":"J Williamson","year":"1980","unstructured":"Williamson, J.: Low-storage Runge\u2013Kutta schemes. J. Comput. Phys. 35(1), 48\u201356 (1980). https:\/\/doi.org\/10.1016\/0021-9991(80)90033-9","journal-title":"J. Comput. Phys."},{"key":"2363_CR65","unstructured":"Winter, J.M., Kaiser, J.W., Adami, S., Adams, N.A.: Numerical investigation of 3d drop-breakup mechanisms using a sharp interface level-set method. In: 11th International Symposium on Turbulence and Shear Flow Phenomena (TSFP 2019) (2019)"},{"key":"2363_CR66","doi-asserted-by":"publisher","DOI":"10.1002\/fld.4849","author":"L Xu","year":"2020","unstructured":"Xu, L., Liu, T.: Modified ghost fluid method for three-dimensional compressible multi-material flows with interfaces exhibiting large curvature and topological change. Int. J. Numer. Methods Fluids (2020). https:\/\/doi.org\/10.1002\/fld.4849","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"2363_CR67","unstructured":"Zeifang, J.: A discontinuous Galerkin method for droplet dynamics in weakly compressible flows. Ph.D. thesis, University of Stuttgart (2020)"},{"key":"2363_CR68","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2021.110475","volume":"441","author":"J Zeifang","year":"2021","unstructured":"Zeifang, J., Beck, A.: A data-driven high order sub-cell artificial viscosity for the discontinuous Galerkin spectral element method. J. Comput. Phys. 441, 110475 (2021). https:\/\/doi.org\/10.1016\/j.jcp.2021.110475","journal-title":"J. Comput. Phys."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-023-02363-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-023-02363-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-023-02363-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,21]],"date-time":"2023-10-21T11:10:56Z","timestamp":1697886656000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-023-02363-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,11]]},"references-count":68,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,11]]}},"alternative-id":["2363"],"URL":"https:\/\/doi.org\/10.1007\/s10915-023-02363-7","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"type":"print","value":"0885-7474"},{"type":"electronic","value":"1573-7691"}],"subject":[],"published":{"date-parts":[[2023,10,11]]},"assertion":[{"value":"13 December 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 July 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 September 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 October 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The corresponding author states on behalf of all authors, that there is no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"50"}}