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Adaptive mesh refinement algorithm based on dual trees for cells and faces for multiphase compressible flows. (English) Zbl 1452.76132
Summary: A novel adaptive mesh refinement method is proposed. The novelty of the method lies in using a dual data structure with two trees: A classical one for the computational cells and an extra one dedicated to computational cell faces. This new dual structure simplifies the algorithm, making the method easy to implement. It results in an efficient adaptive mesh refinement method that preserves an acceptable memory cost. This adaptive mesh refinement method is then applied to compressible multiphase flows in the framework of diffuse-interface methods. Efficiency of the method is demonstrated thanks to computational results for different applications: Transport, shock tube, surface-tension flow, cavitation and water-droplet atomization, in one and multi-dimensions. The test cases are performed with the open-source code ECOGEN and with quantitative comparisons regarding non-adaptive mesh refinement methods to analyze benefits. A discussion specific to parallel computing is also presented.
MSC:
76M12 Finite volume methods applied to problems in fluid mechanics
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
76T10 Liquid-gas two-phase flows, bubbly flows
65Y05 Parallel numerical computation
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
76N15 Gas dynamics, general
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[1] Aftosmis, M.; Melton, J.; Berger, M. J., Adaptation and surface modeling for Cartesian mesh methods, (AIAA Paper, 12th Computational Fluid Dynamics Conference (1995)), 1725
[2] Anderson, M.; Hirschmann, E. W.; Liebling, S. L.; Neilsen, D., Relativistic MHD with adaptive mesh refinement, Class. Quantum Gravity, 23, 22, 6503 (2006) · Zbl 1133.83343
[3] Berger, M. J.; Colella, P., Local adaptive mesh refinement for shock hydrodynamics, J. Comput. Phys., 82, 1, 64-84 (1989) · Zbl 0665.76070
[4] Berger, M. J.; Oliger, J., Adaptive mesh refinement for hyperbolic partial differential equations, J. Comput. Phys., 53, 3, 484-512 (1984) · Zbl 0536.65071
[5] Burstedde, C.; Calhoun, D.; Mandli, K.; Terrel, A. R., ForestClaw: hybrid forest-of-octrees AMR for hyperbolic conservation laws, (Parallel Computing: Accelerating Computational Science and Engineering, vol. 25 (2014)), 253-262
[6] Burstedde, C.; Wilcox, L. C.; Ghattas, O., p4est: scalable algorithms for parallel adaptive mesh refinement on forests of octrees, SIAM J. Sci. Comput., 33, 3, 1103-1133 (2011) · Zbl 1230.65106
[7] Chen, X.; Yang, V., Thickness-based adaptive mesh refinement methods for multi-phase flow simulations with thin regions, J. Comput. Phys., 269, 22-39 (2014) · Zbl 1349.76594
[8] Coirier, W. J., An Adaptively-Refined, Cartesian, Cell-Based Scheme for the Euler and Navier-Stokes Equations (1994), University of Michigan, Ph.D. thesis
[9] Colella, P.; Graves, D. T.; Ligocki, T. J.; Martin, D. F.; Modiano, D.; Serafini, D. B.; Van Straalen, B., Chombo software package for AMR applications design document (2009), (September 2008)
[10] Dumbser, M.; Zanotti, O.; Hidalgo, A.; Balsara, D. S., ADER-WENO finite volume schemes with space-time adaptive mesh refinement, J. Comput. Phys., 248, 257-286 (2013) · Zbl 1349.76325
[11] Favrie, N.; Gavrilyuk, S. L., Diffuse interface model for compressible fluid – compressible elastic – plastic solid interaction, J. Comput. Phys., 231, 7, 2695-2723 (2012) · Zbl 1430.74036
[12] Favrie, N.; Gavrilyuk, S. L., Dynamic compaction of granular materials, Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci., 469, 2160, Article 20130214 pp. (2013) · Zbl 1371.76153
[13] Favrie, N.; Gavrilyuk, S. L.; Ndanou, S., A thermodynamically compatible splitting procedure in hyperelasticity, J. Comput. Phys., 270, 300-324 (2014) · Zbl 1349.74344
[14] Fryxell, B.; Olson, K.; Ricker, P.; Timmes, F. X.; Zingale, M.; Lamb, D. Q.; MacNeice, P.; Rosner, R.; Truran, J. W.; Tufo, H., FLASH: an adaptive mesh hydrodynamics code for modeling astrophysical thermonuclear flashes, Astrophys. J. Suppl. Ser., 131, 1, 273 (2000)
[15] Han, E.; Hantke, M.; Müller, S., Efficient and robust relaxation procedures for multi-component mixtures including phase transition, J. Comput. Phys., 338, 217-239 (2017)
[16] Hank, S.; Favrie, N.; Massoni, J., Modeling hyperelasticity in non-equilibrium multiphase flows, J. Comput. Phys., 330, 65-91 (2017) · Zbl 1378.74022
[17] Harten, A.; Lax, P. D.; van Leer, B., On upstream differencing and Godunov type schemes for hyperbolic conservation laws, SIAM Rev., 25, 33-61 (1983) · Zbl 0565.65051
[18] Hornung, R. D.; Kohn, S. R., Managing application complexity in the SAMRAI object-oriented framework, Concurr. Comput., 14, 5, 347-368 (2002) · Zbl 1008.68527
[19] Hosangadi, A.; Ahuja, V.; Arunajatesan, S., Simulations of cavitating flows using hybrid unstructured meshes, J. Fluids Eng., 123, 331-340 (2001)
[20] Khokhlov, A. M., Fully threaded tree algorithms for adaptive refinement fluid dynamics simulations, J. Comput. Phys., 143, 2, 519-543 (1998) · Zbl 0934.76057
[21] Le Metayer, O.; Massoni, J.; Saurel, R., Elaborating equations of state of a liquid and its vapor for two-phase flow models, Int. J. Therm. Sci., 43, 265-276 (2004)
[22] Le Métayer, O.; Massoni, J.; Saurel, R., Dynamic relaxation processes in compressible multiphase flows. Application to evaporation phenomena, (ESAIM Proc., vol. 40 (2013), EDP Sciences), 103-123 · Zbl 1330.76133
[23] MacNeice, P.; Olson, K. M.; Mobarry, C.; De Fainchtein, R.; Packer, C., PARAMESH: a parallel adaptive mesh refinement community toolkit, Comput. Phys. Commun., 126, 3, 330-354 (2000) · Zbl 0953.65088
[24] Massoni, J.; Saurel, R.; Nkonga, B.; Abgrall, R., Proposition de methodes et modeles Euleriens pour les problemes a interfaces entre fluides compressibles en presence de transfert de chaleur, Int. J. Heat Mass Transf., 45, 1287-1307 (2002) · Zbl 1121.76378
[25] Melton, J.; Berger, M. J.; Aftosmis, M.; Wong, M., 3D applications of a Cartesian grid Euler method, (AIAA Paper, 33rd Aerospace Sciences Meeting and Exhibit (1995)), 853
[26] Meng, J. C., Numerical Simulations of Droplet Aerobreakup (2016), California Institute of Technology, PhD thesis
[27] Murrone, A.; Guillard, H., Behavior of upwind scheme in the low Mach number limit: III. Preconditioned dissipation for a five equation two phase model, Comput. Fluids, 37, 10, 1209-1224 (2008) · Zbl 1237.76089
[28] Pau, G. S.H.; Bell, J. B.; Almgren, A. S.; Fagnan, K. M.; Lijewski, M. J., An adaptive mesh refinement algorithm for compressible two-phase flow in porous media, Comput. Geosci., 16, 3, 577-592 (2012)
[29] Petitpas, F.; Massoni, J.; Saurel, R.; Lapebie, E.; Munier, L., Diffuse interface models for high speed cavitating underwater systems, Int. J. Multiphase Flows, 35, 8, 747-759 (2009)
[30] Petitpas, F.; Saurel, R.; Franquet, E.; Chinnayya, A., Modelling detonation waves in condensed energetic materials: multiphase CJ conditions and multidimensional computations, Shock Waves, 19, 5, 377-401 (2009) · Zbl 1255.76063
[31] Popinet, S., Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries, J. Comput. Phys., 190, 2, 572-600 (2003) · Zbl 1076.76002
[32] Popinet, S.; Rickard, G., A tree-based solver for adaptive ocean modelling, Ocean Model., 16, 3, 224-249 (2007)
[33] Saurel, R.; Gavrilyuk, S. L.; Renaud, F., A multiphase model with internal degrees of freedom: application to shock-bubble interaction, J. Fluid Mech., 495, 283-321 (2003) · Zbl 1080.76062
[34] Saurel, R.; Petitpas, F., Introduction to diffuse interfaces and transformation fronts modelling in compressible media, (ESAIM Proc., vol. 40 (2013), EDP Sciences), 124-143 · Zbl 1330.76117
[35] Saurel, R.; Petitpas, F.; Abgrall, R., Modelling phase transition in metastable liquids: application to cavitating and flashing flows, J. Fluid Mech., 607, 313-350 (2008) · Zbl 1147.76060
[36] Saurel, R.; Petitpas, F.; Berry, R. A., Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures, J. Comput. Phys., 228, 5, 1678-1712 (2009) · Zbl 1409.76105
[37] Schmidmayer, K.; Marty, A.; Petitpas, F.; Daniel, E., ECOGEN, an open-source tool dedicated to multiphase compressible multiphysics flows, (53rd 3AF International Conference on Applied Aerodynamics (2018))
[38] Schmidmayer, K.; Petitpas, F.; Daniel, E.; Favrie, N.; Gavrilyuk, S. L., A model and numerical method for compressible flows with capillary effects, J. Comput. Phys., 334, 468-496 (2017) · Zbl 1375.76198
[39] Teyssier, R., Cosmological hydrodynamics with adaptive mesh refinement - a new high resolution code called RAMSES, Astron. Astrophys., 385, 1, 337-364 (2002)
[40] Tiwari, A.; Freund, J. B.; Pantano, C., A diffuse interface model with immiscibility preservation, J. Comput. Phys., 252, 290-309 (2013) · Zbl 1349.76395
[41] Young, D. P.; Melvin, R. G.; Bieterman, M. B.; Johnson, F. T.; Samant, S. S.; Bussoletti, J. E., A locally refined rectangular grid finite element method: application to computational fluid dynamics and computational physics, J. Comput. Phys., 92, 1, 1-66 (1991) · Zbl 0709.76078
[42] Ziegler, U., The NIRVANA code: parallel computational MHD with adaptive mesh refinement, Comput. Phys. Commun., 179, 4, 227-244 (2008) · Zbl 1197.76102
[43] Zingale, M.; Almgren, A. S.; Barrios Sazo, M. G.; Beckner, V. E.; Bell, J. B.; Friesen, B.; Jacobs, A. M.; Katz, M. P.; Malone, C. M.; Nonaka, A. J.; Willcox, D. E.; Zhang, A., Meeting the challenges of modeling astrophysical thermonuclear explosions: Castro, Maestro, and the AMReX astrophysics suite, J. Phys. Conf. Ser., 1031, Article 012024 pp. (2018)
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