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Adaptive multi-resolution method for compressible multi-phase flows with sharp interface model and pyramid data structure. (English) Zbl 1349.76338
Summary: In this work, we present a block-based multi-resolution method coupled with a sharp interface model (MR-SIM) for the high-resolution simulation of multi-phase flows, where data structure and adaptive multi-resolution approach are tailored to achieve high computational efficiency. The method updates the dynamic topological data structure according to two separate procedures: (i) tracking of the interface position, and (ii) MR analysis on each individual phase. High efficiency is achieved by employing a storage-and-operation-splitting pyramid data structure, in which any two adjacent blocks partially overlap while the overlapping parts share the same data in memory. The non-overlapping data are distributed into fine-grained data packages and stored within a memory pool. The proposed narrow-band technique for the level-set-based interface method also increases the computational and memory efficiency greatly by restricting all interface-relevant data and operations to a neighborhood of the interface. A broad set of test simulations is carried out to demonstrate the potential and performance of the MR-SIM approach.

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
65Y05 Parallel numerical computation
76Nxx Compressible fluids and gas dynamics, general
76Txx Multiphase and multicomponent flows
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References:
[1] Jiang, G. S.; Shu, C. W., Efficient implementation of weighted ENO schemes, J. Comput. Phys., 126, 202-228, (1996) · Zbl 0877.65065
[2] Hu, X. Y.; Wang, Q.; Adams, N. A., An adaptive central-upwind weighted essentially non-oscillatory scheme, J. Comput. Phys., 229, 8952-8965, (2010) · Zbl 1204.65103
[3] Berger, M. J.; Oliger, J., Adaptive mesh refinement for hyperbolic partial differential equations, J. Comput. Phys., 53, 3, 484-512, (1984) · Zbl 0536.65071
[4] Berger, M. J.; Colella, P., Local adaptive mesh refinement for shock hydrodynamics, J. Comput. Phys., 82, 64-84, (1989) · Zbl 0665.76070
[5] Miniati, F.; Colella, P., Block structured adaptive mesh and time refinement for hybrid, hyperbolic + N-body systems, J. Comput. Phys., 227, 400-430, (2007) · Zbl 1128.85007
[6] MacNeice, P.; Olson, K. M.; Mobarry, C.; de Fainchtein, R.; Packer, C., PARAMESH: A parallel adaptive mesh refinement community toolkit, Comput. Phys. Commun., 126, 330-354, (2000) · Zbl 0953.65088
[7] Harten, A., Adaptive multiresolution schemes for shock computations, J. Comput. Phys., 115, 319-338, (1994) · Zbl 0925.65151
[8] Bihari, B. L.; Harten, A., Multiresolution schemes for the numerical solution of 2-D conservation laws I, SIAM J. Sci. Comput., 18, 315-354, (1997) · Zbl 0878.35007
[9] Cohen, A.; Kaber, S. M.; Müller, S.; Postel, M., Fully adaptive multiresolution finite volume schemes for conservation laws, Math. Comput., 72, 183-225, (2003) · Zbl 1010.65035
[10] Roussel, O.; Schneider, K.; Tsigulin, A.; Bockhorn, H., A conservative fully adaptive multiresolution algorithm for parabolic pdes, J. Comput. Phys., 188, 493-523, (2003) · Zbl 1022.65093
[11] Domingues, M. O.; Gomes, S. M.; Roussel, O.; Schneider, K., Adaptive multiresolution methods, (ESAIM Proc., vol. 34, (2011), EDP Sciences), 1-96 · Zbl 1302.65185
[12] Deiterding, R.; Domingues, M. O.; Gomes, S. M.; Roussel, O.; Schneider, K., Adaptive multiresolution or adaptive mesh refinement? A case study for 2D Euler equations, (ESAIM Proc., vol. 29, (2009)), 28-42 · Zbl 1301.76058
[13] Schneider, K.; Vasilyev, O. V., Wavelet methods in computational fluid dynamics, Annu. Rev. Fluid Mech., 42, 473-503, (2010) · Zbl 1345.76085
[14] Cohen, A., Wavelet methods in numerical analysis, Handb. Numer. Anal., 7, 417-711, (2000) · Zbl 0976.65124
[15] Müller, S., Adaptive multiscale schemes for conservation laws, vol. 27, (2003), Springer · Zbl 1016.76004
[16] Osher, S.; Sanders, R., Numerical approximations to nonlinear conservation laws with locally varying time and space grids, Math. Comput., 43, 321-336, (1983) · Zbl 0592.65068
[17] Dawson, C.; Kirby, R., High resolution schemes for conservation laws with locally varying time steps, SIAM J. Sci. Comput., 22, 2256-2281, (2001) · Zbl 0980.35015
[18] Domingues, M. O.; Gomes, S. M.; Roussel, O.; Schneider, K., An adaptive multiresolution scheme with local time stepping for evolutionary pdes, J. Comput. Phys., 227, 3758-3780, (2008) · Zbl 1139.65060
[19] Domingues, M. O.; Gomes, S. M.; Roussel, O.; Schneider, K., Space-time adaptive multiresolution methods for hyperbolic conservation laws: applications to compressible Euler equations, Appl. Numer. Math., 59, 2303-2321, (2009) · Zbl 1165.76031
[20] Hejazialhosseini, B.; Rossinelli, D.; Bergdorf, M.; Koumoutsakos, P., High order finite volume methods on wavelet-adapted grids with local time-stepping on multicore architectures for the simulation of shock-bubble interactions, J. Comput. Phys., 229, 8364-8383, (2010) · Zbl 1381.76218
[21] Han, L. H.; Indinger, T.; Hu, X. Y.; Adams, N. A., Wavelet-based adaptive multi-resolution solver on heterogeneous parallel architecture for computational fluid dynamics, Comput. Sci. Res. Dev., 26, 197-203, (2011)
[22] Rossinelli, D.; Hejazialhosseini, B.; Bergdorf, M.; Koumoutsakos, P., Wavelet-based adaptive solvers on multi-core architectures for the simulation of complex systems, Concurr. Comput., Pract. Exp., 23, 172-186, (2011)
[23] 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, 457-492, (1999) · Zbl 0957.76052
[24] Hu, X. Y.; Khoo, B. C.; Adams, N. A.; Huang, F. L., A conservative interface method for compressible flows, J. Comput. Phys., 219, 553-578, (2006) · Zbl 1102.76038
[25] Hu, X. Y.; Adams, N. A.; Iaccarino, G., On the HLLC Riemann solver for interface interaction in compressible multi-fluid flow, J. Comput. Phys., 228, 6572-6589, (2009) · Zbl 1261.76023
[26] Glimm, J.; Isaacson, E.; Marchesin, D.; McBryan, O., Front tracking for hyperbolic systems, Adv. Appl. Math., 2, 91-119, (1981) · Zbl 0459.76069
[27] S. Zelinka, E. Praun, C. Ohazama, et al., Large-scale image processing using mass parallelization techniques, US Patent 7,965,902, 2011.
[28] Contreras, G.; Martonosi, M., Characterizing and improving the performance of intel threading building blocks, (2008 IEEE International Symposium on Workload Characterization (IISWC 2008), (2008)), 57-66
[29] Hu, X. Y.; Adams, N. A., Scale separation for implicit large eddy simulation, J. Comput. Phys., 230, 19, 7240-7249, (2011) · Zbl 1286.76068
[30] Osher, S.; Sethian, J. A., Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys., 79, 12-49, (1988) · Zbl 0659.65132
[31] Sussman, M.; Fatemi, E.; Smereka, P.; Osher, S., An improved level set method for incompressible two-phase flows, Comput. Fluids, 27, 663-680, (1998) · Zbl 0967.76078
[32] Hu, X. Y.; Khoo, B. C., An interface interaction method for compressible multifluids, J. Comput. Phys., 198, 35-64, (2004) · Zbl 1107.76378
[33] Sussman, M.; Smereka, P.; Osher, S., A level set approach for computing solutions to incompressible two-phase flow, J. Comput. Phys., 114, 146-159, (1994) · Zbl 0808.76077
[34] Lauer, E.; Hu, X. Y.; Hickel, S.; Adams, N. A., Numerical modelling and investigation of symmetric and asymmetric cavitation bubble dynamics, Comput. Fluids, 69, 1-19, (2012) · Zbl 1365.76231
[35] Coquel, F.; Maday, Y.; Müller, S.; Postel, M.; Tran, Q. H., New trends in multiresolution and adaptive methods for convection-dominated problems, (ESAIM Proc., vol. 29, (2009), EDP Sciences), 1-7 · Zbl 1423.35308
[36] Sussman, M.; Almgren, A. S.; Bell, J. B.; Colella, P.; Howell, L. H.; Welcome, M. L., An adaptive level set approach for incompressible two-phase flows, J. Comput. Phys., 148, 81-124, (1999) · Zbl 0930.76068
[37] Nourgaliev, R. R.; Dinh, T. N.; Theofanous, T. G., Adaptive characteristics-based matching for compressible multifluid dynamics, J. Comput. Phys., 213, 500-529, (2006) · Zbl 1136.76396
[38] Peng, D.; Merriman, B.; Osher, S.; Zhao, H.; Kang, M., A PDE-based fast local level set method, J. Comput. Phys., 155, 2, 410-438, (1999) · Zbl 0964.76069
[39] Roe, P. L., Approximate Riemann solvers, parameter vectors, and difference schemes, J. Comput. Phys., 43, 357-372, (1981) · Zbl 0474.65066
[40] Lax, P. D., Weak solutions of nonlinear hyperbolic equations and their numerical computation, Commun. Pure Appl. Math., 7, 159-193, (1954) · Zbl 0055.19404
[41] Harten, A.; Lax, P. D.; Leer, B. V., On upstream differencing and Godunov-type schemes for hyperbolic conservation laws, SIAM Rev., 25, 35-61, (1983) · Zbl 0565.65051
[42] Einfeldt, B., On Godunov-type methods for gas dynamics, SIAM J. Numer. Anal., 25, 294-318, (1988) · Zbl 0642.76088
[43] Toro, E. F.; Spruce, M.; Speares, W., Restoration of the contact surface in the HLL-Riemann solver, Shock Waves, 4, 25-34, (1994) · Zbl 0811.76053
[44] Chung, M. H., A level set approach for computing solutions to inviscid compressible flow with moving solid boundary using fixed Cartesian grids, Int. J. Numer. Methods Fluids, 33, 1121-1151, (2001)
[45] Liu, T. G.; Khoo, B. C.; Yeo, K. S., Ghost fluid method for strong shock impacting on material interface, J. Comput. Phys., 190, 651-681, (2003) · Zbl 1076.76592
[46] Miller, G. H.; Colella, P., A conservative three-dimensional Eulerian method for coupled solid-fluid shock capturing, J. Comput. Phys., 183, 1, 26-82, (2002) · Zbl 1057.76558
[47] So, K. K.; Hu, X. Y.; Adams, N. A., Anti-diffusion interface sharpening technique for two-phase compressible flow simulations, J. Comput. Phys., 231, 4304-4323, (2012) · Zbl 1426.76428
[48] Haas, J. F.; Sturtevant, B., Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities, J. Fluid Mech., 181, 41-76, (1987)
[49] Chen, T.-J.; Cooke, C. H., On the Riemann problem for liquid or gas-liquid media, Int. J. Numer. Methods Fluids, 18, 529-541, (1994) · Zbl 0790.76100
[50] van Aanhold, J. E.; Meijer, G. J.; Lemmen, P. P.M., Underwater shock response analysis of a floating vessel, Shock Vib., 5, 53-59, (1998)
[51] Chang, C.-H.; Liou, M.-S., A robust and accurate approach to computing compressible multiphase flow: stratified flow model and AUSM^+-up scheme, J. Comput. Phys., 225, 840-873, (2007) · Zbl 1192.76030
[52] Chang, C.-H.; Deng, X.; Theofanous, T. G., Direct numerical simulation of interfacial instabilities: A consistent, conservative, all-speed, sharp-interface method, J. Comput. Phys., 242, 0, 946-990, (2013) · Zbl 1299.76097
[53] Grove, J.; Manikoff, R., Anomalous reflection of shock wave at a fluid interface, J. Fluid Mech., 219, 313-336, (1990)
[54] Shyue, K. M., A wave-propagation based volume tracking method for compressible multicomponent flow in two space dimensions, J. Comput. Phys., 215, 219-244, (2006) · Zbl 1140.76401
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