×

HORSES3D: a high-order discontinuous Galerkin solver for flow simulations and multi-physics applications. (English) Zbl 1510.76120

Summary: We present the latest developments of our High-Order Spectral Element Solver (HORSES3D), an open source high-order discontinuous Galerkin framework, capable of solving a variety of flow applications, including compressible flows (with or without shocks), incompressible flows, various RANS and LES turbulence models, particle dynamics, multiphase flows, and aeroacoustics. We provide an overview of the high-order spatial discretisation (including energy/entropy stable schemes) and anisotropic p-adaptation capabilities. The solver is parallelised using MPI and OpenMP showing good scalability for up to 1000 processors. Temporal discretisations include explicit, implicit, multigrid, and dual time-stepping schemes with efficient preconditioners. Additionally, we facilitate meshing and simulating complex geometries through a mesh-free immersed boundary technique. We detail the available documentation and the test cases included in the GitHub repository.

MSC:

76M22 Spectral methods applied to problems in fluid mechanics
76N06 Compressible Navier-Stokes equations
76F65 Direct numerical and large eddy simulation of turbulence
76Q05 Hydro- and aero-acoustics
65Y05 Parallel numerical computation

References:

[1] Wang, Z.; Fidkowski, K.; Abgrall, R.; Bassi, F.; Caraeni, D.; Cary, A.; Deconinck, H.; Hartmann, R.; Hillewaert, K.; Huynh, H.; Kroll, N., Int. J. Numer. Methods Fluids, 72, 811 (2013) · Zbl 1455.76007
[2] Wang, Z., Sci. China, Phys. Mech. Astron., 59, 1 (2016)
[3] Kompenhans, M.; Rubio, G.; Ferrer, E.; Valero, E., J. Comput. Phys., 306, 216 (2016) · Zbl 1352.65353
[4] Kompenhans, M.; Rubio, G.; Ferrer, E.; Valero, E., Comput. Fluids, 139, 36 (2016) · Zbl 1390.76329
[5] Rueda-Ramírez, A. M.; Rubio, G.; Ferrer, E.; Valero, E., J. Sci. Comput., 78, 433 (2019) · Zbl 1410.65353
[6] Rueda-Ramírez, A. M.; Manzanero, J.; Ferrer, E.; Rubio, G.; Valero, E., J. Comput. Phys., 378, 209 (2019) · Zbl 1416.65357
[7] Gottlieb, D.; Orszag, S. A., Numerical Analysis of Spectral Methods: Theory and Applications (1977), SIAM · Zbl 0412.65058
[8] Reed, W. H.; Hill, T. R. (1973), Los Alamos Scientific Lab.: Los Alamos Scientific Lab. N. Mex. (USA), Tech. Rep.
[9] Bassi, F.; Rebay, S., J. Comput. Phys., 131, 267 (1997) · Zbl 0871.76040
[10] Bassi, F.; Rebay, S.; Mariotti, G.; Pedinotti, S.; Savini, M., (Proceedings of the 2nd European Conference on Turbomachinery Fluid Dynamics and Thermodynamics. Proceedings of the 2nd European Conference on Turbomachinery Fluid Dynamics and Thermodynamics, Antwerpen, Belgium (1997)), 99-109
[11] Fischer, P.; Kruse, J.; Mullen, J.; Tufo, H.; Lottes, J.; Kerkemeier, S. (2008), Argonne National Laboratory, Mathematics and Computer Science Division: Argonne National Laboratory, Mathematics and Computer Science Division Argonne, IL
[12] Cantwell, C.; Moxey, D.; Comerford, A.; Bolis, A.; Rocco, G.; Mengaldo, G.; De Grazia, D.; Yakovlev, S.; Lombard, J.-E.; Ekelschot, D., Comput. Phys. Commun., 192, 205 (2015) · Zbl 1380.65465
[13] Moxey, D.; Cantwell, C. D.; Bao, Y.; Cassinelli, A.; Castiglioni, G.; Chun, S.; Juda, E.; Kazemi, E.; Lackhove, K.; Marcon, J., Comput. Phys. Commun., 249, Article 107110 pp. (2020)
[14] Blackburn, H.; Lee, D.; Albrecht, T.; Singh, J., Comput. Phys. Commun., 245, Article 106804 pp. (2019) · Zbl 1515.65256
[15] Bangerth, W.; Hartmann, R.; Kanschat, G., ACM Trans. Math. Softw., 33 (2007), 24-es · Zbl 1365.65248
[16] Gassner, G. J.; Winters, A. R.; Kopriva, D. A., J. Comput. Phys., 327, 39 (2016) · Zbl 1422.65280
[17] Hindenlang, F.; Gassner, G. J.; Altmann, C.; Beck, A.; Staudenmaier, M.; Munz, C.-D., “High Fidelity Flow Simulations”, Onera Scientific Day. “High Fidelity Flow Simulations”, Onera Scientific Day, Comput. Fluids, 61, 86 (2012) · Zbl 1365.00056
[18] Ranocha, H.; Schlottke-Lakemper, M.; Winters, A. R.; Faulhaber, E.; Chan, J.; Gassner, G., Proc. JuliaCon Conf., 1, 77 (2022)
[19] Schlottke-Lakemper, M.; Winters, A. R.; Ranocha, H.; Gassner, G. J., J. Comput. Phys., 442, Article 110467 pp. (2021) · Zbl 07513798
[20] Witherden, F.; Farrington, A.; Vincent, P., Comput. Phys. Commun., 185, 3028 (2014) · Zbl 1348.65005
[21] Geuzaine, C.; Remacle, J.-F., Int. J. Numer. Methods Eng., 79, 1309 (2009) · Zbl 1176.74181
[22] Folk, M.; Cheng, A.; Yates, K., (Proceedings of Supercomputing, vol. 99 (1999)), 5-33
[23] Kopriva, D. A., HOHQMesh, the high order hex-quad mesher
[24] Hindenlang, F.; Bolemann, T.; Munz, C.-D., (IDIHOM: Industrialization of High-Order Methods-A Top-Down Approach (2015), Springer), 133-152
[25] Ahrens, J.; Geveci, B.; Law, C., (The Visualization Handbook, vol. 717 (2005))
[26] Ayachit, U., The Paraview Guide: a Parallel Visualization Application (2015), Kitware, Inc.
[27] Kopriva, D. A., Implementing Spectral Methods for Partial Differential Equations (2009), Springer: Springer Netherlands · Zbl 1172.65001
[28] Manzanero, J.; Rubio, G.; Kopriva, D. A.; Ferrer, E.; Valero, E., J. Comput. Phys., Article 109363 pp. (2020)
[29] Ferrer, E., J. Comput. Phys., 348, 754 (2017) · Zbl 1380.76018
[30] Toro, E., Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction (2009), Springer Berlin Heidelberg, URL · Zbl 1227.76006
[31] Arnold, D.; Brezzi, F.; Cockburn, B.; Marini, L., SIAM J. Numer. Anal., 39, 1749 (2001)
[32] Ferrer, E. (2012), Oxford University: Oxford University UK, Ph.D. thesis
[33] Ferrer, E.; Willden, R., 10th ICFD Conference Series on Numerical Methods for Fluid Dynamics (ICFD 2010). 10th ICFD Conference Series on Numerical Methods for Fluid Dynamics (ICFD 2010), Comput. Fluids, 46, 224 (2011)
[34] Ferrer, E.; Willden, R. H., J. Comput. Phys., 231, 7037 (2012) · Zbl 1284.35311
[35] Beck, A.; Bolemann, T.; Flad, D.; Frank, H.; Gassner, G.; Hindenlang, F.; Munz, C., Int. J. Numer. Methods Fluids, 76, 522 (2014)
[36] Fisher, T. C.; Carpenter, M. H., J. Comput. Phys., 252, 518 (2013) · Zbl 1349.65293
[37] Carpenter, M. H.; Fisher, T. C.; Nielsen, E. J.; Frankel, S. H., SIAM J. Sci. Comput., 36, B835 (2014) · Zbl 1457.65140
[38] Manzanero, J.; Rubio, G.; Ferrer, E.; Valero, E.; Kopriva, D. A., J. Sci. Comput., 75, 1262 (2018) · Zbl 1422.65263
[39] Kopriva, D. A.; Gassner, G. J., SIAM J. Sci. Comput., 36, Article A2076 pp. (2014) · Zbl 1303.65086
[40] Gassner, G. J.; Winters, A. R.; Kopriva, D. A., J. Comput. Phys., 327, 39 (2016) · Zbl 1422.65280
[41] Gassner, G. J.; Winters, A. R.; Hindenlang, F. J.; Kopriva, D. A., J. Sci. Comput., 77, 154 (2018)
[42] Chen, T.; Shu, C.-W., J. Comput. Phys., 345, 427 (2017) · Zbl 1380.65253
[43] Winters, A. R.; Moura, R. C.; Mengaldo, G.; Gassner, G. J.; Walch, S.; Peiro, J.; Sherwin, S. J., J. Comput. Phys., 372, 1 (2018) · Zbl 1415.76461
[44] Gassner, G. J., SIAM J. Sci. Comput., 35, Article A1233 pp. (2013)
[45] Winters, A. R.; Kopriva, D. A.; Gassner, G. J.; Hindenlang, F., (Efficient High-Order Discretizations for Computational Fluid Dynamics (2021), Springer), 117-196 · Zbl 1472.76066
[46] Chen, T.; Shu, C.-W., CSIAM Trans. Appl. Math., 1, 1 (2020)
[47] Morinishi, Y., J. Comput. Phys., 229, 276 (2010) · Zbl 1375.76113
[48] Ducros, F.; Laporte, F.; Soulères, T.; Guinot, V.; Moinat, P.; Caruelle, B., J. Comput. Phys., 161, 114 (2000) · Zbl 0972.76066
[49] Kennedy, C. A.; Gruber, A., J. Comput. Phys., 227, 1676 (2008) · Zbl 1290.76135
[50] Pirozzoli, S., J. Comput. Phys., 229, 7180 (2010) · Zbl 1426.76485
[51] Chandrashekar, P., Commun. Comput. Phys., 14, 1252-1286 (2013) · Zbl 1373.76121
[52] Chandrashekar, P., J. Comput. Phys., 233, 527 (2013) · Zbl 1286.65120
[53] Manzanero, J.; Rubio, G.; Kopriva, D. A.; Ferrer, E.; Valero, E., J. Comput. Phys., 408, Article 109241 pp. (2020) · Zbl 07505602
[54] Guermond, J.-L.; Quartapelle, L., J. Comput. Phys., 165, 167 (2000) · Zbl 0994.76051
[55] Lodares, D.; Manzanero, J.; Ferrer, E.; Valero, E., J. Comput. Phys., 455, Article 110998 pp. (2022) · Zbl 07518083
[56] Ntoukas, G.; Manzanero, J.; Rubio, G.; Valero, E.; Ferrer, E., J. Comput. Phys., 458, Article 111093 pp. (2022) · Zbl 07527720
[57] Kopriva, D. A.; Hindenlang, F. J.; Bolemann, T.; Gassner, G. J., J. Sci. Comput., 79, 1389 (2019) · Zbl 1448.76111
[58] Kopriva, D. A.; Woodruff, S. L.; Hussaini, M. Y., Int. J. Numer. Methods Eng., 53, 105 (2002) · Zbl 0994.78020
[59] Roy, C., (47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition (2009)), 1302
[60] Fraysse, F.; Rubio, G.; De Vicente, J.; Valero, E., Aerosp. Sci. Technol., 38, 76 (2014)
[61] Rubio, G.; Fraysse, F.; de Vicente, J.; Valero, E., J. Sci. Comput., 57, 146 (2013) · Zbl 1282.65125
[62] Rubio, G.; Fraysse, F.; Kopriva, D. A.; Valero, E., J. Sci. Comput., 64, 425 (2015) · Zbl 1325.65138
[63] Laskowski, W.; Rubio, G.; Valero, E.; Ferrer, E., J. Comput. Phys., 451, Article 110883 pp. (2022) · Zbl 07517169
[64] Ntoukas, G.; Manzanero, J.; Rubio, G.; Valero, E.; Ferrer, E., J. Comput. Phys., 442, Article 110409 pp. (2021) · Zbl 07513792
[65] Williamson, J., J. Comput. Phys., 35, 48 (1980) · Zbl 0425.65038
[66] Carpenter, M. H.; Kennedy, C. A. (1994), NASA Langley Research Center, NASA Report TM 109112
[67] Joshi, S.; Hurtado-de Mendoza, A.; Kou, J.; Puri, K.; Hirsch, C.; Ferrer, E., (WCCM-ECCOMAS2020 (2021))
[68] Vermeire, B.; Loppi, N.; Vincent, P., J. Comput. Phys., 383, 55 (2019) · Zbl 1451.65112
[69] Fidkowski, K. J.; Oliver, T. A.; Lu, J.; Darmofal, D. L., J. Comput. Phys., 207, 92 (2005) · Zbl 1177.76194
[70] Parsani, M.; Van den Abeele, K.; Lacor, C.; Turkel, E., J. Comput. Phys., 229, 828 (2010) · Zbl 1253.76029
[71] Ghidoni, A.; Colombo, A.; Bassi, F.; Rebay, S., Int. J. Numer. Methods Fluids, 75, 134 (2014) · Zbl 1455.65168
[72] Bassi, F.; Botti, L.; Colombo, A.; Ghidoni, A.; Massa, F., Comput. Fluids, 118, 305 (2015) · Zbl 1390.76833
[73] Coleman, T. F.; Moré, J. J., SIAM J. Numer. Anal., 20, 187 (1983) · Zbl 0527.65033
[74] Gebremedhin, A. H.; Manne, F.; Pothen, A., SIAM Rev., 47, 629 (2005) · Zbl 1076.05034
[75] Taylor, G. I.; Green, A. E., Proc. R. Soc. A, Math. Phys. Eng. Sci., 158, 499-521 (1937) · JFM 63.1358.03
[76] Moura, R. C.; Mengaldo, G.; Peiró, J.; Sherwin, S. J., (Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2016 (2017), Springer), 161-173 · Zbl 1388.76101
[77] Manzanero, J.; Ferrer, E.; Rubio, G.; Valero, E., Comput. Fluids, 200, Article 104440 pp. (2020) · Zbl 1519.76095
[78] Bsc-Cns, Marenostrum web page
[79] Laskowski, W. (2022), ETSIAE-UPM, Ph.D. thesis
[80] Sagaut, P., Large Eddy Simulation for Incompressible Flows: an Introduction (2006), Springer Science & Business Media · Zbl 1091.76001
[81] Oliver, T. A. (2008), Massachusetts Inst of Tech Cambridge Dept of Aeronautics and Astronautics, Tech. Rep.
[82] Vassberg, J.; Dehaan, M.; Rivers, M.; Wahls, R., (26th AIAA Applied Aerodynamics Conference (2008)), 6919
[83] de Barros Ceze, M. A. (2013), University of Michigan, Ph.D. thesis
[84] Smagorinsky, J., Mon. Weather Rev., 91, 99 (1963)
[85] Lilly, D. K., Mon. Weather Rev., 93, 11 (1965)
[86] Nicoud, F.; Ducros, F., Flow Turbul. Combust., 62, 183 (1999) · Zbl 0980.76036
[87] Vreman, A., Phys. Fluids, 16, 3670 (2004) · Zbl 1187.76543
[88] Grinstein, F. F.; Margolin, L. G.; Rider, W. J., Implicit Large Eddy Simulation, vol. 10 (2007), Cambridge University Press: Cambridge University Press Cambridge · Zbl 1135.76001
[89] Gassner, G.; Kopriva, D. A., SIAM J. Sci. Comput., 33, 2560 (2011) · Zbl 1255.65089
[90] Kou, J.; Le Clainche, S.; Ferrer, E., J. Comput. Phys., 449, Article 110798 pp. (2022) · Zbl 07524794
[91] Manzanero, J.; Ferrer, E.; Rubio, G.; Valero, E. (2018)
[92] Manzanero, J.; Rubio, G.; Ferrer, E.; Valero, E., SIAM J. Sci. Comput., 40, A747 (2018) · Zbl 1453.65337
[93] Solán-Fustero, P.; Navas-Montilla, A.; Ferrer, E.; Manzanero, J.; García-Navarro, P., J. Comput. Phys., 435, Article 110246 pp. (2021) · Zbl 07503728
[94] Flad, D.; Gassner, G., J. Comput. Phys., 350, 782 (2017) · Zbl 1380.76019
[95] Uranga, A.; Persson, P.; Drela, M.; Peraire, J., Int. J. Numer. Methods Eng., 87, 232 (2011) · Zbl 1242.76085
[96] Ferrer, E.; Manzanero, J.; Rueda-Ramirez, A. M.; Rubio, G.; Valero, E., (Sherwin, S. J.; Moxey, D.; Peiró, J.; Vincent, P. E.; Schwab, C., Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018 (2020), Springer International Publishing: Springer International Publishing Cham), 477-487 · Zbl 1462.65006
[97] Fernandez, P.; Nguyen, N.; Peraire, J., J. Comput. Phys., 336, 308 (2017) · Zbl 1375.76069
[98] Ferrer, E.; Saito, N.; Blackburn, H.; Pullin, D., Comput. Fluids, 191, Article 104239 pp. (2019) · Zbl 1519.76085
[99] Shen, J., (Proceedings of the 1994 Beijing Symposium on Nonlinear Evolution Equations and Infinite Dynamical Systems (1997), ZhongShan University Press: ZhongShan University Press Zhongshan), 68-78
[100] Karniadakis, G.; Sherwin, S., Spectral/hp Element Methods for Computational Fluid Dynamics (2005), Oxford Science Publications · Zbl 1116.76002
[101] Ferrer, E.; Moxey, D.; Willden, R. H.J.; Sherwin, S. J., Commun. Comput. Phys., 16, 817-840 (2014)
[102] Cahn, J. W.; Hilliard, J. E., J. Chem. Phys., 28, 258 (1958) · Zbl 1431.35066
[103] Allen, S. M.; Cahn, J. W., Acta Metall., 20, 423 (1972)
[104] Manzanero, J.; Rubio, G.; Kopriva, D. A.; Ferrer, E.; Valero, E., J. Comput. Phys., 403, Article 109072 pp. (2020) · Zbl 1453.65338
[105] Manzanero, J.; Redondo, C.; Rubio, G.; Ferrer, E.; Rivero-Jiménez, Ángel, Comput. Fluids, 225, Article 104971 pp. (2021) · Zbl 1521.76353
[106] von Mises, R., J. Aeronaut. Sci., 17, 551 (1950)
[107] Guermond, J. L.; Popov, B., SIAM J. Appl. Math., 74, 284 (2014) · Zbl 1446.76147
[108] Tadmor, E., SIAM J. Numer. Anal., 26, 30 (1989) · Zbl 0667.65079
[109] Maday, Y.; Kaber, S. Ould; Tadmor, E., SIAM J. Numer. Anal., 30, 321 (1993) · Zbl 0774.65072
[110] Moura, R.; Sherwin, S.; Peiro, J., J. Comput. Phys., 307, 401 (2016) · Zbl 1352.65362
[111] Friedrichs, K. O.; Lax, P. D., Proc. Natl. Acad. Sci. USA, 68, 1686 (1971) · Zbl 0229.35061
[112] Tadmor, E., Appl. Numer. Math., 2, 211 (1986) · Zbl 0625.76084
[113] Mateo-Gabín, A.; Manzanero, J.; Valero, E., J. Comput. Phys., 471, Article 111618 pp. (2022) · Zbl 07605589
[114] Frankel, A.; Pouransari, H.; Coletti, F.; Mani, A., J. Fluid Mech., 792, 869 (2016) · Zbl 1381.76086
[115] Pouransari, H.; Mani, A., J. Sol. Energy Eng., 139 (2017)
[116] Lele, S. K.; Nichols, J. W., Trans. R. Soc. A, 372 (2014)
[117] Williams, J. E.F.; Hawkings, D. L., Philos. Trans. R. Soc. Lond. Ser. A, Math. Phys. Sci., 264, 321 (1969) · Zbl 0182.59205
[118] Najafi-Yazdi, A.; Brès, G. A.; Mongeau, L., Proc. R. Soc. A, Math. Phys. Eng. Sci., 467, 144 (2010)
[119] Ghorbaniasl, G.; Lacor, C., J. Sound Vib., 331, 117 (2012)
[120] Garrick, I. E.; Watkins, C. E.; Garrick, I. E.; Watkins, C. E. (1954), Tech. Rep.
[121] Farassat, F. (2007), Tech. Rep.
[122] Brentner, K. S.; Farassat, F., Prog. Aerosp. Sci., 39, 83 (2003)
[123] Lockard, D., (8th AIAA/CEAS Aeroacoustics Conference Exhibit (2002), American Institute of Aeronautics and Astronautics)
[124] Paterson, R. W.; Vogt, P. G.; Fink, M. R.; Munch, C. L., J. Aircr., 10, 296 (1973)
[125] Desquesnes, G.; Terracol, M.; Sagaut, P., J. Fluid Mech., 591, 155 (2007) · Zbl 1125.76380
[126] Peskin, C. S., J. Comput. Phys., 10, 252 (1972) · Zbl 0244.92002
[127] Kim, W.; Choi, H., Int. J. Heat Fluid Flow, 75, 301 (2019)
[128] Kou, J.; de Mendoza, A. H.; Joshi, S.; Le Clainche, S.; Ferrer, E., J. Comput. Phys., 449, Article 110817 pp. (2022) · Zbl 07524806
[129] Kou, J.; Joshi, S.; de Mendoza, A. H.; Puri, K.; Hirsch, C.; Ferrer, E., J. Comput. Phys., 448, Article 110721 pp. (2022) · Zbl 1537.76087
[130] Kou, J.; Ferrer, E., J. Comput. Phys., 472, Article 111678 pp. (2023)
[131] Wu, Z.; Zhao, F.; Liu, X., (Proceedings of the ACM SIGGRAPH Symposium on High Performance Graphics (2011)), 71-78
[132] Giannenas, A. E.; Bempedelis, N.; Schuch, F. N.; Laizet, S., Flow Turbul. Combust., 109, 931 (2022)
[133] Manrique de Lara, F.; Ferrer, E., Comput. Fluids, 235, Article 105274 pp. (2022) · Zbl 1521.76325
[134] Manrique de Lara, F.; Ferrer, E. (2022), arXiv preprint
[135] mfem, MFEM: modular finite element methods [software]
[136] Anderson, R.; Andrej, J.; Barker, A.; Bramwell, J.; Camier, J.-S.; Dobrev, J. C.V.; Dudouit, Y.; Fisher, A.; Kolev, T.; Pazner, W., Comput. Math. Appl., 81, 42 (2021) · Zbl 1524.65001
[137] Perea, D. H. (2022)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.