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Computational thermo-fluid analysis of a disk brake. (English) Zbl 1382.74044

Summary: We present computational thermo-fluid analysis of a disk brake, including thermo-fluid analysis of the flow around the brake and heat conduction analysis of the disk. The computational challenges include proper representation of the small-scale thermo-fluid behavior, high-resolution representation of the thermo-fluid boundary layers near the spinning solid surfaces, and bringing the heat transfer coefficient (HTC) calculated in the thermo-fluid analysis of the flow to the heat conduction analysis of the spinning disk. The disk brake model used in the analysis closely represents the actual configuration, and this adds to the computational challenges. The components of the method we have developed for computational analysis of the class of problems with these types of challenges include the Space-Time Variational Multiscale method for coupled incompressible flow and thermal transport, ST Slip Interface method for high-resolution representation of the thermo-fluid boundary layers near spinning solid surfaces, and a set of projection methods for different parts of the disk to bring the HTC calculated in the thermo-fluid analysis. With the HTC coming from the thermo-fluid analysis of the flow around the brake, we do the heat conduction analysis of the disk, from the start of the breaking until the disk spinning stops, demonstrating how the method developed works in computational analysis of this complex and challenging problem.

MSC:

74F05 Thermal effects in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76D05 Navier-Stokes equations for incompressible viscous fluids

Software:

SUPG
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Full Text: DOI

References:

[1] Takizawa K, Tezduyar TE, Kuraishi T (2015) Multiscale ST methods for thermo-fluid analysis of a ground vehicle and its tires. Math Model Methods Appl Sci 25:2227-2255. doi:10.1142/S0218202515400072 · Zbl 1325.76139 · doi:10.1142/S0218202515400072
[2] Takizawa K, Tezduyar TE (2011) Multiscale space-time fluid-structure interaction techniques. Comput Mech 48:247-267. doi:10.1007/s00466-011-0571-z · Zbl 1398.76128 · doi:10.1007/s00466-011-0571-z
[3] Takizawa K, Tezduyar TE (2012) Space-time fluid-structure interaction methods. Math Model Methods Appl Sci 22:1230001. doi:10.1142/S0218202512300013 · Zbl 1248.76118 · doi:10.1142/S0218202512300013
[4] Tezduyar TE (1992) Stabilized finite element formulations for incompressible flow computations. Adv Appl Mech 28:1-44. doi:10.1016/S0065-2156(08)70153-4 · Zbl 0747.76069 · doi:10.1016/S0065-2156(08)70153-4
[5] Tezduyar TE (2003) Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43:555-575. doi:10.1002/fld.505 · Zbl 1032.76605 · doi:10.1002/fld.505
[6] Tezduyar TE, Sathe S (2007) Modeling of fluid-structure interactions with the space-time finite elements: solution techniques. Int J Numer Methods Fluids 54:855-900. doi:10.1002/fld.1430 · Zbl 1144.74044 · doi:10.1002/fld.1430
[7] Hughes TJR (1995) Multiscale phenomena: green’s functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles, and the origins of stabilized methods. Comput Methods Appl Mech Eng 127:387-401 · Zbl 0866.76044 · doi:10.1016/0045-7825(95)00844-9
[8] Hughes TJR, Oberai AA, Mazzei L (2001) Large eddy simulation of turbulent channel flows by the variational multiscale method. Phys Fluids 13:1784-1799 · Zbl 1184.76237 · doi:10.1063/1.1367868
[9] Bazilevs Y, Calo VM, Cottrell JA, Hughes TJR, Reali A, Scovazzi G (2007) Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows. Comput Methods Appl Mech Eng 197:173-201 · Zbl 1169.76352 · doi:10.1016/j.cma.2007.07.016
[10] Bazilevs Y, Akkerman I (2010) Large eddy simulation of turbulent Taylor-Couette flow using isogeometric analysis and the residual-based variational multiscale method. J Comput Phys 229:3402-3414 · Zbl 1290.76037 · doi:10.1016/j.jcp.2010.01.008
[11] Takizawa K, Bazilevs Y, Tezduyar TE (2012) Space-time and ALE-VMS techniques for patient-specific cardiovascular fluid-structure interaction modeling. Arch Comput Methods Eng 19:171-225. doi:10.1007/s11831-012-9071-3 · Zbl 1354.92023 · doi:10.1007/s11831-012-9071-3
[12] Bazilevs Y, Hsu M-C, Takizawa K, Tezduyar TE (2012) ALE-VMS and ST-VMS methods for computer modeling of wind-turbine rotor aerodynamics and fluid-structure interaction. Math Models Methods Appl Sci 22:1230002. doi:10.1142/S0218202512300025 · Zbl 1404.76187 · doi:10.1142/S0218202512300025
[13] Bazilevs Y, Calo VM, Hughes TJR, Zhang Y (2008) Isogeometric fluid-structure interaction: theory, algorithms, and computations. Comput Mech 43:3-37 · Zbl 1169.74015 · doi:10.1007/s00466-008-0315-x
[14] Hughes TJR, Liu WK, Zimmermann TK (1981) Lagrangian-Eulerian finite element formulation for incompressible viscous flows. Comput Methods Appl Mech Eng 29:329-349 · Zbl 0482.76039 · doi:10.1016/0045-7825(81)90049-9
[15] Hughes TJR, Cottrell JA, Bazilevs Y (2005) Isogeometric analysis: CAD, finite elements, NURBS, exact geometry, and mesh refinement. Comput Methods Appl Mech Eng 194:4135-4195 · Zbl 1151.74419 · doi:10.1016/j.cma.2004.10.008
[16] Bazilevs Y, Calo VM, Zhang Y, Hughes TJR (2006) Isogeometric fluid-structure interaction analysis with applications to arterial blood flow. Comput Mech 38:310-322 · Zbl 1161.74020 · doi:10.1007/s00466-006-0084-3
[17] Bazilevs Y, Hughes TJR (2008) NURBS-based isogeometric analysis for the computation of flows about rotating components. Computl Mech 43:143-150 · Zbl 1171.76043 · doi:10.1007/s00466-008-0277-z
[18] Bazilevs Y, Gohean JR, Hughes TJR, Moser RD, Zhang Y (2009) Patient-specific isogeometric fluid-structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device. Comput Methods Appl Mech Eng 198:3534-3550 · Zbl 1229.74096 · doi:10.1016/j.cma.2009.04.015
[19] Bazilevs Y, Hsu M-C, Benson D, Sankaran S, Marsden A (2009) Computational fluid-structure interaction: methods and application to a total cavopulmonary connection. Comput Mech 45:77-89 · Zbl 1398.92056 · doi:10.1007/s00466-009-0419-y
[20] Bazilevs Y, Hsu M-C, Akkerman I, Wright S, Takizawa K, Henicke B, Spielman T, Tezduyar TE (2011) 3D simulation of wind turbine rotors at full scale. Part I: geometry modeling and aerodynamics. Int J Numer Methods Fluids 65:207-235. doi:10.1002/fld.2400 · Zbl 1428.76086 · doi:10.1002/fld.2400
[21] Bazilevs Y, Hsu M-C, Kiendl J, Wüchner R, Bletzinger K-U (2011) 3D simulation of wind turbine rotors at full scale. Part II: fluid-structure interaction modeling with composite blades. Int J Numer Methods Fluids 65:236-253 · Zbl 1428.76087 · doi:10.1002/fld.2454
[22] Hsu M-C, Akkerman I, Bazilevs Y (2012) Wind turbine aerodynamics using ALE-VMS: validation and role of weakly enforced boundary conditions. Comput Mech 50:499-511 · Zbl 06128533 · doi:10.1007/s00466-012-0686-x
[23] Hsu M-C, Bazilevs Y (2012) Fluid-structure interaction modeling of wind turbines: simulating the full machine. Comput Mech 50:821-833 · Zbl 1311.74038 · doi:10.1007/s00466-012-0772-0
[24] Bazilevs Y, Takizawa K (2013) Computational fluid-structure interaction: methods and applications. Wiley, Chichester · Zbl 1286.74001 · doi:10.1002/9781118483565
[25] Bazilevs Y, Takizawa K, Tezduyar TE (2013) Challenges and directions in computational fluid-structure interaction. Math Models Methods Appl Sci 23:215-221. doi:10.1142/S0218202513400010 · Zbl 1261.76025 · doi:10.1142/S0218202513400010
[26] Korobenko A, Hsu M-C, Akkerman I, Tippmann J, Bazilevs Y (2013) Structural mechanics modeling and FSI simulation of wind turbines. Math Models Methods Appl Sci 23:249-272 · Zbl 1261.74011 · doi:10.1142/S0218202513400034
[27] Korobenko A, Hsu M-C, Akkerman I, Bazilevs Y (2013) Aerodynamic simulation of vertical-axis wind turbines. J Appl Mech 81:021011. doi:10.1115/1.4024415 · Zbl 1261.74011 · doi:10.1115/1.4024415
[28] Bazilevs Y, Takizawa K, Tezduyar TE, Hsu M-C, Kostov N, McIntyre S (2014) Aerodynamic and FSI analysis of wind turbines with the ALE-VMS and ST-VMS methods. Arch Comput Methods Eng 21:359-398. doi:10.1007/s11831-014-9119-7 · Zbl 1348.74095 · doi:10.1007/s11831-014-9119-7
[29] Bazilevs Y, Korobenko A, Deng X, Yan J, Kinzel M, Dabiri JO (2014) FSI modeling of vertical-axis wind turbines. J Appl Mech 81:081006. doi:10.1115/1.4027466 · doi:10.1115/1.4027466
[30] Hsu M-C, Akkerman I, Bazilevs Y (2014) Finite element simulation of wind turbine aerodynamics: validation study using NREL phase VI experiment. Wind Energy 17:461-481 · doi:10.1002/we.1599
[31] Long CC, Esmaily-Moghadam M, Marsden AL, Bazilevs Y (2014) Computation of residence time in the simulation of pulsatile ventricular assist devices. Comput Mech 54:911-919. doi:10.1007/s00466-013-0931-y · Zbl 1311.74041 · doi:10.1007/s00466-013-0931-y
[32] Long CC, Marsden AL, Bazilevs Y (2014) Shape optimization of pulsatile ventricular assist devices using FSI to minimize thrombotic risk. Comput Mech 54:921-932. doi:10.1007/s00466-013-0967-z · Zbl 1314.74056 · doi:10.1007/s00466-013-0967-z
[33] Hsu M-C, Kamensky D, Bazilevs Y, Sacks MS, Hughes TJR (2014) Fluid-structure interaction analysis of bioprosthetic heart valves: significance of arterial wall deformation. Comput Mech 54:1055-1071. doi:10.1007/s00466-014-1059-4 · Zbl 1311.74039 · doi:10.1007/s00466-014-1059-4
[34] Augier B, Yan J, Korobenko A, Czarnowski J, Ketterman G, Bazilevs Y (2015) Experimental and numerical FSI study of compliant hydrofoils. Comput Mech 55:1079-1090. doi:10.1007/s00466-014-1090-5 · Zbl 1390.76375 · doi:10.1007/s00466-014-1090-5
[35] Bazilevs Y, Korobenko A, Yan J, Pal A, Gohari SMI, Sarkar S (2015) ALE-VMS formulation for stratified turbulent incompressible flows with applications. Math Models Methods Appl Sci 25:2349-2375. doi:10.1142/S0218202515400114 · Zbl 1329.76050 · doi:10.1142/S0218202515400114
[36] Bazilevs Y, Takizawa K, Tezduyar TE (2015) New directions and challenging computations in fluid dynamics modeling with stabilized and multiscale methods. Math Models Methods Appl Sci 25:2217-2226. doi:10.1142/S0218202515020029 · Zbl 1329.76007 · doi:10.1142/S0218202515020029
[37] Takizawa K, Henicke B, Tezduyar TE, Hsu M-C, Bazilevs Y (2011) Stabilized space-time computation of wind-turbine rotor aerodynamics. Comput Mech 48:333-344. doi:10.1007/s00466-011-0589-2 · Zbl 1398.76127 · doi:10.1007/s00466-011-0589-2
[38] Takizawa K, Henicke B, Montes D, Tezduyar TE, Hsu M-C, Bazilevs Y (2011) Numerical-performance studies for the stabilized space-time computation of wind-turbine rotor aerodynamics. Comput Mech 48:647-657. doi:10.1007/s00466-011-0614-5 · Zbl 1334.74032 · doi:10.1007/s00466-011-0614-5
[39] Takizawa K, Tezduyar TE, McIntyre S, Kostov N, Kolesar R, Habluetzel C (2014) Space-time VMS computation of wind-turbine rotor and tower aerodynamics. Comput Mech 53:1-15. doi:10.1007/s00466-013-0888-x · Zbl 1398.76129 · doi:10.1007/s00466-013-0888-x
[40] Takizawa K, Bazilevs Y, Tezduyar TE, Hsu M-C, Øiseth O, Mathisen KM, Kostov N, McIntyre S (2014) Engineering analysis and design with ALE-VMS and space-time methods. Arch Comput Methods Eng 21:481-508. doi:10.1007/s11831-014-9113-0 · Zbl 1348.74104 · doi:10.1007/s11831-014-9113-0
[41] Takizawa K (2014) Computational engineering analysis with the new-generation space-time methods. Comput Mech 54:193-211. doi:10.1007/s00466-014-0999-z · Zbl 06327161 · doi:10.1007/s00466-014-0999-z
[42] Takizawa K, Tezduyar TE, Mochizuki H, Hattori H, Mei S, Pan L, Montel K (2015) Space-time VMS method for flow computations with slip interfaces (ST-SI). Math Models Methods Appl Sci 25:2377-2406. doi:10.1142/S0218202515400126 · Zbl 1329.76345 · doi:10.1142/S0218202515400126
[43] Takizawa K, Henicke B, Puntel A, Spielman T, Tezduyar TE (2012) Space-time computational techniques for the aerodynamics of flapping wings. J Appl Mech 79:010903. doi:10.1115/1.4005073 · Zbl 1286.76179 · doi:10.1115/1.4005073
[44] Takizawa K, Henicke B, Puntel A, Kostov N, Tezduyar TE (2012) Space-time techniques for computational aerodynamics modeling of flapping wings of an actual locust. Comput Mech 50:743-760. doi:10.1007/s00466-012-0759-x · Zbl 1286.76179 · doi:10.1007/s00466-012-0759-x
[45] Takizawa K, Kostov N, Puntel A, Henicke B, Tezduyar TE (2012) Space-time computational analysis of bio-inspired flapping-wing aerodynamics of a micro aerial vehicle. Comput Mech 50:761-778. doi:10.1007/s00466-012-0758-y · Zbl 1286.76180 · doi:10.1007/s00466-012-0758-y
[46] Takizawa K, Henicke B, Puntel A, Kostov N, Tezduyar TE (2013) Computer modeling techniques for flapping-wing aerodynamics of a locust. Comput Fluids 85:125-134. doi:10.1016/j.compfluid.2012.11.008 · Zbl 1290.76170 · doi:10.1016/j.compfluid.2012.11.008
[47] Takizawa K, Tezduyar TE, Buscher A, Asada S (2014) Space-time interface-tracking with topology change (ST-TC). Comput Mech 54:955-971. doi:10.1007/s00466-013-0935-7 · Zbl 1311.74045 · doi:10.1007/s00466-013-0935-7
[48] Takizawa K, Tezduyar TE, Kostov N (2014) Sequentially-coupled space-time FSI analysis of bio-inspired flapping-wing aerodynamics of an MAV. Comput Mech 54:213-233. doi:10.1007/s00466-014-0980-x · Zbl 06327162 · doi:10.1007/s00466-014-0980-x
[49] Takizawa K, Tezduyar TE, Buscher A (2015) Space-time computational analysis of MAV flapping-wing aerodynamics with wing clapping. Comput Mech 55:1131-1141. doi:10.1007/s00466-014-1095-0 · doi:10.1007/s00466-014-1095-0
[50] Takizawa K, Schjodt K, Puntel A, Kostov N, Tezduyar TE (2012) Patient-specific computer modeling of blood flow in cerebral arteries with aneurysm and stent. Comput Mech 50:675-686. doi:10.1007/s00466-012-0760-4 · Zbl 1311.76157 · doi:10.1007/s00466-012-0760-4
[51] Takizawa K, Schjodt K, Puntel A, Kostov N, Tezduyar TE (2013) Patient-specific computational analysis of the influence of a stent on the unsteady flow in cerebral aneurysms. Comput Mech 51:1061-1073. doi:10.1007/s00466-012-0790-y · Zbl 1366.76106 · doi:10.1007/s00466-012-0790-y
[52] Takizawa K, Bazilevs Y, Tezduyar TE, Long CC, Marsden AL, Schjodt K (2014) ST and ALE-VMS methods for patient-specific cardiovascular fluid mechanics modeling. Math Models Methods Appl Sci 24:2437-2486. doi:10.1142/S0218202514500250 · Zbl 1296.76113 · doi:10.1142/S0218202514500250
[53] Suito H, Takizawa K, Huynh VQH, Sze D, Ueda T (2014) FSI analysis of the blood flow and geometrical characteristics in the thoracic aorta. Comput Mech 54:1035-1045. doi:10.1007/s00466-014-1017-1 · Zbl 1311.74044 · doi:10.1007/s00466-014-1017-1
[54] Takizawa K, Tezduyar TE, Buscher A, Asada S (2014) Space-time fluid mechanics computation of heart valve models. Comput Mech 54:973-986. doi:10.1007/s00466-014-1046-9 · Zbl 1311.74083 · doi:10.1007/s00466-014-1046-9
[55] Takizawa K, Montes D, Fritze M, McIntyre S, Boben J, Tezduyar TE (2013) Methods for FSI modeling of spacecraft parachute dynamics and cover separation. Math Models Methods Appl Sci 23:307-338. doi:10.1142/S0218202513400058 · Zbl 1261.76013 · doi:10.1142/S0218202513400058
[56] Takizawa K, Montes D, McIntyre S, Tezduyar TE (2013) Space-time VMS methods for modeling of incompressible flows at high Reynolds numbers. Math Models Methods Appl Sci 23:223-248. doi:10.1142/s0218202513400022 · Zbl 1261.76037 · doi:10.1142/s0218202513400022
[57] Hattori H, Takizawa K, Tezduyar TE, Miyagawa K, Nomi M, Isono M, Uchida H, Kawai M (2015) Computational analysis of flow-driven string dynamics in a turbomachinery. In: Proceedings of 13th Asian International Conference on Fluid Machinery, Paper No. AICFM13-154, Tokyo
[58] Otoguro Y, Terahara T, Takizawa K, Tezduyar TE, Kuraishi T, Hattori H (2015) A higher-order ST-VMS method for turbocharger analysis. In: Proceedings of 13th Asian International Conference on Fluid Machinery, Paper No. AICFM13-153, Tokyo · Zbl 1390.76689
[59] Brooks AN, Hughes TJR (1982) Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput Methods Appl Mech Eng 32:199-259 · Zbl 0497.76041 · doi:10.1016/0045-7825(82)90071-8
[60] Bazilevs Y, Korobenko A, Deng X, Yan J (2015) Novel structural modeling and mesh moving techniques for advanced FSI simulation of wind turbines. Int J Numer Methods Eng 102:766-783. doi:10.1002/nme.4738 · Zbl 1352.76033 · doi:10.1002/nme.4738
[61] Tezduyar TE, Osawa Y (2000) Finite element stabilization parameters computed from element matrices and vectors. Comput Methods Appl Mech Eng 190:411-430. doi:10.1016/S0045-7825(00)00211-5 · Zbl 0973.76057 · doi:10.1016/S0045-7825(00)00211-5
[62] Tezduyar TE, Ganjoo DK (1986) Petrov-Galerkin formulations with weighting functions dependent upon spatial and temporal discretization: Applications to transient convection-diffusion problems. Comput Methods Appl Mech Eng 59:49-71. doi:10.1016/0045-7825(86)90023-X · Zbl 0604.76077 · doi:10.1016/0045-7825(86)90023-X
[63] Le Beau GJ, Ray SE, Aliabadi SK, Tezduyar TE (1993) SUPG finite element computation of compressible flows with the entropy and conservation variables formulations. Comput Methods Appl Mech Eng 104:397-422. doi:10.1016/0045-7825(93)90033-T · Zbl 0772.76037 · doi:10.1016/0045-7825(93)90033-T
[64] Tezduyar TE (2007) Finite elements in fluids: Stabilized formulations and moving boundaries and interfaces. Comput Fluids 36:191-206. doi:10.1016/j.compfluid.2005.02.011 · Zbl 1177.76202 · doi:10.1016/j.compfluid.2005.02.011
[65] Tezduyar TE, Senga M (2006) Stabilization and shock-capturing parameters in SUPG formulation of compressible flows. Comput Methods Appl Mech Eng 195:1621-1632. doi:10.1016/j.cma.2005.05.032 · Zbl 1122.76061 · doi:10.1016/j.cma.2005.05.032
[66] Tezduyar TE, Senga M (2007) SUPG finite element computation of inviscid supersonic flows with YZ \[\beta\] β shock-capturing. Comput Fluids 36:147-159. doi:10.1016/j.compfluid.2005.07.009 · Zbl 1127.76029 · doi:10.1016/j.compfluid.2005.07.009
[67] Tezduyar TE, Senga M, Vicker D (2006) Computation of inviscid supersonic flows around cylinders and spheres with the SUPG formulation and YZ \[\beta\] β shock-capturing. Comput Mech 38:469-481. doi:10.1007/s00466-005-0025-6 · Zbl 1176.76077 · doi:10.1007/s00466-005-0025-6
[68] Tezduyar TE, Sathe S (2006) Enhanced-discretization selective stabilization procedure (EDSSP). Comput Mech 38:456-468. doi:10.1007/s00466-006-0056-7 · Zbl 1187.76712 · doi:10.1007/s00466-006-0056-7
[69] Corsini A, Rispoli F, Santoriello A, Tezduyar TE (2006) Improved discontinuity-capturing finite element techniques for reaction effects in turbulence computation. Comput Mech 38:356-364. doi:10.1007/s00466-006-0045-x · Zbl 1177.76192 · doi:10.1007/s00466-006-0045-x
[70] Rispoli F, Corsini A, Tezduyar TE (2007) Finite element computation of turbulent flows with the discontinuity-capturing directional dissipation (DCDD). Comput Fluids 36:121-126. doi:10.1016/j.compfluid.2005.07.004 · Zbl 1181.76098 · doi:10.1016/j.compfluid.2005.07.004
[71] Tezduyar TE, Ramakrishnan S, Sathe S (2008) Stabilized formulations for incompressible flows with thermal coupling. Int J Numer Methods Fluids 57:1189-1209. doi:10.1002/fld.1743 · Zbl 1140.76024 · doi:10.1002/fld.1743
[72] Rispoli F, Saavedra R, Corsini A, Tezduyar TE (2007) Computation of inviscid compressible flows with the V-SGS stabilization and YZ \[\beta\] β shock-capturing. Int J Numer Methods Fluids 54:695-706. doi:10.1002/fld.1447 · Zbl 1207.76104 · doi:10.1002/fld.1447
[73] Bazilevs Y, Calo VM, Tezduyar TE, Hughes TJR (2007) YZ \[\beta\] β discontinuity-capturing for advection-dominated processes with application to arterial drug delivery. Int J Numer Methods Fluids 54:593-608. doi:10.1002/fld.1484 · Zbl 1207.76049 · doi:10.1002/fld.1484
[74] Corsini A, Menichini C, Rispoli F, Santoriello A, Tezduyar TE (2009) A multiscale finite element formulation with discontinuity capturing for turbulence models with dominant reactionlike terms. J Appl Mech 76:021211. doi:10.1115/1.3062967 · doi:10.1115/1.3062967
[75] Rispoli F, Saavedra R, Menichini F, Tezduyar TE (2009) Computation of inviscid supersonic flows around cylinders and spheres with the V-SGS stabilization and YZ \[\beta\] β shock-capturing. J Appl Mech 76:021209. doi:10.1115/1.3057496 · doi:10.1115/1.3057496
[76] Corsini A, Iossa C, Rispoli F, Tezduyar TE (2010) A DRD finite element formulation for computing turbulent reacting flows in gas turbine combustors. Comput Mech 46:159-167. doi:10.1007/s00466-009-0441-0 · Zbl 1301.76045 · doi:10.1007/s00466-009-0441-0
[77] Hsu M-C, Bazilevs Y, Calo VM, Tezduyar TE, Hughes TJR (2010) Improving stability of stabilized and multiscale formulations in flow simulations at small time steps. Comput Methods Appl Mech Eng 199:828-840. doi:10.1016/j.cma.2009.06.019 · Zbl 1406.76028 · doi:10.1016/j.cma.2009.06.019
[78] Corsini A, Rispoli F, Tezduyar TE (2011) Stabilized finite element computation of NOx emission in aero-engine combustors. Int J Numer Methods Fluids 65:254-270. doi:10.1002/fld.2451 · Zbl 1426.76240 · doi:10.1002/fld.2451
[79] Corsini A, Rispoli F, Tezduyar TE (2012) Computer modeling of wave-energy air turbines with the SUPG/PSPG formulation and discontinuity-capturing technique. J Appl Mech 79:010910. doi:10.1115/1.4005060 · doi:10.1115/1.4005060
[80] Corsini A, Rispoli F, Sheard AG, Tezduyar TE (2012) Computational analysis of noise reduction devices in axial fans with stabilized finite element formulations. Comput Mech 50:695-705. doi:10.1007/s00466-012-0789-4 · Zbl 1311.76121 · doi:10.1007/s00466-012-0789-4
[81] Kler PA, Dalcin LD, Paz RR, Tezduyar TE (2013) SUPG and discontinuity-capturing methods for coupled fluid mechanics and electrochemical transport problems. Comput Mech 51:171-185. doi:10.1007/s00466-012-0712-z · Zbl 1312.76062
[82] Corsini A, Rispoli F, Sheard AG, Takizawa K, Tezduyar TE, Venturini P (2014) A variational multiscale method for particle-cloud tracking in turbomachinery flows. Comput Mech 54:1191-1202. doi:10.1007/s00466-014-1050-0 · Zbl 1311.76030 · doi:10.1007/s00466-014-1050-0
[83] Rispoli F, Delibra G, Venturini P, Corsini A, Saavedra R, Tezduyar TE (2015) Particle tracking and particle-shock interaction in compressible-flow computations with the V-SGS stabilization and YZ \[\beta\] β shock-capturing. Comput Mech 55:1201-1209. doi:10.1007/s00466-015-1160-3 · Zbl 1325.76121 · doi:10.1007/s00466-015-1160-3
[84] Bazilevs Y, Hughes TJR (2007) Weak imposition of Dirichlet boundary conditions in fluid mechanics. Comput Fluids 36:12-26 · Zbl 1115.76040 · doi:10.1016/j.compfluid.2005.07.012
[85] Tezduyar TE, Sathe S, Pausewang J, Schwaab M, Christopher J, Crabtree J (2008) Interface projection techniques for fluid-structure interaction modeling with moving-mesh methods. Comput Mech 43:39-49. doi:10.1007/s00466-008-0261-7 · Zbl 1310.74049 · doi:10.1007/s00466-008-0261-7
[86] Takizawa K, Tezduyar TE (2012) Computational methods for parachute fluid-structure interactions. Arch Comput Methods Eng 19:125-169. doi:10.1007/s11831-012-9070-4 · Zbl 1354.76113 · doi:10.1007/s11831-012-9070-4
[87] Saad Y, Schultz M (1986) GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Stat Comput 7:856-869 · Zbl 0599.65018 · doi:10.1137/0907058
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