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Ventricle-valve-aorta flow analysis with the space-time isogeometric discretization and topology change. (English) Zbl 1465.76118

Summary: We address the computational challenges of and presents results from ventricle-valve-aorta flow analysis. Including the left ventricle (LV) in the model makes the flow into the valve, and consequently the flow into the aorta, anatomically more realistic. The challenges include accurate representation of the boundary layers near moving solid surfaces even when the valve leaflets come into contact, computation with high geometric complexity, anatomically realistic representation of the LV motion, and flow stability at the inflow boundary, which has a traction condition. The challenges are mainly addressed with a Space-Time (ST) method that integrates three special ST methods around the core, ST Variational Multiscale (ST-VMS) method. The three special methods are the ST Slip Interface (ST-SI) and ST Topology Change (ST-TC) methods and ST Isogeometric Analysis (ST-IGA). The ST-discretization feature of the integrated method, ST-SI-TC-IGA, provides higher-order accuracy compared to standard discretization methods. The VMS feature addresses the computational challenges associated with the multiscale nature of the unsteady flow in the LV, valve and aorta. The moving-mesh feature of the ST framework enables high-resolution computation near the leaflets. The ST-TC enables moving-mesh computation even with the TC created by the contact between the leaflets, dealing with the contact while maintaining high-resolution representation near the leaflets. The ST-IGA provides smoother representation of the LV, valve and aorta surfaces and increased accuracy in the flow solution. The ST-SI connects the separately generated LV, valve and aorta NURBS meshes, enabling easier mesh generation, connects the mesh zones containing the leaflets, enabling a more effective mesh moving, helps the ST-TC deal with leaflet-leaflet contact location change and contact sliding, and helps the ST-TC and ST-IGA keep the element density in the narrow spaces near the contact areas at a reasonable level. The ST-SI-TC-IGA is supplemented with two other special methods in this article. A structural mechanics computation method generates the LV motion from the CT scans of the LV and anatomically realistic values for the LV volume ratio. The Constrained-Flow-Profile (CFP) Traction provides flow stability at the inflow boundary. Test computation with the CFP Traction shows its effectiveness as an inflow stabilization method, and computation with the LV-valve-aorta model shows the effectiveness of the ST-SI-TC-IGA and the two supplemental methods.

MSC:

76Z05 Physiological flows
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76M99 Basic methods in fluid mechanics
74S22 Isogeometric methods applied to problems in solid mechanics

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References:

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[88] Takizawa, K.; Tezduyar, TE; Boswell, C.; Kolesar, R.; Montel, K., FSI modeling of the reefed stages and disreefing of the Orion spacecraft parachutes, Comput Mech, 54, 1203-1220 (2014) · doi:10.1007/s00466-014-1052-y
[89] Takizawa, K.; Tezduyar, TE; Kolesar, R.; Boswell, C.; Kanai, T.; Montel, K., Multiscale methods for gore curvature calculations from FSI modeling of spacecraft parachutes, Comput Mech, 54, 1461-1476 (2014) · Zbl 1309.74025 · doi:10.1007/s00466-014-1069-2
[90] Takizawa, K.; Tezduyar, TE; Kolesar, R., FSI modeling of the Orion spacecraft drogue parachutes, Comput Mech, 55, 1167-1179 (2015) · Zbl 1325.74169 · doi:10.1007/s00466-014-1108-z
[91] Takizawa, K.; Henicke, B.; Tezduyar, TE; Hsu, M-C; Bazilevs, Y., Stabilized space-time computation of wind-turbine rotor aerodynamics, Comput Mech, 48, 333-344 (2011) · Zbl 1398.76127 · doi:10.1007/s00466-011-0589-2
[92] Takizawa, K.; Henicke, B.; Montes, D.; Tezduyar, TE; Hsu, M-C; Bazilevs, Y., Numerical-performance studies for the stabilized space-time computation of wind-turbine rotor aerodynamics, Comput Mech, 48, 647-657 (2011) · Zbl 1334.74032 · doi:10.1007/s00466-011-0614-5
[93] Takizawa, K.; Tezduyar, TE; McIntyre, S.; Kostov, N.; Kolesar, R.; Habluetzel, C., Space-time VMS computation of wind-turbine rotor and tower aerodynamics, Comput Mech, 53, 1-15 (2014) · Zbl 1398.76129 · doi:10.1007/s00466-013-0888-x
[94] Takizawa, K.; Bazilevs, Y.; Tezduyar, TE; Hsu, M-C; Øiseth, O.; Mathisen, KM; Kostov, N.; McIntyre, S., Engineering analysis and design with ALE-VMS and space-time methods, Arch Comput Methods Eng, 21, 481-508 (2014) · Zbl 1348.74104 · doi:10.1007/s11831-014-9113-0
[95] Takizawa, K., Computational engineering analysis with the new-generation space-time methods, Comput Mech, 54, 193-211 (2014) · doi:10.1007/s00466-014-0999-z
[96] Takizawa, K.; Henicke, B.; Puntel, A.; Kostov, N.; Tezduyar, TE, Space-time techniques for computational aerodynamics modeling of flapping wings of an actual locust, Comput Mech, 50, 743-760 (2012) · Zbl 1286.76179 · doi:10.1007/s00466-012-0759-x
[97] Takizawa, K.; Henicke, B.; Puntel, A.; Kostov, N.; Tezduyar, TE, Computer modeling techniques for flapping-wing aerodynamics of a locust, Comput Fluids, 85, 125-134 (2013) · Zbl 1290.76170 · doi:10.1016/j.compfluid.2012.11.008
[98] Takizawa, K.; Kostov, N.; Puntel, A.; Henicke, B.; Tezduyar, TE, Space-time computational analysis of bio-inspired flapping-wing aerodynamics of a micro aerial vehicle, Comput Mech, 50, 761-778 (2012) · Zbl 1286.76180 · doi:10.1007/s00466-012-0758-y
[99] Takizawa, K.; Tezduyar, TE; Kostov, N., Sequentially-coupled space-time FSI analysis of bio-inspired flapping-wing aerodynamics of an MAV, Comput Mech, 54, 213-233 (2014) · doi:10.1007/s00466-014-0980-x
[100] Takizawa, K.; Tezduyar, TE; Buscher, A., Space-time computational analysis of MAV flapping-wing aerodynamics with wing clapping, Comput Mech, 55, 1131-1141 (2015) · doi:10.1007/s00466-014-1095-0
[101] Takizawa, K.; Bazilevs, Y.; Tezduyar, TE; Long, CC; Marsden, AL; Schjodt, K., ST and ALE-VMS methods for patient-specific cardiovascular fluid mechanics modeling, Math Models Methods Appl Sci, 24, 2437-2486 (2014) · Zbl 1296.76113 · doi:10.1142/S0218202514500250
[102] Takizawa, K.; Schjodt, K.; Puntel, A.; Kostov, N.; Tezduyar, TE, Patient-specific computer modeling of blood flow in cerebral arteries with aneurysm and stent, Comput Mech, 50, 675-686 (2012) · Zbl 1311.76157 · doi:10.1007/s00466-012-0760-4
[103] Takizawa, K.; Schjodt, K.; Puntel, A.; Kostov, N.; Tezduyar, TE, Patient-specific computational analysis of the influence of a stent on the unsteady flow in cerebral aneurysms, Comput Mech, 51, 1061-1073 (2013) · Zbl 1366.76106 · doi:10.1007/s00466-012-0790-y
[104] Suito, H.; Takizawa, K.; Huynh, VQH; Sze, D.; Ueda, T., FSI analysis of the blood flow and geometrical characteristics in the thoracic aorta, Comput Mech, 54, 1035-1045 (2014) · Zbl 1311.74044 · doi:10.1007/s00466-014-1017-1
[105] Suito, H.; Takizawa, K.; Huynh, VQH; Sze, D.; Ueda, T.; Tezduyar, TE; Bazilevs, Y.; Takizawa, K., A geometrical-characteristics study in patient-specific FSI analysis of blood flow in the thoracic aorta, Advances in computational fluid-structure interaction and flow simulation: new methods and challenging computations, modeling and simulation in science, engineering and technology, 379-386 (2016), Berlin: Springer, Berlin · Zbl 1356.76471
[106] Takizawa, K.; Tezduyar, TE; Uchikawa, H.; Terahara, T.; Sasaki, T.; Shiozaki, K.; Yoshida, A.; Komiya, K.; Inoue, G.; Tezduyar, TE, Aorta flow analysis and heart valve flow and structure analysis, Frontiers in computational fluid-structure interaction and flow simulation: research from lead investigators under forty - 2018, modeling and simulation in science, engineering and technology, 29-89 (2018), Berlin: Springer, Berlin · Zbl 1406.76003
[107] Takizawa, K.; Tezduyar, TE; Uchikawa, H.; Terahara, T.; Sasaki, T.; Yoshida, A., Mesh refinement influence and cardiac-cycle flow periodicity in aorta flow analysis with isogeometric discretization, Comput Fluids, 179, 790-798 (2019) · Zbl 1411.76184 · doi:10.1016/j.compfluid.2018.05.025
[108] Takizawa, K.; Bazilevs, Y.; Tezduyar, TE; Hsu, M-C, Computational cardiovascular flow analysis with the variational multiscale methods, J Adv Eng Comput, 3, 366-405 (2019) · doi:10.25073/jaec.201932.245
[109] Takizawa, K.; Tezduyar, TE; Bazilevs, Y.; Takizawa, K., New directions in space-time computational methods, Advances in computational fluid-structure interaction and flow simulation: new methods and challenging computations, modeling and simulation in science, engineering and technology, 159-178 (2016), Berlin: Springer, Berlin · Zbl 1356.76291
[110] Takizawa, K.; Tezduyar, TE; Terahara, T.; Sasaki, T.; Wriggers, P.; Lenarz, T., Heart valve flow computation with the space-time slip interface topology change (ST-SI-TC) method and isogeometric analysis (IGA), Biomedical technology: modeling, experiments and simulation, lecture notes in applied and computational mechanics, 77-99 (2018), Berlin: Springer, Berlin
[111] Terahara, T.; Takizawa, K.; Tezduyar, TE; Bazilevs, Y.; Hsu, M-C, Heart valve isogeometric sequentially-coupled FSI analysis with the space-time topology change method, Comput Mech (2020) · Zbl 1462.74119 · doi:10.1007/s00466-019-01813-0
[112] Yu, Y.; Zhang, YJ; Takizawa, K.; Tezduyar, TE; Sasaki, T., Anatomically realistic lumen motion representation in patient-specific space-time isogeometric flow analysis of coronary arteries with time-dependent medical-image data, Comput Mech (2019) · Zbl 1490.76260 · doi:10.1007/s00466-019-01774-4
[113] Takizawa, K.; Montes, D.; McIntyre, S.; Tezduyar, TE, Space-time VMS methods for modeling of incompressible flows at high Reynolds numbers, Math Models Methods Appl Sci, 23, 223-248 (2013) · Zbl 1261.76037 · doi:10.1142/s0218202513400022
[114] Takizawa, K.; Tezduyar, TE; Hattori, H., Computational analysis of flow-driven string dynamics in turbomachinery, Comput Fluids, 142, 109-117 (2017) · Zbl 1390.76011 · doi:10.1016/j.compfluid.2016.02.019
[115] Komiya, K.; Kanai, T.; Otoguro, Y.; Kaneko, M.; Hirota, K.; Zhang, Y.; Takizawa, K.; Tezduyar, TE; Nohmi, M.; Tsuneda, T.; Kawai, M.; Isono, M., Computational analysis of flow-driven string dynamics in a pump and residence time calculation, IOP Conf Ser Earth Environ Sci, 240, 062014 (2019) · doi:10.1088/1755-1315/240/6/062014
[116] Kanai, T.; Takizawa, K.; Tezduyar, TE; Komiya, K.; Kaneko, M.; Hirota, K.; Nohmi, M.; Tsuneda, T.; Kawai, M.; Isono, M., Methods for computation of flow-driven string dynamics in a pump and residence time, Math Models Methods Appl Sci, 29, 839-870 (2019) · Zbl 1425.76139 · doi:10.1142/S021820251941001X
[117] Otoguro, Y.; Takizawa, K.; Tezduyar, TE, Space-time VMS computational flow analysis with isogeometric discretization and a general-purpose NURBS mesh generation method, Comput Fluids, 158, 189-200 (2017) · Zbl 1390.76345 · doi:10.1016/j.compfluid.2017.04.017
[118] Otoguro, Y.; Takizawa, K.; Tezduyar, TE; Tezduyar, TE, A general-purpose NURBS mesh generation method for complex geometries, Frontiers in computational fluid-structure interaction and flow simulation: research from lead investigators under forty—2018, modeling and simulation in science, engineering and technology, 399-434 (2018), Berlin: Springer, Berlin · Zbl 1406.76003
[119] Otoguro, Y.; Takizawa, K.; Tezduyar, TE; Nagaoka, K.; Mei, S., Turbocharger turbine and exhaust manifold flow computation with the space-time variational multiscale method and isogeometric analysis, Comput Fluids, 179, 764-776 (2019) · Zbl 1411.76070 · doi:10.1016/j.compfluid.2018.05.019
[120] Otoguro, Y.; Takizawa, K.; Tezduyar, TE; Nagaoka, K.; Avsar, R.; Zhang, Y., Space-time VMS flow analysis of a turbocharger turbine with isogeometric discretization: computations with time-dependent and steady-inflow representations of the intake/exhaust cycle, Comput Mech, 64, 1403-1419 (2019) · Zbl 1467.76044 · doi:10.1007/s00466-019-01722-2
[121] Takizawa, K.; Tezduyar, TE; Asada, S.; Kuraishi, T., Space-time method for flow computations with slip interfaces and topology changes (ST-SI-TC), Comput Fluids, 141, 124-134 (2016) · Zbl 1390.76358 · doi:10.1016/j.compfluid.2016.05.006
[122] Kuraishi, T.; Takizawa, K.; Tezduyar, TE; Tezduyar, TE, Space-time computational analysis of tire aerodynamics with actual geometry, road contact and tire deformation, Frontiers in computational fluid-structure interaction and flow simulation: research from lead investigators under forty—2018, modeling and simulation in science, engineering and technology, 337-376 (2018), Berlin: Springer, Berlin · Zbl 1406.76003
[123] Kuraishi, T.; Takizawa, K.; Tezduyar, TE, Space-time Isogeometric flow analysis with built-in Reynolds-equation limit, Math Models Methods Appl Sci, 29, 871-904 (2019) · Zbl 1425.76142 · doi:10.1142/S0218202519410021
[124] Takizawa, K.; Tezduyar, TE; Terahara, T., Ram-air parachute structural and fluid mechanics computations with the space-time isogeometric analysis (ST-IGA), Comput Fluids, 141, 191-200 (2016) · Zbl 1390.76359 · doi:10.1016/j.compfluid.2016.05.027
[125] Takizawa, K.; Tezduyar, TE; Kanai, T., Porosity models and computational methods for compressible-flow aerodynamics of parachutes with geometric porosity, Math Models Methods Appl Sci, 27, 771-806 (2017) · Zbl 1361.76017 · doi:10.1142/S0218202517500166
[126] Kanai, T.; Takizawa, K.; Tezduyar, TE; Tanaka, T.; Hartmann, A., Compressible-flow geometric-porosity modeling and spacecraft parachute computation with isogeometric discretization, Comput Mech, 63, 301-321 (2019) · Zbl 1462.76145 · doi:10.1007/s00466-018-1595-4
[127] Hsu, M-C; Bazilevs, Y.; Calo, VM; Tezduyar, TE; Hughes, TJR, Improving stability of stabilized and multiscale formulations in flow simulations at small time steps, Comput Methods Appl Mech Eng, 199, 828-840 (2010) · Zbl 1406.76028 · doi:10.1016/j.cma.2009.06.019
[128] Takizawa, K.; Tezduyar, TE; Otoguro, Y., Stabilization and discontinuity-capturing parameters for space-time flow computations with finite element and isogeometric discretizations, Comput Mech, 62, 1169-1186 (2018) · Zbl 1462.76128 · doi:10.1007/s00466-018-1557-x
[129] Takizawa, K.; Ueda, Y.; Tezduyar, TE, A node-numbering-invariant directional length scale for simplex elements, Math Models Methods Appl Sci (2019) · doi:10.1142/S0218202519500581
[130] Otoguro, Y.; Takizawa, K.; Tezduyar, TE, Element length calculation in B-spline meshes for complex geometries, Comput Mech (2020) · Zbl 1462.76148 · doi:10.1007/s00466-019-01809-w
[131] Corsini, A.; Menichini, C.; Rispoli, F.; Santoriello, A.; Tezduyar, TE, A multiscale finite element formulation with discontinuity capturing for turbulence models with dominant reaction like terms, J Appl Mech, 76, 021211 (2009) · doi:10.1115/1.3062967
[132] Rispoli, F.; Saavedra, R.; Menichini, F.; Tezduyar, TE, Computation of inviscid supersonic flows around cylinders and spheres with the V-SGS stabilization and YZ \(\beta\) shock-capturing, J Appl Mech, 76, 021209 (2009) · doi:10.1115/1.3057496
[133] Corsini, A.; Iossa, C.; Rispoli, F.; Tezduyar, TE, A DRD finite element formulation for computing turbulent reacting flows in gas turbine combustors, Comput Mech, 46, 159-167 (2010) · Zbl 1301.76045 · doi:10.1007/s00466-009-0441-0
[134] Corsini, A.; Rispoli, F.; Tezduyar, TE, Stabilized finite element computation of NOx emission in aero-engine combustors, Int J Numer Methods Fluids, 65, 254-270 (2011) · Zbl 1426.76240 · doi:10.1002/fld.2451
[135] Corsini, A.; Rispoli, F.; Tezduyar, TE, Computer modeling of wave-energy air turbines with the SUPG/PSPG formulation and discontinuity-capturing technique, J Appl Mech, 79, 010910 (2012) · doi:10.1115/1.4005060
[136] Corsini, A.; Rispoli, F.; Sheard, AG; Tezduyar, TE, Computational analysis of noise reduction devices in axial fans with stabilized finite element formulations, Comput Mech, 50, 695-705 (2012) · Zbl 1311.76121 · doi:10.1007/s00466-012-0789-4
[137] Kler, PA; Dalcin, LD; Paz, RR; Tezduyar, TE, SUPG and discontinuity-capturing methods for coupled fluid mechanics and electrochemical transport problems, Comput Mech, 51, 171-185 (2013) · Zbl 1312.76062 · doi:10.1007/s00466-012-0712-z
[138] Corsini, A.; Rispoli, F.; Sheard, AG; Takizawa, K.; Tezduyar, TE; Venturini, P., A variational multiscale method for particle-cloud tracking in turbomachinery flows, Comput Mech, 54, 1191-1202 (2014) · Zbl 1311.76030 · doi:10.1007/s00466-014-1050-0
[139] Rispoli, F.; Delibra, G.; Venturini, P.; Corsini, A.; Saavedra, R.; Tezduyar, TE, Particle tracking and particle-shock interaction in compressible-flow computations with the V-SGS stabilization and YZ \(\beta\) shock-capturing, Comput Mech, 55, 1201-1209 (2015) · Zbl 1325.76121 · doi:10.1007/s00466-015-1160-3
[140] Cardillo, L.; Corsini, A.; Delibra, G.; Rispoli, F.; Tezduyar, TE, Flow analysis of a wave-energy air turbine with the SUPG/PSPG stabilization and discontinuity-capturing directional dissipation, Comput Fluids, 141, 184-190 (2016) · Zbl 1390.76295 · doi:10.1016/j.compfluid.2016.07.011
[141] Castorrini, A.; Corsini, A.; Rispoli, F.; Venturini, P.; Takizawa, K.; Tezduyar, TE, Computational analysis of wind-turbine blade rain erosion, Comput Fluids, 141, 175-183 (2016) · Zbl 1390.76298 · doi:10.1016/j.compfluid.2016.08.013
[142] Castorrini, A.; Corsini, A.; Rispoli, F.; Venturini, P.; Takizawa, K.; Tezduyar, TE, Computational analysis of performance deterioration of a wind turbine blade strip subjected to environmental erosion, Comput Mech, 64, 1133-1153 (2019) · Zbl 1467.74083 · doi:10.1007/s00466-019-01697-0
[143] Tezduyar, TE; Aliabadi, SK; Behr, M.; Mittal, S., Massively parallel finite element simulation of compressible and incompressible flows, Comput Methods Appl Mech Eng, 119, 157-177 (1994) · Zbl 0848.76040 · doi:10.1016/0045-7825(94)00082-4
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[145] Takizawa, K.; Takagi, H.; Tezduyar, TE; Torii, R., Estimation of element-based zero-stress state for arterial FSI computations, Comput Mech, 54, 895-910 (2014) · Zbl 1398.74096 · doi:10.1007/s00466-013-0919-7
[146] Takizawa, K.; Torii, R.; Takagi, H.; Tezduyar, TE; Xu, XY, Coronary arterial dynamics computation with medical-image-based time-dependent anatomical models and element-based zero-stress state estimates, Comput Mech, 54, 1047-1053 (2014) · Zbl 1311.76158 · doi:10.1007/s00466-014-1049-6
[147] Takizawa, K.; Tezduyar, TE; Sasaki, T.; Wriggers, P.; Lenarz, T., Estimation of element-based zero-stress state in arterial FSI computations with isogeometric wall discretization, Biomedical technology: modeling, experiments and simulation, lecture notes in applied and computational mechanics, 101-122 (2018), Berlin: Springer, Berlin
[148] Takizawa, K.; Tezduyar, TE; Sasaki, T., Aorta modeling with the element-based zero-stress state and isogeometric discretization, Comput Mech, 59, 265-280 (2017) · doi:10.1007/s00466-016-1344-5
[149] Sasaki, T.; Takizawa, K.; Tezduyar, TE, Aorta zero-stress state modeling with T-spline discretization, Comput Mech, 63, 1315-1331 (2019) · Zbl 1465.74125 · doi:10.1007/s00466-018-1651-0
[150] Sasaki, T.; Takizawa, K.; Tezduyar, TE, Medical-image-based aorta modeling with zero-stress-state estimation, Comput Mech, 64, 249-271 (2019) · Zbl 1469.74085 · doi:10.1007/s00466-019-01669-4
[151] Takizawa, K.; Tezduyar, TE; Sasaki, T., Isogeometric hyperelastic shell analysis with out-of-plane deformation mapping, Comput Mech, 63, 681-700 (2019) · Zbl 1464.74107 · doi:10.1007/s00466-018-1616-3
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