×

Space-time SUPG finite element computation of shallow-water flows with moving shorelines. (English) Zbl 1398.76126

Summary: We show that combination of the Deforming-Spatial-Domain/Stabilized Space-Time and the Streamline-Upwind/Petrov-Galerkin formulations can be used quite effectively for computation of shallow-water flows with moving shorelines. The combined formulation is supplemented with a stabilization parameter that was originally introduced for compressible flows, a compressible-flow shock-capturing parameter adapted for shallow-water flows, and remeshing based on using a background mesh. We present a number of test computations and provide comparisons to theoretical results, experimental data and results computed with nonmoving meshes.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76D05 Navier-Stokes equations for incompressible viscous fluids
76Z05 Physiological flows
65Y05 Parallel numerical computation
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] 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
[2] 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
[3] Tezduyar TE, Behr M, Liou J (1992) A new strategy for finite element computations involving moving boundaries and interfaces–the deforming-spatial-domain/space–time procedure: I. The concept and the preliminary numerical tests. Comput Methods Appl Mech Eng 94: 339–351. doi: 10.1016/0045-7825(92)90059-S · Zbl 0745.76044
[4] Tezduyar TE, Behr M, Mittal S, Liou J (1992) A new strategy for finite element computations involving moving boundaries and interfaces–the deforming-spatial-domain/space–time procedure: II. Computation of free-surface flows, two-liquid flows, and flows with drifting cylinders. Comput Methods Appl Mech Eng 94: 353–371. doi: 10.1016/0045-7825(92)90060-W · Zbl 0745.76045
[5] Tezduyar T, Aliabadi S, Behr M, Johnson A, Mittal S (1993) Parallel finite-element computation of 3D flows. Computer 26: 27–36. doi: 10.1109/2.237441 · Zbl 05090697
[6] Behr M, Johnson A, Kennedy J, Mittal S, Tezduyar T (1993) Computation of incompressible flows with implicit finite element implementations on the connection machine. Comput Methods Appl Mech Eng 108: 99–118. doi: 10.1016/0045-7825(93)90155-Q · Zbl 0784.76046
[7] Tezduyar TE, Aliabadi SK, Behr M, Mittal S (1994) Massively parallel finite element simulation of compressible and incompressible flows. Comput Methods Appl Mech Eng 119: 157–177. doi: 10.1016/0045-7825(94)00082-4 · Zbl 0848.76040
[8] Mittal S, Tezduyar TE (1994) Massively parallel finite element computation of incompressible flows involving fluid-body interactions. Comput Methods Appl Mech Eng 112: 253–282. doi: 10.1016/0045-7825(94)90029-9 · Zbl 0846.76048
[9] Mittal S, Tezduyar TE (1995) Parallel finite element simulation of 3D incompressible flows–fluid-structure interactions. Int J Numer Methods Fluids 21: 933–953. doi: 10.1002/fld.1650211011 · Zbl 0873.76047
[10] Aliabadi SK, Tezduyar TE (1995) Parallel fluid dynamics computations in aerospace applications. Int J Numer Methods Fluids 21: 783–805. doi: 10.1002/fld.1650211003 · Zbl 0862.76033
[11] Tezduyar T, Aliabadi S, Behr M, Johnson A, Kalro V, Litke M (1996) Flow simulation and high performance computing. Comput Mech 18: 397–412. doi: 10.1007/BF00350249 · Zbl 0893.76046
[12] Johnson AA, Tezduyar TE (1997) Parallel computation of incompressible flows with complex geometries. Int J Numer Methods Fluids 24: 1321–1340. doi: 10.1002/(SICI)1097-0363(199706)24:12<1321::AID-FLD562>3.3.CO;2-C · Zbl 0882.76044
[13] Guler I, Behr M, Tezduyar T (1999) Parallel finite element computation of free-surface flows. Comput Mech 23: 117–123. doi: 10.1007/s004660050391 · Zbl 0948.76039
[14] Johnson AA, Tezduyar TE (1999) Advanced mesh generation and update methods for 3D flow simulations. Comput Mech 23: 130–143. doi: 10.1007/s004660050393 · Zbl 0949.76049
[15] Behr M, Tezduyar T (1999) The shear-slip mesh update method. Comput Methods Appl Mech Eng 174: 261–274. doi: 10.1016/S0045-7825(98)00299-0 · Zbl 0959.76037
[16] Kalro V, Tezduyar TE (2000) A parallel 3D computational method for fluid–structure interactions in parachute systems. Comput Methods Appl Mech Eng 190: 321–332. doi: 10.1016/S0045-7825(00)00204-8 · Zbl 0993.76044
[17] Stein K, Benney R, Kalro V, Tezduyar TE, Leonard J, Accorsi M (2000) Parachute fluid–structure interactions: 3-D computation. Comput Methods Appl Mech Eng 190: 373–386. doi: 10.1016/S0045-7825(00)00208-5 · Zbl 0973.76055
[18] Tezduyar TE (2001) Finite element methods for flow problems with moving boundaries and interfaces. Arch Comput Methods Eng 8: 83–130. doi: 10.1007/BF02897870 · Zbl 1039.76037
[19] Tezduyar T, Osawa Y (2001) Fluid–structure interactions of a parachute crossing the far wake of an aircraft. Comput Methods Appl Mech Eng 191: 717–726. doi: 10.1016/S0045-7825(01)00311-5 · Zbl 1113.76407
[20] Stein K, Benney R, Tezduyar T, Potvin J (2001) Fluid–structure interactions of a cross parachute: Numerical simulation. Comput Methods Appl Mech Eng 191: 673–687. doi: 10.1016/S0045-7825(01)00312-7 · Zbl 0999.76085
[21] Ohayon R (2001) Reduced symmetric models for modal analysis of internal structural-acoustic and hydroelastic-sloshing systems. Comput Methods Appl Mech Eng 190: 3009–3019 · Zbl 0971.74032
[22] Stein K, Tezduyar T, Benney R (2003) Mesh moving techniques for fluid–structure interactions with large displacements. J Appl Mech 70: 58–63. doi: 10.1115/1.1530635 · Zbl 1110.74689
[23] 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
[24] Stein K, Tezduyar TE, Benney R (2004) Automatic mesh update with the solid-extension mesh moving technique. Comput Methods Appl Mech Eng 193: 2019–2032. doi: 10.1016/j.cma.2003.12.046 · Zbl 1067.74587
[25] van Brummelen EH, de Borst R (2005) On the nonnormality of subiteration for a fluid-structure interaction problem. SIAM J Sci Comput 27: 599–621 · Zbl 1136.65334
[26] Tezduyar TE, Sathe S, Keedy R, Stein K (2006) Space–time finite element techniques for computation of fluid–structure interactions. Comput Methods Appl Mech Eng 195: 2002–2027. doi: 10.1016/j.cma.2004.09.014 · Zbl 1118.74052
[27] Tezduyar TE, Sathe S, Stein K (2006) Solution techniques for the fully-discretized equations in computation of fluid–structure interactions with the space–time formulations. Comput Methods Appl Mech Eng 195: 5743–5753. doi: 10.1016/j.cma.2005.08.023 · Zbl 1123.76035
[28] Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2006) Computer modeling of cardiovascular fluid–structure interactions with the deforming-spatial-domain/stabilized space–time formulation. Comput Methods Appl Mech Eng 195: 1885–1895. doi: 10.1016/j.cma.2005.05.050 · Zbl 1178.76241
[29] Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2006) Fluid–structure interaction modeling of aneurysmal conditions with high and normal blood pressures. Comput Mech 38: 482–490. doi: 10.1007/s00466-006-0065-6 · Zbl 1160.76061
[30] 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
[31] Khurram RA, Masud A (2006) A multiscale/stabilized formulation of the incompressible Navier–Stokes equations for moving boundary flows and fluid–structure interaction. Comput Mech 38: 403–416 · Zbl 1184.76720
[32] 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
[33] Brenk M, Bungartz H-J, Mehl M, Neckel T (2006) Fluid–structure interaction on Cartesian grids: flow simulation and coupling environment. In: Bungartz H-J, Schafer M (eds) Fluid–structure interaction. Lecture notes in computational science and engineering, vol 53. Springer, Berlin, pp 233–269 · Zbl 1323.76047
[34] Tezduyar TE, Sathe S, Cragin T, Nanna B, Conklin BS, Pausewang J, Schwaab M (2007) Modeling of fluid–structure interactions with the space–time finite elements: arterial fluid mechanics. Int J Numer Methods Fluids 54: 901–922. doi: 10.1002/fld.1443 · Zbl 1276.76043
[35] Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2007) Influence of wall elasticity in patient-specific hemodynamic simulations. Comput Fluids 36: 160–168. doi: 10.1016/j.compfluid.2005.07.014 · Zbl 1113.76105
[36] Cruchaga MA, Celentano DJ, Tezduyar TE (2007) Collapse of a liquid column: numerical simulation and experimental validation. Comput Mech 39: 453–476. doi: 10.1007/s00466-006-0043-z · Zbl 1160.76013
[37] Sawada T, Hisada T (2007) Fluid–structure interaction analysis of the two dimensional flag-in-wind problem by an interface tracking ALE finite element method. Comput Fluids 36: 136–146 · Zbl 1181.76099
[38] 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
[39] Takizawa K, Yabe T, Tsugawa Y, Tezduyar TE, Mizoe H (2007) Computation of free–surface flows and fluid–object interactions with the CIP method based on adaptive meshless Soroban grids. Comput Mech 40: 167–183. doi: 10.1007/s00466-006-0093-2 · Zbl 1177.76300
[40] Takizawa K, Tanizawa K, Yabe T, Tezduyar TE (2007) Ship hydrodynamics computations with the CIP method based on adaptive Soroban grids. Int J Numer Methods Fluids 54: 1011–1019. doi: 10.1002/fld.1466 · Zbl 1375.76153
[41] Yabe T, Takizawa K, Tezduyar TE, Im H-N (2007) Computation of fluid–solid and fluid–fluid interfaces with the CIP method based on adaptive Soroban grids–an overview. Int J Numer Methods Fluids 54: 841–853. doi: 10.1002/fld.1473 · Zbl 1375.76154
[42] Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2007) Numerical investigation of the effect of hypertensive blood pressure on cerebral aneurysm–dependence of the effect on the aneurysm shape. Int J Numer Methods Fluids 54: 995–1009. doi: 10.1002/fld.1497 · Zbl 1317.76107
[43] Manguoglu M, Sameh AH, Tezduyar TE, Sathe S (2008) A nested iterative scheme for computation of incompressible flows in long domains. Comput Mech 43: 73–80. doi: 10.1007/s00466-008-0276-0 · Zbl 1279.76024
[44] 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
[45] Tezduyar TE, Sathe S, Pausewang J, Schwaab M, Christopher J, Crabtree J (2008) Fluid–structure interaction modeling of ringsail parachutes. Comput Mech 43: 133–142. doi: 10.1007/s00466-008-0260-8 · Zbl 1209.74022
[46] Tezduyar TE, Sathe S, Schwaab M, Conklin BS (2008) Arterial fluid mechanics modeling with the stabilized space–time fluid–structure interaction technique. Int J Numer Methods Fluids 57: 601–629. doi: 10.1002/fld.1633 · Zbl 1230.76054
[47] Sathe S, Tezduyar TE (2008) Modeling of fluid–structure interactions with the space–time finite elements: contact problems. Comput Mech 43: 51–60. doi: 10.1007/s00466-008-0299-6 · Zbl 1297.74129
[48] Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2008) Fluid–structure interaction modeling of a patient-specific cerebral aneurysm: influence of structural modeling. Comput Mech 43: 151–159. doi: 10.1007/s00466-008-0325-8 · Zbl 1169.74032
[49] 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
[50] Isaksen JG, Bazilevs Y, Kvamsdal T, Zhang Y, Kaspersen JH, Waterloo K, Romner B, Ingebrigtsen T (2008) Determination of wall tension in cerebral artery aneurysms by numerical simulation. Stroke 39: 3172–3178
[51] Dettmer WG, Peric D (2008) On the coupling between fluid flow and mesh motion in the modelling of fluid–structure interaction. Comput Mech 43: 81–90 · Zbl 1235.74272
[52] Tezduyar TE, Schwaab M, Sathe S (2009) Sequentially-coupled arterial fluid–structure interaction (SCAFSI) technique. Comput Methods Appl Mech Eng 198: 3524–3533. doi: 10.1016/j.cma.2008.05.024 · Zbl 1229.74100
[53] Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2009) Fluid–structure interaction modeling of blood flow and cerebral aneurysm: significance of artery and aneurysm shapes. Comput Methods Appl Mech Eng 198: 3613–3621. doi: 10.1016/j.cma.2008.08.020 · Zbl 1229.74101
[54] Manguoglu M, Sameh AH, Saied F, Tezduyar TE, Sathe S (2009) Preconditioning techniques for nonsymmetric linear systems in computation of incompressible flows. J Appl Mech 76: 021204. doi: 10.1115/1.3059576
[55] 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
[56] 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
[57] Takizawa K, Christopher J, Tezduyar TE, Sathe S (2010) Space–time finite element computation of arterial fluid–structure interactions with patient-specific data. Int J Numer Methods Biomed Eng 26: 101–116. doi: 10.1002/cnm.1241 · Zbl 1180.92023
[58] Takizawa K, Moorman C, Wright S, Christopher J, Tezduyar TE (2010) Wall shear stress calculations in space–time finite element computation of arterial fluid–structure interactions. Comput Mech 46: 31–41. doi: 10.1007/s00466-009-0425-0 · Zbl 1301.92019
[59] Tezduyar TE, Takizawa K, Moorman C, Wright S, Christopher J (2010) Multiscale sequentially-coupled arterial FSI technique. Comput Mech 46: 17–29. doi: 10.1007/s00466-009-0423-2 · Zbl 1261.92010
[60] Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2010) Influence of wall thickness on fluid–structure interaction computations of cerebral aneurysms. Int J Numer Methods Biomed Eng 26: 336–347. doi: 10.1002/cnm.1289 · Zbl 1183.92050
[61] Manguoglu M, Takizawa K, Sameh AH, Tezduyar TE (2010) Solution of linear systems in arterial fluid mechanics computations with boundary layer mesh refinement. Comput Mech 46: 83–89. doi: 10.1007/s00466-009-0426-z · Zbl 1301.76087
[62] Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2010) Role of 0D peripheral vasculature model in fluid–structure interaction modeling of aneurysms. Comput Mech 46: 43–52. doi: 10.1007/s00466-009-0439-7 · Zbl 1301.92020
[63] Bazilevs Y, Hsu M-C, Zhang Y, Wang W, Liang X, Kvamsdal T, Brekken R, Isaksen J (2010) A fully-coupled fluid–structure interaction simulation of cerebral aneurysms. Comput Mech 46: 3–16 · Zbl 1301.92014
[64] Tezduyar TE, Takizawa K, Moorman C, Wright S, Christopher J (2010) Space–time finite element computation of complex fluid–structure interactions. Int J Numer Methods Fluids 64: 1201–1218. doi: 10.1002/fld.2221 · Zbl 1427.76148
[65] Bazilevs Y, Hsu M-C, Zhang Y, Wang W, Kvamsdal T, Hentschel S, Isaksen J (2010) Computational fluid–structure interaction: methods and application to cerebral aneurysms. Biomech Model Mechanobiol 9: 481–498
[66] Kiendl J, Bazilevs Y, Hsu M-C, Wüchner R, Bletzinger K-U (2010) The bending strip method for isogeometric analysis of Kirchhoff–Love shell structures comprised of multiple patches. Comput Methods Appl Mech Eng 199: 2403–2416 · Zbl 1231.74482
[67] 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
[68] 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
[69] Takizawa K, Moorman C, Wright S, Spielman T, Tezduyar TE (2011) Fluid–structure interaction modeling and performance analysis of the Orion spacecraft parachutes. Int J Numer Methods Fluids 65: 271–285. doi: 10.1002/fld.2348 · Zbl 1428.76011
[70] Takizawa K, Moorman C, Wright S, Purdue J, McPhail T, Chen PR, Warren J, Tezduyar TE (2011) Patient-specific arterial fluid–structure interaction modeling of cerebral aneurysms. Int J Numer Methods Fluids 65: 308–323. doi: 10.1002/fld.2360 · Zbl 1203.92044
[71] Hsu M-C, Bazilevs Y (2011) Blood vessel tissue prestress modeling for vascular fluid–structure interaction simulations. Finite Elem Anal Des 47: 593–599
[72] Akkerman I, Bazilevs Y, Kees CE, Farthing MW (2011) Isogeometric analysis of free-surface flow. J Comput Phys 230: 4137–4152 · Zbl 1343.76040
[73] Takizawa K, Wright S, Moorman C, Tezduyar TE (2011) Fluid–structure interaction modeling of parachute clusters. Int J Numer Methods Fluids 65: 286–307. doi: 10.1002/fld.2359 · Zbl 1426.76312
[74] Manguoglu M, Takizawa K, Sameh AH, Tezduyar TE (2011) Nested and parallel sparse algorithms for arterial fluid mechanics computations with boundary layer mesh refinement. Int J Numer Methods Fluids 65: 135–149. doi: 10.1002/fld.2415 · Zbl 1427.76285
[75] Kees CE, Akkerman I, Farthing MW, Bazilevs Y (2011) A conservative level set method suitable for variable-order approximations and unstructured meshes. J Comput Phys 230: 4536–4558 · Zbl 1416.76214
[76] Tezduyar TE, Takizawa K, Brummer T, Chen PR (2011) Space–time fluid–structure interaction modeling of patient-specific cerebral aneurysms. Int J Numer Methods Biomed Eng (published online). doi: 10.1002/cnm.1433 , Feb 2011 · Zbl 1244.92036
[77] Takizawa K, Tezduyar TE (2011) Multiscale space–time fluid–structure interaction techniques. Computat Mech (published online). doi: 10.1007/s00466-011-0571-z , Feb 2011 · Zbl 1398.76128
[78] Takizawa K, Henicke B, Tezduyar TE, Hsu M-C, Bazilevs Y (2011) Stabilized space–time computation of wind-turbine rotor aerodynamics. Comput Mech (published online). doi: 10.1007/s00466-011-0589-2 , March 2011 · Zbl 1398.76127
[79] Takizawa K, Spielman T, Tezduyar TE (2011) Space–time FSI modeling and dynamical analysis of spacecraft parachutes and parachute clusters. Comput Mech (published online). doi: 10.1007/s00466-011-0590-9 , April 2011 · Zbl 1398.74095
[80] Takizawa K, Spielman T, Moorman C, Tezduyar TE (2011) Fluid–structure interaction modeling of spacecraft parachutes for simulation-based design. J Appl Mech (to appear) · Zbl 1428.76011
[81] Takizawa K, Brummer T, Tezduyar TE, Chen PR (2011) A comparative study based on patient-specific fluid–structure interaction modeling of cerebral aneurysms. J Appl Mech (to appear) · Zbl 1244.92036
[82] Takizawa K, Henicke B, Puntel A, Spielman T, Tezduyar TE (2011) Space–time computational techniques for the aerodynamics of flapping wings. J Appl Mech (to appear)
[83] 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 (published online). doi: 10.1007/s00466-011-0614-5 , July 2011 · Zbl 1334.74032
[84] Akkerman I, Bazilevs Y, Benson DJ, Farthing MW, Kees CE (2011) Free-surface flow and fluid–object interaction modeling with emphasis on ship hydrodynamics. J Appl Mech (accepted)
[85] Hsu M-C, Akkerman I, Bazilevs Y (2011) High-performance computing of wind turbine aerodynamics using isogeometric analysis. Comput Fluids (published online). doi: 10.1016/j.compfluid.2011.05.002 · Zbl 1271.76276
[86] Bazilevs Y, Hsu M-C, Kiendl J, Benson DJ (2011) A computational procedure for pre-bending of wind turbine blades. Int J Numer Methods Eng (accepted) · Zbl 1242.74026
[87] Tezduyar T, Aliabadi S, Behr M (1998) Enhanced-discretization interface-capturing technique (EDICT) for computation of unsteady flows with interfaces. Comput Methods Appl Mech Eng 155: 235–248. doi: 10.1016/S0045-7825(97)00194-1 · Zbl 0961.76046
[88] 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
[89] Hughes TJR, Tezduyar TE (1984) Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations. Comput Methods Appl Mech Eng 45: 217–284. doi: 10.1016/0045-7825(84)90157-9 · Zbl 0542.76093
[90] Tezduyar TE, Mittal S, Ray SE, Shih R (1992) Incompressible flow computations with stabilized bilinear and linear equal-order-interpolation velocity-pressure elements. Comput Methods Appl Mech Eng 95: 221–242. doi: 10.1016/0045-7825(92)90141-6 · Zbl 0756.76048
[91] 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
[92] 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
[93] Bazilevs Y, Calo VM, Cottrel 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
[94] Johnson AA, Tezduyar TE (1994) Mesh update strategies in parallel finite element computations of flow problems with moving boundaries and interfaces. Comput Methods Appl Mech Eng 119: 73–94. doi: 10.1016/0045-7825(94)00077-8 · Zbl 0848.76036
[95] Behr M, Tezduyar T (2001) Shear-slip mesh update in 3D computation of complex flow problems with rotating mechanical components. Comput Methods Appl Mech Eng 190: 3189–3200. doi: 10.1016/S0045-7825(00)00388-1 · Zbl 1012.76042
[96] Torii R, Oshima M, Kobayashi T, Takagi K, Tezduyar TE (2004) Influence of wall elasticity on image-based blood flow simulation. Jpn Soc Mech Eng J Ser A 70:1224–1231 (in Japanese)
[97] Aliabadi SK, Tezduyar TE (1993) Space–time finite element computation of compressible flows involving moving boundaries and interfaces. Comput Methods Appl Mech Eng 107: 209–223. doi: 10.1016/0045-7825(93)90176-X · Zbl 0798.76037
[98] 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
[99] Tezduyar TE, Hughes TJR (1982) Development of time-accurate finite element techniques for first-order hyperbolic systems with particular emphasis on the compressible Euler equations. NASA technical report NASA-CR-204772, NASA. http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19970023187_1997034954.pdf
[100] Tezduyar TE, Hughes TJR (1983) Finite element formulations for convection dominated flows with particular emphasis on the compressible Euler equations. In: Proceedings of AIAA 21st aerospace sciences meeting, AIAA paper 83-0125, Reno, Nevada
[101] Hughes TJR, Mallet M (1986) A new finite element formulation for computational fluid dynamics: IV. A discontinuity-capturing operator for multidimensional advective-diffusive systems. Comput Methods Appl Mech Eng 58: 329–339 · Zbl 0587.76120
[102] Hughes TJR, Franca LP, Mallet M (1987) A new finite element formulation for computational fluid dynamics: VI. Convergence analysis of the generalized SUPG formulation for linear time-dependent multi-dimensional advective-diffusive systems. Comput Methods Appl Mech Eng 63: 97–112 · Zbl 0635.76066
[103] Le Beau GJ, Tezduyar TE (1991) Finite element computation of compressible flows with the SUPG formulation. In: Advances in finite element analysis in fluid dynamics, FED-vol 123. ASME, New York, pp 21–27
[104] Tezduyar TE, Park YJ (1986) Discontinuity capturing finite element formulations for nonlinear convection-diffusion-reaction equations. Comput Methods Appl Mech Eng 59: 307–325. doi: 10.1016/0045-7825(86)90003-4 · Zbl 0593.76096
[105] 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
[106] Catabriga L, Coutinho ALGA, Tezduyar TE (2005) Compressible flow SUPG parameters computed from element matrices. Commun Numer Methods Eng 21: 465–476. doi: 10.1002/cnm.759 · Zbl 1329.76161
[107] Catabriga L, Coutinho ALGA, Tezduyar TE (2006) Compressible flow SUPG parameters computed from degree-of-freedom submatrices. Comput Mech 38: 334–343. doi: 10.1007/s00466-006-0033-1 · Zbl 1176.76061
[108] Tezduyar TE (2004) Finite element methods for fluid dynamics with moving boundaries and interfaces. In: Stein E, Borst RD, Hughes TJR (eds) Encyclopedia of computational mechanics. Fluids, vol 3, Chap 17. Wiley, New York
[109] 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
[110] Tezduyar TE, Senga M (2007) SUPG finite element computation of inviscid supersonic flows with YZ{\(\beta\)} shock-capturing. Comput Fluids 36: 147–159. doi: 10.1016/j.compfluid.2005.07.009 · Zbl 1127.76029
[111] Tezduyar TE, Senga M, Vicker D (2006) Computation of inviscid supersonic flows around cylinders and spheres with the SUPG formulation and YZ{\(\beta\)} shock-capturing. Comput Mech 38: 469–481. doi: 10.1007/s00466-005-0025-6 · Zbl 1176.76077
[112] Corsini A, Rispoli F, Santoriello A (2005) A variational multiscale high-order finite element formulation for turbomachinery flow computations. Comput Methods Appl Mech Eng 194: 4797–4823 · Zbl 1093.76032
[113] Rispoli F, Saavedra R (2006) A stabilized finite element method based on SGS models for compressible flows. Comput Methods Appl Mech Eng 196: 652–664 · Zbl 1120.76331
[114] Rispoli F, Saavedra R, Corsini A, Tezduyar TE (2007) Computation of inviscid compressible flows with the V-SGS stabilization and YZ{\(\beta\)} shock-capturing. Int J Numer Methods Fluids 54: 695–706. doi: 10.1002/fld.1447 · Zbl 1207.76104
[115] 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{\(\beta\)} shock-capturing. J Appl Mech 76: 021209. doi: 10.1115/1.3057496
[116] Catabriga L, de Souza DAF, Coutinho ALGA, Tezduyar TE (2009) Three-dimensional edge-based SUPG computation of inviscid compressible flows with YZ{\(\beta\)} shock-capturing. J Appl Mech 76: 021208. doi: 10.1115/1.3062968
[117] Kawahara M, Takeuchi N, Yoshida T (1978) Two step explicit finite element method for tsunami wave-propagation analysis. Int J Numer Methods Eng 12: 331–351 · Zbl 0375.76003
[118] Kawahara M, Hirano H, Tsubota K, Inagaki K (1982) Selective lumping finite element method for shallow water flow. Int J Numer Methods Fluids 2: 89–112 · Zbl 0483.76023
[119] Gopalakrishnan TC, Tung CC (1983) Numerical analysis of moving boundary problem in coastal hydrodynamics. Int J Numer Methods Fluids 3: 179–200 · Zbl 0521.76022
[120] Kawahara M, Kashiyama K (1984) Selective lumping finite element method for nearshore current. Int J Numer Methods Fluids 4: 71–97 · Zbl 0553.76035
[121] Kawahara M, Umetsu T (1986) Finite element method for moving boundary problems in river flow. Int J Numer Methods Fluids 6: 365–386 · Zbl 0597.76014
[122] Okamoto T, Kawahara M, Ioki N, Nagaoka H (1992) Two-dimensional wave runup analysis by selective lumping finite element method. Int J Numer Methods Fluids 14: 1219–1243 · Zbl 0753.76102
[123] Kashiyama K, Ito H, Behr M, Tezduyar T (1995) Three-step explicit finite element computation of shallow water flows on a massively parallel computer. Int J Numer Methods Fluids 21: 885–900. doi: 10.1002/fld.1650211009 · Zbl 0861.76044
[124] Luettich RA, Westerink JJ (1995) Implementation and testing of elemental flooding and drying in the ADCIRC hydrodynamic model. Final contract report DACW39-94-M-5869, US Army Corps of Engineers
[125] Kashiyama K, Saitoh K, Behr M, Tezduyar TE (1997) Parallel finite element methods for large-scale computation of storm surges and tidal flows. Int J Numer Methods n Fluids 24: 1371–1389. doi: 10.1002/(SICI)1097-0363(199706)24:12<1371::AID-FLD565>3.0.CO;2-7 · Zbl 0881.76052
[126] Kashiyama K, Ohba Y, Takagi T, Behr M, Tezduyar T (1999) Parallel finite element method utilizing the mode splitting and sigma coordinate for shallow water flows. Comput Mech 23: 144–150. doi: 10.1007/s004660050394 · Zbl 0949.76050
[127] Kashiyama K, Sugano S, Behr M, Tezduyar TE (1999) Space–time finite element method for shallow water flows considering moving boundaries. In: Proceedings of the 3rd ASME/JSME joint fluids engineering conference, San Francisco, California (1999)
[128] Heniche M, Secretan Y, Boudreau P, Leclerc M (2000) A two-dimensional finite element drying-wetting shallow water model for rivers and estuaries. Adv Water Resour 23: 360–371
[129] Dawson C, Westerink JJ, Feyen JC, Pothian D (2006) Edge-based finite element method for shallow water equations. Int J Numer Methods Fluids 52: 63–88 · Zbl 1097.76048
[130] Kubatko EJ, Bunya S, Dawson C, Westerink JJ (2009) Dynamic p-adaptive Runge-Kutta discontinuous Galerkin methods for the shallow water equations. Comput Methods Appl Mech Eng 198: 1766–1774 · Zbl 1227.76032
[131] Bunya S, Kubatko EJ, Westerink JJ, Dawson C (2009) Wetting and drying treatment for the Runge–Kutta discontinuous Galerkin solution to the shallow water equations. Comput Methods Appl Mech Eng 198: 1548–1562 · Zbl 1227.76026
[132] Takase S, Kashiyama K, Tanaka S, Tezduyar TE (2010) Space–time SUPG formulation of the shallow-water equations. Int J Numer Methods Fluids 64: 1379–1394. doi: 10.1002/fld.2464 · Zbl 1427.35212
[133] 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
[134] Tanaka S, Kashiyama K (2006) A new mesh re-generation technique for free surface flow analysis based on interface-tracking method. J Struct Mech Earthq Eng 2: 269–277
[135] Tanaka S, Kashiyama K (2006) ALE finite element method for FSI problems with free surface using mesh re-generation method based on background mesh. Int J Comput Fluid Dyn 20: 229–236 · Zbl 1131.76037
[136] Dean RG, Dalrymple RA (1984) Water wave mechanics for engineers and scientists. Prentice-Hall, New Jersey
[137] Mittal S, Aliabadi S, Tezduyar T (1999) Parallel computation of unsteady compressible flows with the EDICT. Comput Mech 23: 151–157. doi: 10.1007/s004660050395 · Zbl 0951.76045
[138] 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
[139] 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
[140] 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
[141] 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
[142] Tanaka N (1999) The CIVA method for mesh-free approaches: improvement of the CIP method for n-simplex. Comput Fluid Dyn J 8: 121–127
[143] Carrier GF, Greenspan HP (1958) Water waves of finite amplitude on a sloping beach. J Fluid Mech 4: 97–109 · Zbl 0080.19504
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.