Time-accurate multi-scale anisotropic mesh adaptation for unsteady flows in CFD. (English) Zbl 1416.65321
Summary: This paper deals with anisotropic mesh adaptation applied to unsteady inviscid CFD simulations. Anisotropic metric-based mesh adaptation is an efficient strategy to reduce the extensive CPU time currently required by time-dependent simulations in an industrial context. In this work, we detail the time-accurate extension of multi-scale anisotropic mesh adaptation for steady flows [the second and the first author, “Optimal 3D highly anisotropic mesh adaptation based on the continuous mesh framework”, in: Proceedings of the 18th international meshing roundtable, IMR 2009. Berlin, Heidelberg: Springer. 575–594 (2009; doi:10.1007/978-3-642-04319-2_33)] (a control of the interpolation error in \(L^p\) norm to capture all the scales of the solution contrary to the \(L^\infty\) norm that only focuses on the larger scales) to unsteady flows when time advancing discretizations are considered. This is based on a space-time error analysis and an enhanced version of the fixed-point algorithm [the first author et al., J. Comput. Phys. 222, No. 2, 592–623 (2007; Zbl 1158.76388)]. We also show that each stage – remeshing, metric field computation, solution transfer, and flow solution – is important to design an efficient time-accurate anisotropic mesh adaptation process. The parallelization of the whole mesh adaptation platform is also discussed. The efficiency of the approach is emphasized on three-dimensional problems with convergence rate and CPU time analysis.
MSC:
| 65M50 | Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs |
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 65Y05 | Parallel numerical computation |
| 65Y20 | Complexity and performance of numerical algorithms |
Keywords:
anisotropic mesh adaptation; time-accurate; multiscale; metric; fixed-point algorithm; unsteady flowsCitations:
Zbl 1158.76388Software:
EdgePackReferences:
| [1] | Alauzet, F., Size gradation control of anisotropic meshes, Finite Elem. Anal. Des., 46, 181-202 (2010) |
| [2] | Alauzet, F., A parallel matrix-free conservative solution interpolation on unstructured tetrahedral meshes, Comput. Methods Appl. Mech. Eng., 299, 116-142 (2016) · Zbl 1425.65142 |
| [3] | Alauzet, F.; Frey, P. J.; George, P. L.; Mohammadi, B., 3D transient fixed point mesh adaptation for time-dependent problems: application to CFD simulations, J. Comput. Phys., 222, 592-623 (2007) · Zbl 1158.76388 |
| [4] | Alauzet, F.; Loseille, A., On the use of space filling curves for parallel anisotropic mesh adaptation, (Proceedings of the 18th International Meshing Roundtable (2009), Springer), 337-357 |
| [5] | Alauzet, F.; Loseille, A., High order sonic boom modeling by adaptive methods, J. Comput. Phys., 229, 561-593 (2010) · Zbl 1253.76052 |
| [6] | Belme, A.; Dervieux, A.; Alauzet, F., Time accurate anisotropic goal-oriented mesh adaptation for unsteady flows, J. Comput. Phys., 231, 6323-6348 (2012) · Zbl 1284.65126 |
| [7] | Berland, J.; Bogey, C.; Marsden, O.; Bailly, C., High-order, low dispersive and low dissipative explicit schemes for multiple-scale and boundary problems, J. Comput. Phys., 224, 637-662 (2007) · Zbl 1120.65323 |
| [8] | Blades, E.; Marcum, D., Numerical simulation of a spinning missile with dithering canards using unstructured grids, J. Spacecr. Rockets, 41, 2, 248-256 (2004) |
| [9] | Bottasso, C. L., Anisotropic mesh adaption by metric-driven optimization, Int. J. Numer. Methods Eng., 60, 597-639 (2004) · Zbl 1059.65109 |
| [10] | Cassagne, A.; Boussuge, J.-F.; Puigt, G., HORSE: high-order method for a new generation of large eddy simulation solver, Partnership for Advanced Computing in Europe, available online |
| [11] | Compère, G.; Marchandise, E.; Remacle, J.-F., Transient adaptivity applied to two-phase incompressible flows, J. Comput. Phys., 227, 3, 1923-1942 (2008) · Zbl 1135.76031 |
| [12] | Constantinescu, E. M.; Sandu, A., Multirate timestepping methods for hyperbolic conservation laws, J. Sci. Comput., 33, 239-278 (2007) · Zbl 1127.76033 |
| [13] | Coupez, T.; Jannoun, G.; Nassif, N.; Nguyen, H. C.; Digonnet, H.; Hachem, E., Adaptive time-step with anisotropic meshing for incompressible flows, J. Comput. Phys., 241, 195-211 (2013) · Zbl 1349.76597 |
| [14] | Courty, F.; Leservoisier, D.; George, P. L.; Dervieux, A., Continuous metrics and mesh adaptation, Appl. Numer. Math., 56, 2, 117-145 (2006) · Zbl 1092.65017 |
| [15] | de Sampaio, P. A.; Lyra, P. R.; Morgan, K.; Weatherill, N., Petrov-Galerkin solutions of the incompressible Navier-Stokes equations in primitive variables with adaptive remeshing, Comput. Methods Appl. Mech. Eng., 106, 143-178 (1993) · Zbl 0783.76053 |
| [16] | Debiez, C.; Dervieux, A., Mixed-element-volume MUSCL methods with weak viscosity for steady and unsteady flow calculations, Comput. Fluids, 29, 89-118 (2000) · Zbl 0949.76052 |
| [17] | Dervieux, A.; Thomasset, F., Multifluid incompressible flows by a finite element method, Lect. Notes Phys., 11, 158-163 (1981) |
| [18] | Elias, R. N.; Coutinho, A. L.G. A., Stabilized edge-based finite element simulation of free-surface flows, Int. J. Numer. Methods Fluids, 54, 6-8, 965-993 (2007) · Zbl 1258.76111 |
| [19] | Frey, P. J., About surface remeshing, (Proceedings of the 9th International Meshing Roundtable. Proceedings of the 9th International Meshing Roundtable, New Orleans, LO, USA (2000)), 123-136 |
| [20] | Frey, P. J.; Alauzet, F., Anisotropic mesh adaptation for CFD computations, Comput. Methods Appl. Mech. Eng., 194, 48-49, 5068-5082 (2005) · Zbl 1092.76054 |
| [21] | Frey, P. J.; George, P. L., Mesh Generation. Application to Finite Elements (2008), ISTE Ltd and John Wiley & Sons · Zbl 1156.65018 |
| [22] | George, P. L.; Hecht, F.; Vallet, M. G., Creation of internal points in Voronoi’s type method. Control and adaptation, Adv. Eng. Softw., 13, 5-6, 303-312 (1991) · Zbl 0754.65095 |
| [23] | Gourdain, N.; Gicquel, L.; Montagnac, M.; Vermorel, O.; Gazaix, M.; Staffelbach, G.; Garcia, M.; Boussuge, J.-F.; Poinsot, T., High performance parallel computing of flows in complex geometries: I. Methods, Comput. Sci. Discov., 2, Article 015003 pp. (2009) |
| [24] | Gruau, C.; Coupez, T., 3D tetrahedral, unstructured and anisotropic mesh generation with adaptation to natural and multidomain metric, Comput. Methods Appl. Mech. Eng., 194, 48-49, 4951-4976 (2005) · Zbl 1102.65122 |
| [25] | Guégan, D.; Allain, O.; Dervieux, A.; Alauzet, F., An \(L^\infty-L^p\) mesh adaptive method for computing unsteady bi-fluid flows, Int. J. Numer. Methods Eng., 84, 11, 1376-1406 (2010) · Zbl 1202.76094 |
| [26] | Huang, W., Metric tensors for anisotropic mesh generation, J. Comput. Phys., 204, 2, 633-665 (2005) · Zbl 1067.65140 |
| [27] | Jones, W. T.; Nielsen, E. J.; Park, M. A., Validation of 3D adjoint based error estimation and mesh adaptation for sonic boom reduction, (44th AIAA Aerospace Sciences Meeting. 44th AIAA Aerospace Sciences Meeting, Reno, NV, USA (Jan. 2006)), AIAA Paper 2006-1150 |
| [28] | Kleefsman, K. M.T.; Fekken, G.; Veldman, A. E.P.; Iwanowski, B.; Buchner, B., A volume-of-fluid based simulation method for wave impact problems, J. Comput. Phys., 206, 1, 363-393 (2005) · Zbl 1087.76539 |
| [29] | Li, X.; Remacle, J.-F.; Chevaugeon, N.; Shephard, M. S., Anisotropic mesh gradation control, (Proceedings of the 13th International Meshing Roundtable (2004), Springer), 401-412 |
| [30] | Li, X. L.; Jin, B. X.; Glimm, J., Numerical study for the three-dimensional Rayleigh-Taylor instability through the TVD/AC scheme and parallel computation, J. Comput. Phys., 126, 343-355 (1996) · Zbl 0858.76055 |
| [31] | Löhner, R., Three-dimensional fluid-structure interaction using a finite element solver and adaptive remeshing, Comput. Syst. Eng., 1, 2-4, 257-272 (1990) |
| [32] | Löhner, R., Applied CFD Techniques. An Introduction Based on Finite Element Methods (2001), John Wiley & Sons, Ltd: John Wiley & Sons, Ltd New York · Zbl 1136.76300 |
| [33] | Löhner, R.; Baum, J. D., Adaptive h-refinement on 3D unstructured grids for transient problems, Int. J. Numer. Methods Fluids, 14, 12, 1407-1419 (1992) · Zbl 0753.76099 |
| [34] | Loseille, A., Unstructured mesh generation and adaptation, (Abgrall, R.; Shu, C.-W., Handbook of Numerical Methods for Hyperbolic Problems. Handbook of Numerical Methods for Hyperbolic Problems, Handbook of Numerical Analysis, vol. 18 (2017), Elsevier), 263-302, (Chapter 10) · Zbl 1368.65182 |
| [35] | Loseille, A.; Alauzet, F., Optimal 3D highly anisotropic mesh adaptation based on the continuous mesh framework, (Proceedings of the 18th International Meshing Roundtable (2009), Springer), 575-594 |
| [36] | Loseille, A.; Alauzet, F., Continuous mesh framework. Part I: well-posed continuous interpolation error, SIAM J. Numer. Anal., 49, 1, 38-60 (2011) · Zbl 1230.65018 |
| [37] | Loseille, A.; Alauzet, F., Continuous mesh framework. Part II: validations and applications, SIAM J. Numer. Anal., 49, 1, 61-86 (2011) · Zbl 1230.65019 |
| [38] | Loseille, A.; Dervieux, A.; Frey, P. J.; Alauzet, F., Achievement of global second-order mesh convergence for discontinuous flows with adapted unstructured meshes, (37th AIAA Fluid Dynamics Conference. 37th AIAA Fluid Dynamics Conference, Miami, FL, USA (June 2007)), AIAA Paper 2007-4186 |
| [39] | Loseille, A.; Menier, V., Serial and parallel mesh modification through a unique cavity-based primitive, (Proceedings of the 22nd International Meshing Roundtable (2013), Springer), 541-558 |
| [40] | L. Maréchal, A parallelization framework for numerical simulation, The LP3 library, Documentation, INRIA, Jun 2010.; L. Maréchal, A parallelization framework for numerical simulation, The LP3 library, Documentation, INRIA, Jun 2010. |
| [41] | Michal, T. R.; Krakos, J., Anisotropic mesh adaptation through edge primitive operations, (50th AIAA Aerospace Sciences Meeting. 50th AIAA Aerospace Sciences Meeting, Nashville, TN, USA (Jan. 2012)), AIAA Paper 2012-0159 |
| [42] | Olivier, G., Anisotropic Metric-Based Mesh Adaptation for Unsteady CFD Simulations Involving Moving Geometries (2011), Université Pierre et Marie Curie, Paris VI: Université Pierre et Marie Curie, Paris VI Paris, France, PhD thesis |
| [43] | Pain, C. C.; Humpleby, A. P.; de Oliveira, C. R.E.; Goddard, A. J.H., Tetrahedral mesh optimisation and adaptivity for steady-state and transient finite element calculations, Comput. Methods Appl. Mech. Eng., 190, 3771-3796 (2001) · Zbl 1008.76041 |
| [44] | Pirzadeh, S. Z., Vortical flow prediction using an adaptive unstructured grid method, (Proceedings of RTO AVT Symposium on Advanced Flow Management: Part A. Vortex Flows and High Angle of Attack for Military Vehicles (2001)) |
| [45] | Rausch, R. D.; Batina, J. T.; Yang, H. T.Y., Spatial adaptation procedures on tetrahedral meshes for unsteady aerodynamic flow calculations, AIAA J., 30, 1243-1251 (1992) |
| [46] | Remacle, J.-F.; Li, X.; Shephard, M. S.; Flaherty, J. E., Anisotropic adaptive simulation of transient flows using discontinuous Galerkin methods, Int. J. Numer. Methods Eng., 62, 899-923 (2005) · Zbl 1078.76042 |
| [47] | Robertson, B. E.; Kravtsov, A. V.; Gnedin, N. Y.; Abel, T.; Rudd, D. H., Computational Eulerian hydrodynamics and Galilean invariance, Mon. Not. R. Astron. Soc., 401, 4, 2463-2476 (2010) |
| [48] | Sagan, H., Space-Filling Curves (1994), Springer: Springer New York, NY · Zbl 0806.01019 |
| [49] | Schulz-Rinne, C. W.; Collins, J. P.; Glaz, H. M., Numerical solution of the Riemann problem for two-dimensional gas dynamics, SIAM J. Sci. Comput., 14, 6, 1394-1414 (1993) · Zbl 0785.76050 |
| [50] | Seny, B.; Lambrechts, J.; Comblen, R.; Legat, V.; Remacle, J. F., Multirate time stepping for accelerating explicit discontinuous Galerkin computations with application to geophysical flows, Int. J. Numer. Methods Fluids, 71, 41-64 (2013) · Zbl 1431.65178 |
| [51] | Sharp, D. H., An overview of Rayleigh-Taylor instability, Physica D, 12, 3-18 (1984) · Zbl 0577.76047 |
| [52] | Skelboe, S., Stability properties of backward differentiation multirate formulas, Appl. Numer. Math., 5, 151-160 (1989) · Zbl 0675.65089 |
| [53] | Speares, W.; Berzins, M., A 3D unstructured mesh adaptation algorithm for time-dependent shock-dominated problems, Int. J. Numer. Methods Fluids, 25, 81-104 (1997) · Zbl 0881.76074 |
| [54] | Spiteri, R. J.; Ruuth, S. J., A new class of optimal high-order strong-stability-preserving time discretization methods, SIAM J. Numer. Anal., 40, 2, 469-491 (2002) · Zbl 1020.65064 |
| [55] | Tam, A.; Ait-Ali-Yahia, D.; Robichaud, M. P.; Moore, M.; Kozel, V.; Habashi, W. G., Anisotropic mesh adaptation for 3D flows on structured and unstructured grids, Comput. Methods Appl. Mech. Eng., 189, 1205-1230 (2000) · Zbl 1005.76061 |
| [56] | Wu, J.; Zhu, J. Z.; Szmelter, J.; Zienkiewicz, O. C., Error estimation and adaptivity in Navier-Stokes incompressible flows, Comput. Mech., 6, 259-270 (1990) · Zbl 0699.76035 |
| [57] | Yano, M.; Modisette, J. M.; Darmofal, D. L., The importance of mesh adaptation for higher-order discretizations of aerodynamics flows, (20th AIAA Computational Fluid Dynamics Conference. 20th AIAA Computational Fluid Dynamics Conference, Honolulu, HI, USA (June 2011)), AIAA-2011-3852 |
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.
