×

Isogeometric boundary element analysis of problems in potential flow. (English) Zbl 1440.76102

Summary: The aim of the paper is to show that the isogeometric Boundary Element Method (isoBEM) has advantages over other numerical methods when applied to problems in potential flow. The problems presented here range from the flow past an obstacle to confined and unconfined seepage problems in isotropic and anisotropic media. It is shown how accurate results can be obtained with very few unknowns. The superior capability of NURBS to describe geometry and the variation of the unknowns is exploited.

MSC:

76M15 Boundary element methods applied to problems in fluid mechanics
65N38 Boundary element methods for boundary value problems involving PDEs
65D07 Numerical computation using splines
76B07 Free-surface potential flows for incompressible inviscid fluids

Software:

INSANE
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Scott, M. A.; Simpson, R. N.; Evans, J. A.; Lipton, S.; Bordas, S. P.A.; Hughes, T. J.R.; Sederberg, T. W., Isogeometric boundary element analysis using unstructured T-splines, Comput. Methods Appl. Mech. Engrg., 254, 0, 197-221 (2013) · Zbl 1297.74156
[2] Simpson, R. N.; Bordas, S. P.A.; Trevelyan, J.; Rabczuk, T., A two-dimensional isogeometric boundary element method for elastostatic analysis, Comput. Methods Appl. Mech. Engrg., 209-212, 0, 87-100 (2012) · Zbl 1243.74193
[3] Beer, G.; Marussig, B.; Duenser, C., Isogeometric boundary element method for the simulation of underground excavations, Géotech. Lett., 3, 108-111 (2013)
[4] Beer, G.; Marussig, B.; Zechner, J.; Duenser, C.; Fries, T.-P., Isogeometric boundary element analysis with elasto-plastic inclusions. Part 1: Plane problems, Comput. Methods Appl. Mech. Engrg., 308, 552-570 (2016) · Zbl 1439.74057
[5] Beer, G.; Mallardo, V.; Ruocco, E.; Marussig, B.; Zechner, J.; Duenser, C.; Fries, T. P., Isogeometric boundary element analysis with elasto-plastic inclusions. Part 2: 3-D problems, Comput. Methods Appl. Mech. Engrg., 315, 418-433 (2017) · Zbl 1439.74056
[6] Beer, G.; Mallardo, V.; Ruocco, E.; Duenser, C., Isogeometric boundary element analysis of steady incompressible viscous flow, Part 1: Plane problems, Comput. Methods Appl. Mech. Engrg., 326C, 51-69 (2017) · Zbl 1439.76115
[7] Beer, G.; Mallardo, V.; Ruocco, E.; Duenser, C., Isogeometric boundary element analysis of steady incompressible viscous flow, Part 2: 3-D problems, Comput. Methods Appl. Mech. Engrg., 332, 440-461 (2018) · Zbl 1440.76103
[8] Heltai, L.; Arroyo, M.; DeSimone, A., Nonsingular isogeometric boundary element method for stokes flows in 3d, Comput. Methods Appl. Mech. Engrg., 268, 514-539 (2014), URL http://www.sciencedirect.com/science/article/pii/S0045782513002442 · Zbl 1295.76022
[9] Nguyen, V. P.; Anitescu, C.; Bordas, S. P.; Rabczuk, T., Isogeometric analysis: An overview and computer implementation aspects, Math. Comput. Simulation, 117, 89-116 (2015), URL http://www.sciencedirect.com/science/article/pii/S0378475415001214 · Zbl 07313396
[10] Kostas, K.; Ginnis, A.; Politis, C.; Kaklis, P., Shape-optimization of 2D hydrofoils using an isogeometric BEM solver, Comput. Aided Des., 82, 79-87 (2017), Isogeometric Design and Analysis, http://dx.doi.org/10.1016/j.cad.2016.07.002, URL http://www.sciencedirect.com/science/article/pii/S0010448516300653
[11] Wrobel, L. C., The Boundary Element Method, Volume 1, Applications in Thermo-Fluids and Acoustics (2002), Wiley
[12] Bonnet, M., Boundary Integral Equation Methods for Solids and Fluids (1995), Wiley
[13] Beer, G., Advanced Numerical Simulation Methods - From CAD Data Directly to Simulation Results (2015), CRC Press/Balkema · Zbl 1344.65021
[14] Marussig, B.; Zechner, J.; Beer, G.; Fries, T.-P., Fast isogeometric boundary element method based on independent field approximation, Comput. Methods Appl. Mech. Engrg., 284, 458-488 (2015), Isogeometric Analysis Special Issue · Zbl 1423.74101
[15] Atroshchenko, E.; Xu, G.; Tomar, S.; Bordas, S., Weakening the tight coupling between geometry and simulation in isogeometric analysis: from sub-and super-geometric analysis to Geometry Independent Field approximaTion (GIFT), Internat. J. Numer. Methods Engrg., 114, 10, 1131-1159 (2018)
[16] Anacleto, F.; Ribeiro, T.; Ribeiro, G.; Pitangueira, R.; Penna, S., An object-oriented tridimensional self-regular boundary element method implementation, Eng. Anal. Bound. Elem., 37, 1276-1284 (2013) · Zbl 1287.65120
[17] Butterfield, R.; Tomlin, G., Integral techniques for solving zoned anisotropic continuum problems, (Variational Methods in Engineering, vol. 9 (1972)), 31-53
[18] Banerjee, P., The Boundary Element Method in Engineering (1994), McGraw-Hill
[19] Cividini, A.; Gioda, G., On the variable mesh finite element analysis of unconfined seepage problems, Geotechnique, 2, 251-267 (1989)
[20] Liggett, J. A., Location of free surface in porous media, ASCE J. Hydraul. Div., 103, 353-366 (1977)
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.