Bigay, P.; Oger, G.; Guilcher, P.-M.; Le Touzé, D. A weakly-compressible Cartesian grid approach for hydrodynamic flows. (English) Zbl 1411.76081 Comput. Phys. Commun. 220, 31-43 (2017). Summary: The present article aims at proposing an original strategy to solve hydrodynamic flows. In introduction, the motivations for this strategy are developed. It aims at modeling viscous and turbulent flows including complex moving geometries, while avoiding meshing constraints. The proposed approach relies on a weakly-compressible formulation of the Navier-Stokes equations. Unlike most hydrodynamic CFD (Computational Fluid Dynamics) solvers usually based on implicit incompressible formulations, a fully-explicit temporal scheme is used. A purely Cartesian grid is adopted for numerical accuracy and algorithmic simplicity purposes. This characteristic allows an easy use of Adaptive Mesh Refinement (AMR) methods embedded within a massively parallel framework. Geometries are automatically immersed within the Cartesian grid with an AMR compatible treatment. The method proposed uses an Immersed Boundary Method (IBM) adapted to the weakly-compressible formalism and imposed smoothly through a regularization function, which stands as another originality of this work. All these features have been implemented within an in-house solver based on this WCCH (Weakly-Compressible Cartesian Hydrodynamic) method which meets the above requirements whilst allowing the use of high-order (\(> 3\)) spatial schemes rarely used in existing hydrodynamic solvers. The details of this WCCH method are presented and validated in this article. Cited in 1 ReviewCited in 9 Documents MSC: 76M12 Finite volume methods applied to problems in fluid mechanics 76N99 Compressible fluids and gas dynamics 65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs Keywords:weakly-compressible formulation; fully-explicit scheme; WENO 5; local mesh refinement; numerical diffusion; high-order schemes; immersed-boundary method (IBM); mobile geometries Software:HE-E1GODF PDFBibTeX XMLCite \textit{P. Bigay} et al., Comput. Phys. Commun. 220, 31--43 (2017; Zbl 1411.76081) Full Text: DOI References: [1] Berger, M. J.; Colella, P., J. Comput. Phys., 82, 64-84 (1989) [2] MacNeice, P.; Olson, K. M.; Mobarry, C.; de Fainchtein, R.; Packer, C., Comput. Phys. Comm., 126, 330-354 (2000) [3] Monaghan, J. J., Annu. Rev. Astron. Astrophys., 30, 543-574 (1992) [4] Oger, G.; Marrone, S.; Le Touzé, D.; de Leffe, M., J. Comput. Phys., 313, 76-98 (2016) [5] Oger, G.; Le Touzé, D.; Guibert, D.; de Leffe, M.; Biddiscombe, J.; Soumagne, J.; Piccinali, J.-G., Comput. Phys. Comm., 200, 1-14 (2016) [6] Marrone, S.; Colagrossi, A.; Di Mascio, A.; Touzé, D. Le, J. Fluids Struct., 54, 802-822 (2015) [7] Toro, E. F., Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction (1999), Springer Science & Business Media · Zbl 0923.76004 [8] van Leer, B., J. Comput. Phys., 32, 101-136 (1979) [9] Liu, X.-D.; Osher, S.; Chan, T., J. Comput. Phys., 115, 200-212 (1994) [10] Titarev, V. A.; Toro, E. F., J. Comput. Phys., 201, 238-260 (2004) [11] Roe, P. L., Annu. Rev. Fluid Mech., 18, 337-365 (1986) [12] van Leer, B., J. Comput. Phys., 14, 361-370 (1974) [13] http://elearning.cerfacs.fr/numerical/benchmarks/vortex2d/; http://elearning.cerfacs.fr/numerical/benchmarks/vortex2d/ [14] Berger, M.; Aftosmis, M. J.; Allmaras, S., (Proceedings of the AIAA Conference Paper2012-1301 (2012)) [15] Morris, J. P.; Fox, P. J.; Zhu, Y., J. Comput. Phys., 136, 214-226 (1997) [16] Antuono, M.; Colagrossi, A.; Marrone, S., Comput. Phys. Comm., 183, 2570-2580 (2012) [17] Ghia, U.; Ghia, K. N.; Shin, C. T., J. Comput. Phys., 48, 387-411 (1982) [18] Botella, O.; Peyret, R., Comput. & Fluids, 27, 421-433 (1998) [19] Hu, X.; Khoo, B.; Adams, N.; Huang, F., J. Comput. Phys., 219, 553-578 (2006) [20] Kirkpatrick, M.; Armfield, S., J. Comput. Phys., 184, 1-36 (2003) [21] Udaykumar, R.; Mittal, H.; Rampunggoon, P.; Khanna, A., J. Comput. Phys., 174, 345-380 (2001) [22] Ye, T.; Mittal, R.; Udaykumar, H. S.; Shyy, W., J. Comput. Phys., 156, 2, 209-240 (1999) [23] Berthelsen, P. A.; Faltinsen, O. M., J. Comput. Phys., 227, 4354-4397 (2008) [24] Marshall, D. D.; Ruffin, S. M., (AIAA-2004-0581 (2004)) [25] Mittal, R.; Dong, H.; Bozkurttas, M.; Najjar, F. M.; Vargas, A.; von Loebbecke, A., J. Comput. Phys., 227, 4825-4852 (2008) [26] Peskin, C. S., J. Comput. Phys., 10, 252-271 (1972) [27] Mittal, R.; Iaccarino, G., Annu. Rev. Fluid Mech., 37, 239-261 (2005) [28] Goldstein, D.; Handler, R.; Sirovich, L., J. Comput. Phys., 105, 354-366 (1993) [29] Fadlun, E. A.; Verzicco, R.; Orlandi, P.; Mohd-Yusof, J., J. Comput. Phys., 161, 35-60 (2000) [30] Mohd-Yosuf, J., Annu. Res Briefs, Cent. Turbul. Res., 317-328 (1997) [31] Tseng, Y. H.; Ferziger, J. H., J. Comput. Phys., 192, 593-623 (2003) [32] Uhlmann, M., J. Comput. Phys., 209, 448-476 (2005) [33] Verzicco, R.; Mohd-Yusof, J.; Orlandi, P.; Haworth, D., AIAA J., 38, 427-433 (2000) [34] Balaras, E., Comput. & Fluids, 33, 375-404 (2004) [35] Dennis, S.; Chang, G., J.Fluid Mech., 42, 471-489 (1970) [36] Grove, A. S.; Shair, F. H.; Petersen, E. E.; Acrivos, A., J. Fluid Mech., 19, 60-80 (1964) [37] Tritton, D. J., J. Fluid Mech., 6, 547-567 (1959) [38] Bouard, R.; Coutanceau, M., J. Fluid Mech., 101, 583-607 (1980) [39] Gautier, R.; Biau, D.; Lamballais, E., Comput. & Fluids, 75, 103-111 (2013) 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.