Unified semi-analytical wall boundary conditions in SPH: analytical extension to 3-D
Solid wall boundary conditions have been an area of active research within the context of Smoothed Particle Hydrodynamics (SPH) for quite a while. Ferrand et al. (Int. J. Numer. Methods Fluids 71(4), 446–472, 2012) presented a novel approach using a renormalization factor in the SPH approximation. The computation of this factor depends on an integral along the boundary of the domain and in their original paper Ferrand et al. gave an analytical formulation for the 2-D case using the Wendland kernel. In this paper the formulation will be extended to 3-D, again providing analytical formulae. Due to the boundary being two dimensional a domain decomposition algorithm needs to be employed in order to obtain special integration domains. For these the analytical formulae will be presented when using the Wendland kernel. The algorithm presented within this paper is applied to several academic test-cases for which either analytical results or simulations with other methods are available. It will be shown that the present formulation produces accurate results and provides a significant improvement compared to approximative methods.
KeywordsFluid mechanics Smoothed particle hydrodynamics Unified semi-analytical Wall boundary conditions
Unable to display preview. Download preview PDF.
- 1.Amicarelli, A., Agate, G., Guandalini, R.: Development and validation of a SPH model using discrete surface elements at boundaries. In: Proceedings of the 7th International SPHERIC Workshop, pp. 369–374. Prato (2012)Google Scholar
- 6.Kleefsman, K., Fekken, G., Veldman, A., Iwanowski, B., Buchner, B.: A volume-of-fluid based simulation method for wave impact problems. J. Comput. Phys. 206(1), 363–393 (2005). doi: 10.1016/j.jcp.2004.12.007. http://www.sciencedirect.com/science/article/pii/S0021999104005170 CrossRefMATHMathSciNetGoogle Scholar
- 7.Libersky, L.D., Petschek, A.G., Carney, T.C., Hipp, J.R., Allahdadi, F.A.: High strain lagrangian hydrodynamics: a three-dimensional SPH code for dynamic material response. J. Comput. Phys. 109(1), 67–75 (1993). doi: 10.1006/jcph.1993.1199. http://www.sciencedirect.com/science/article/pii/S002199918371199X CrossRefMATHGoogle Scholar
- 9.Mayrhofer, A., Rogers, B.D., Violeau, D., Ferrand, M.: Investigation of wall bounded flows using SPH and the unified semi-analytical wall boundary conditions. Comput. Phys. Commun. 184(11), 2515–2527 (2013). doi: 10.1016/j.cpc.2013.07.004. http://www.sciencedirect.com/science/article/pii/S0010465513002324 CrossRefMathSciNetGoogle Scholar
- 13.Violeau, D.: Fluid Mechanics and the SPH Method: Theory and Applications. Oxford University Press (2012). http://ukcatalogue.oup.com/product/academic/earthsciences/hydrology/9780199655526.do
- 14.Weller, H., Greenshields, C., Janssens, M.: OpenFOAM (2012). www.openfoam.org