Coherent Vorticity and Discontinuous Flow in Particle-Based Sph Modeling

Coherent Vorticity and Discontinuous Flow in Particle-Based Sph Modeling

Oddny H. Brun Joseph T. Kider JR., R. Paul Wiegand

School of Modeling, Simulation, and Training, University of Central Florida, Florida

Department of Computer Science and Quantitative Methods, Winthrop University, South Carolina

224 - 236
Available online: 
| Citation

© 2022 IIETA. This article is published by IIETA and is licensed under the CC BY 4.0 license (



Smoothing sequences in smoothed particle hydrodynamics (SPH) contain numerous discontinuities. In general, in science, discontinuities are well known to cause inaccuracy if smoothing is performed without taking the discontinuity into consideration, most commonly referred to as the Gibbs phenomenon. We found that 24%–27% of the fluid particles at any given time step have sequences containing one or more discontinuities in typical benchmark fluid problems. The effect of taking the discontinuities into consideration for the fluid particles that show coherent vorticity resulted typically in a 50% of change in particle movement compared to that particle’s movement from its current time step to the next. First and second generation wavelets were used for discontinuity identification and vorticity analysis, respectively. Results of a sloshing tank case simulated by the SPH method were used for the analysis.


Discontinuities, second-generation wavelets, smoothing, smoothed particle hydrodynamics (SPH), vorticity.


[1] Abramovich, F., Benjamini, J., Donoho, D. L. & Johnstone, I. M., Adapting to unknownsparcity by controlling the false discovery rate. The Annals of Statistics, 34, pp. 584–653, 2006.

[2] Abramovich, F., Antoniadis, A. & Pensky, M., Estimation of piecewise-smooth functionsby amalgamated bridge regression splines. Sankhya: The Indian Journal of statistics,69, pp. 1–27, 2007.

[3] Brun, O. H., Kider Jr., J. T. & Wiegand, R. P., Particle-based flow vorticity analysisby use of second-generation wavelets. WIT Transactions on Engineering Science, 130,WIT Press, ISSN 1743-3533, 2021.

[4] Brun, O. H., Improved interpolation in SPH in cases of less smooth flow (Master’s thesis).Institute for Simulation and Training, University of Central Florida, 2016.

[5] Cabezón, R. M., Garćia-Senz, D. & Relanõ, A., A oneparameter family of interpolatingkernels for smoothed particle hydrodynamics studies. Journal of Computational Physics,227, pp. 8523–8540. 2008.

[6] Domínguez, J. M., Crespo, A. J. C. & Rogers, B. D., Users guide for dualsphysics code,2016.

[7] Donoho, D. L. & Johnstone, I. M., Adapting to unknown smoothness via waveletshrinkage. Journal of the American Statistical Association, 90, pp. 1200–1224, 1995.

[8] Farge, M., Schneider, K. & Kevlahan, N., Non-gaussian and coherent vortex simulationfor two-dimensional turbulence using an adaptive orthogonal wavelet basis. Physics ofFluids, 1999.

[9] Farge, M., Wavelet transforms and their applications to turbulence. Ann. Rev. FluidMech., 1992.

[10] Farge, M., Schneider, K. & Kevlahan, N. K. R., Coherent structure eduction in waveletforcedtwo-dimensional turbulent flow. Krause E, Gersten K eds., IUTAM Symposiumon Dynamics of Slender Vortices, 1998.

[11] Kamm, J., Rider, W., Rightley, P., Prestridge, K., Benjamin, R. & Vorobieff, P., Thegas curtain experimental technique and analysis methodologies. WIT Transactions onModeling and Simulation, 2001.

[12] Khorasanizade, S. & Sousa, J. M. M., Dynamic flow-based particle splitting in smoothedparticle hydrodynamics. International Journal for Numerical Methods in Engineering,2016.

[13] Lucy, L. B., A numerical approach to the testing of the fission theory. The AstronomicalJournal, 82, pp. 1013–1024, 1977.

[14] Math Works. Lifting method for constructing wavelets. 2021.

[15] Monaghan, J. J., Particle methods for hydrodynamics. Computer Physics Report, 1985.

[16] Monaghan, J. J., Smoothed particle hydrodynamics. Annu. Rev. Astron. Astrophys.,1992.

[17] Monaghan, J.J., SPH without a tensile instability. Journal of Computational Physics,2000.

[18] Okamoto, N., Yoshimatsu, K., Schneider, K., Farge, M. & Kaneda, Y., Coherent vorticesin high resolution direct numerical simulation of homogeneous isotropic turbulence: Awavelet viewpoint. Physics of Fluids, 2007.

[19] Olejnik, M., Szewc, K. & Pozorski, J., Sph with dynamic smoothing length adjustmentbased on the local flow kinematics. Journal of Computational Physics, 2017.

[20] Rightley, P. M., Vorobieff, R., Martin, R. & Benjamin, R. F. Experimental observationsof the mixing transition in a shock-accelerated gas curtain. Physics of Fluids, 1999.

[21] Schneider, K., Ziuber, J., Farge, M. & Azzalini, A., Coherent vortex extraction andsimulation of 2d isotropic turbulence. Journal of Turbulence, 2006.

[22] Sweldens, W., The lifting scheme: A custom-design construction of biorthogonal wavelets.Applied and Computational Harmonic Analysis, 1996.

[23] Sweldens, W., The lifting scheme: A construction of second generation wavelets. SiamJ. Math. Anal., 1998.

[24] Vacondio, R., Rogers, B. D. & Stansby, P. K., Accurate particle splitting for smoothedparticle hydrodynamics in shallow water with shock capturing. International Journalfor Numerical Methods in Fluids, 2012.

[25] Vorobieff, P. & Rockwell, D., Wavelet filtering for topological decomposition of flowfields. International Journal of Imaging Systems and Technology, 1996.