Numerical simulation of two-dimensional Kelvin-Helmholtz instability using weakly compressible smoothed particle hydrodynamics
The growth of the Kelvin–Helmholtz instability generated at the interface between two ideal gases is studied by means of a Smoothed Particle Hydrodynamics (SPH) scheme suitable for multi-fluids. The SPH scheme is based on the continuity equation approach where the densities of SPH particles are evol...
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| Format: | Article |
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Wiley
2015
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| Online Access: | https://eprints.nottingham.ac.uk/44723/ |
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| author | Yue, Thomas Pearce, Frazer Kruisbrink, Arno Morvan, Herve |
| author_facet | Yue, Thomas Pearce, Frazer Kruisbrink, Arno Morvan, Herve |
| author_sort | Yue, Thomas |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | The growth of the Kelvin–Helmholtz instability generated at the interface between two ideal gases is studied by means of a Smoothed Particle Hydrodynamics (SPH) scheme suitable for multi-fluids. The SPH scheme is based on the continuity equation approach where the densities of SPH particles are evolved during the simulation, in combination with a momentum equation previously proposed in the literature. A series of simulations were carried out to investigate the influence of viscosity, smoothing, the thickness of density and velocity transition layers. It was found that the effective viscosity of the presented results are strongly dependent on the artificial viscosity parameter αAV, with a linear dependence of 0.15. The utilisation of a viscosity switch is found to significantly reduce the spurious viscosity dependence to 1.68 × 10−4 and generated qualitatively improved behaviour for inviscid fluids. The linear growth rate in the numerical solutions is found to be in satisfactory agreement with analytical expectations, with an average relative error 〈ηsmooth〉=13%. In addition, the role played by velocity and density transition layers is also in general agreement with the analytical theory, except for the sharp-velocity, finite-density gradient cases where the larger growth rate than the classical growth rate is expected. We argue the inherited smoothing properties of the velocity field during the simulations are responsible for causing this discrepancy. Finally, the SPH results are in good agreement for finite velocity and density gradient scenarios, where an average relative error of 〈ηsmooth〉=11.5% is found in our work. |
| first_indexed | 2025-11-14T19:56:39Z |
| format | Article |
| id | nottingham-44723 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:56:39Z |
| publishDate | 2015 |
| publisher | Wiley |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-447232020-05-04T17:10:02Z https://eprints.nottingham.ac.uk/44723/ Numerical simulation of two-dimensional Kelvin-Helmholtz instability using weakly compressible smoothed particle hydrodynamics Yue, Thomas Pearce, Frazer Kruisbrink, Arno Morvan, Herve The growth of the Kelvin–Helmholtz instability generated at the interface between two ideal gases is studied by means of a Smoothed Particle Hydrodynamics (SPH) scheme suitable for multi-fluids. The SPH scheme is based on the continuity equation approach where the densities of SPH particles are evolved during the simulation, in combination with a momentum equation previously proposed in the literature. A series of simulations were carried out to investigate the influence of viscosity, smoothing, the thickness of density and velocity transition layers. It was found that the effective viscosity of the presented results are strongly dependent on the artificial viscosity parameter αAV, with a linear dependence of 0.15. The utilisation of a viscosity switch is found to significantly reduce the spurious viscosity dependence to 1.68 × 10−4 and generated qualitatively improved behaviour for inviscid fluids. The linear growth rate in the numerical solutions is found to be in satisfactory agreement with analytical expectations, with an average relative error 〈ηsmooth〉=13%. In addition, the role played by velocity and density transition layers is also in general agreement with the analytical theory, except for the sharp-velocity, finite-density gradient cases where the larger growth rate than the classical growth rate is expected. We argue the inherited smoothing properties of the velocity field during the simulations are responsible for causing this discrepancy. Finally, the SPH results are in good agreement for finite velocity and density gradient scenarios, where an average relative error of 〈ηsmooth〉=11.5% is found in our work. Wiley 2015-06-25 Article PeerReviewed Yue, Thomas, Pearce, Frazer, Kruisbrink, Arno and Morvan, Herve (2015) Numerical simulation of two-dimensional Kelvin-Helmholtz instability using weakly compressible smoothed particle hydrodynamics. International Journal for Numerical Methods in Fluids, 78 (5). pp. 283-303. ISSN 1097-0363 smoothed particle hydrodynamics; mesh-free method; hydrodynamic instabilities http://onlinelibrary.wiley.com/doi/10.1002/fld.4017/abstract; doi:10.1002/fld.4017 doi:10.1002/fld.4017 |
| spellingShingle | smoothed particle hydrodynamics; mesh-free method; hydrodynamic instabilities Yue, Thomas Pearce, Frazer Kruisbrink, Arno Morvan, Herve Numerical simulation of two-dimensional Kelvin-Helmholtz instability using weakly compressible smoothed particle hydrodynamics |
| title | Numerical simulation of two-dimensional Kelvin-Helmholtz instability using weakly compressible smoothed particle hydrodynamics |
| title_full | Numerical simulation of two-dimensional Kelvin-Helmholtz instability using weakly compressible smoothed particle hydrodynamics |
| title_fullStr | Numerical simulation of two-dimensional Kelvin-Helmholtz instability using weakly compressible smoothed particle hydrodynamics |
| title_full_unstemmed | Numerical simulation of two-dimensional Kelvin-Helmholtz instability using weakly compressible smoothed particle hydrodynamics |
| title_short | Numerical simulation of two-dimensional Kelvin-Helmholtz instability using weakly compressible smoothed particle hydrodynamics |
| title_sort | numerical simulation of two-dimensional kelvin-helmholtz instability using weakly compressible smoothed particle hydrodynamics |
| topic | smoothed particle hydrodynamics; mesh-free method; hydrodynamic instabilities |
| url | https://eprints.nottingham.ac.uk/44723/ https://eprints.nottingham.ac.uk/44723/ https://eprints.nottingham.ac.uk/44723/ |