An SPH multi-fluid model based on quasi-buoyancy for interface stabilization up to high density ratios and realistic wave speed ratios
We introduce a Smoothed Particle Hydrodynamics (SPH) concept for the stabilization of the interface between two fluids. It is demonstrated that the change in the pressure gradient across the interface leads to a force imbalance. This force imbalance is attributed to the particle approximation implic...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Published: |
Wiley
2018
|
| Subjects: | |
| Online Access: | https://eprints.nottingham.ac.uk/50120/ |
| _version_ | 1848798160017686528 |
|---|---|
| author | Kruisbrink, Arno C.H. Pearce, F.R. Yue, T. Morvan, H.P. |
| author_facet | Kruisbrink, Arno C.H. Pearce, F.R. Yue, T. Morvan, H.P. |
| author_sort | Kruisbrink, Arno C.H. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | We introduce a Smoothed Particle Hydrodynamics (SPH) concept for the stabilization of the interface between two fluids. It is demonstrated that the change in the pressure gradient across the interface leads to a force imbalance. This force imbalance is attributed to the particle approximation implicit to SPH. To stabilize the interface a pressure gradient correction is proposed. In this approach the multi-fluid pressure gradients are related to the (gravitational and fluid) accelerations. This leads to a quasi-buoyancy correction for hydrostatic (stratified) flows, which is extended to non-hydrostatic flows. The result is a simple density correction which involves no parameters or coefficients. This correction is included as an extra term in the SPH momentum equation.
The new concept for the stabilization of the interface is explored in five case studies and compared with other multi-fluid models. The first case is the stagnant flow in a tank: the interface remains stable up to density ratios of 1:1000 (typical for water and air) in combination with artificial wave speed ratios up to 1:4. The second and third cases are the Rayleigh-Taylor instability and the rising bubble, where a reasonable agreement between SPH and level-set models is achieved. The fourth case is an air flow across a water surface up to density ratios of 1:100, artificial wave speeds for water higher than that of air, and high air velocities. The fifth case is about the propagation of internal gravity waves up to density ratios of 1:100 and artificial wave speed ratios of 1:2.
It is demonstrated that the quasi-buoyancy model may be used to stabilize the interface between two fluids up to high density ratios, with real (low) viscosities and more realistic wave speed ratios than achieved by other WCSPH multi-fluid models. Real wave speed ratios can be achieved, as long as the fluid velocities are not very high. Although the wave speeds may be artificial in many cases, correct and realistic wave speed ratios are essential in the modelling of heat transfer between two fluids (e.g. in engineering applications such as gas turbines). |
| first_indexed | 2025-11-14T20:15:21Z |
| format | Article |
| id | nottingham-50120 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T20:15:21Z |
| publishDate | 2018 |
| publisher | Wiley |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-501202020-05-04T19:48:23Z https://eprints.nottingham.ac.uk/50120/ An SPH multi-fluid model based on quasi-buoyancy for interface stabilization up to high density ratios and realistic wave speed ratios Kruisbrink, Arno C.H. Pearce, F.R. Yue, T. Morvan, H.P. We introduce a Smoothed Particle Hydrodynamics (SPH) concept for the stabilization of the interface between two fluids. It is demonstrated that the change in the pressure gradient across the interface leads to a force imbalance. This force imbalance is attributed to the particle approximation implicit to SPH. To stabilize the interface a pressure gradient correction is proposed. In this approach the multi-fluid pressure gradients are related to the (gravitational and fluid) accelerations. This leads to a quasi-buoyancy correction for hydrostatic (stratified) flows, which is extended to non-hydrostatic flows. The result is a simple density correction which involves no parameters or coefficients. This correction is included as an extra term in the SPH momentum equation. The new concept for the stabilization of the interface is explored in five case studies and compared with other multi-fluid models. The first case is the stagnant flow in a tank: the interface remains stable up to density ratios of 1:1000 (typical for water and air) in combination with artificial wave speed ratios up to 1:4. The second and third cases are the Rayleigh-Taylor instability and the rising bubble, where a reasonable agreement between SPH and level-set models is achieved. The fourth case is an air flow across a water surface up to density ratios of 1:100, artificial wave speeds for water higher than that of air, and high air velocities. The fifth case is about the propagation of internal gravity waves up to density ratios of 1:100 and artificial wave speed ratios of 1:2. It is demonstrated that the quasi-buoyancy model may be used to stabilize the interface between two fluids up to high density ratios, with real (low) viscosities and more realistic wave speed ratios than achieved by other WCSPH multi-fluid models. Real wave speed ratios can be achieved, as long as the fluid velocities are not very high. Although the wave speeds may be artificial in many cases, correct and realistic wave speed ratios are essential in the modelling of heat transfer between two fluids (e.g. in engineering applications such as gas turbines). Wiley 2018-08-10 Article PeerReviewed Kruisbrink, Arno C.H., Pearce, F.R., Yue, T. and Morvan, H.P. (2018) An SPH multi-fluid model based on quasi-buoyancy for interface stabilization up to high density ratios and realistic wave speed ratios. International Journal for Numerical Methods in Fluids, 87 (10). pp. 487-507. ISSN 1097-0363 Smoothed particle hydrodynamics multi-fluid interface treatment https://onlinelibrary.wiley.com/doi/abs/10.1002/fld.4498 doi:10.1002/fld.4498 doi:10.1002/fld.4498 |
| spellingShingle | Smoothed particle hydrodynamics multi-fluid interface treatment Kruisbrink, Arno C.H. Pearce, F.R. Yue, T. Morvan, H.P. An SPH multi-fluid model based on quasi-buoyancy for interface stabilization up to high density ratios and realistic wave speed ratios |
| title | An SPH multi-fluid model based on quasi-buoyancy for interface stabilization up to high density ratios and realistic wave speed ratios |
| title_full | An SPH multi-fluid model based on quasi-buoyancy for interface stabilization up to high density ratios and realistic wave speed ratios |
| title_fullStr | An SPH multi-fluid model based on quasi-buoyancy for interface stabilization up to high density ratios and realistic wave speed ratios |
| title_full_unstemmed | An SPH multi-fluid model based on quasi-buoyancy for interface stabilization up to high density ratios and realistic wave speed ratios |
| title_short | An SPH multi-fluid model based on quasi-buoyancy for interface stabilization up to high density ratios and realistic wave speed ratios |
| title_sort | sph multi-fluid model based on quasi-buoyancy for interface stabilization up to high density ratios and realistic wave speed ratios |
| topic | Smoothed particle hydrodynamics multi-fluid interface treatment |
| url | https://eprints.nottingham.ac.uk/50120/ https://eprints.nottingham.ac.uk/50120/ https://eprints.nottingham.ac.uk/50120/ |