### Abstract

This paper, investigates the feasibility of performing a robust numerical simulation of the dynamics of vortex cavitation. An equilibrium cavitation model is employed, which assumes local thermodynamic and mechanical equilibrium in the two-phase flow region. Furthermore, the phase transition does not depend on empirical constants in this model. The computational method assumes a compressible flow together with appropriate thermodynamic equations of state i.e. Tait's equation for the liquid phase, a perfect gas for the vapor phase, and an equilibrium model for the mixture phase. The unsteady compressible Euler equations are employed using a cell-centered structured multi-block finite volume scheme. The viscous terms are not taken into account, because the numerical issues encountered are typically caused by (the discretization of) the inviscid equations. The 3D vortex cavitation simulations using a MUSCL scheme on an Arndt's elliptic hydrofoil are presented. The results show that the common MUSCL schemes are not well-suited for such complex simulations. For an accurate representation of the cavitating flow, the higher-order accurate Weighted Essentially Non-Oscillatory (WENO) schemes are considered. In order to avoid negative density and/or internal energy, the scheme must fulfill the positivity-preserving property. The existing positivity-preserving approaches use limiter functions to preserve the monotonicity of the solution near the discontinuities. It is well-known that the limiter functions introduce considerable amount of artificial dissipation, which is highly undesirable in vortex cavitation simulations. We propose a non-limiting (no slope/flux limiters) positivity-preserving strategy for WENO schemes, which is rather simple and computationally low-cost. Some 1D test case simulations with or without cav-itation are presented to assess the developed positivity-preserving WENO aproach.

Original language | English |
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Title of host publication | 11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014 |

Editors | Antonio Huerta, Eugenio Onate, Xavier Oliver |

Publisher | International Center for Numerical Methods in Engineering |

Pages | 4765-4778 |

Number of pages | 14 |

ISBN (Electronic) | 9788494284472 |

Publication status | Published - 1 Jul 2014 |

Event | Joint 11th World Congress on Computational Mechanics, WCCM 2014, the 5th European Conference on Computational Mechanics, ECCM 2014 and the 6th European Conference on Computational Fluid Dynamics, ECFD 2014 - Barcelona, Spain Duration: 20 Jul 2014 → 25 Jul 2014 http://congress.cimne.com/iacm-eccomas2014/ |

### Conference

Conference | Joint 11th World Congress on Computational Mechanics, WCCM 2014, the 5th European Conference on Computational Mechanics, ECCM 2014 and the 6th European Conference on Computational Fluid Dynamics, ECFD 2014 |
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Country | Spain |

City | Barcelona |

Period | 20/07/14 → 25/07/14 |

Internet address |

### Fingerprint

### Keywords

- Cavitation
- Positivity-preserving
- Vortex dynamics
- WENO

### Cite this

*11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014*(pp. 4765-4778). International Center for Numerical Methods in Engineering.

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*11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014.*International Center for Numerical Methods in Engineering, pp. 4765-4778, Joint 11th World Congress on Computational Mechanics, WCCM 2014, the 5th European Conference on Computational Mechanics, ECCM 2014 and the 6th European Conference on Computational Fluid Dynamics, ECFD 2014, Barcelona, Spain, 20/07/14.

**Numerical issues in higher-order accurate simulations of flows with vortex cavitation.** / Khatami, Faraz; van der Weide, Edwin T.A.; Hoeijmakers, Harry W.M.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Numerical issues in higher-order accurate simulations of flows with vortex cavitation

AU - Khatami, Faraz

AU - van der Weide, Edwin T.A.

AU - Hoeijmakers, Harry W.M.

PY - 2014/7/1

Y1 - 2014/7/1

N2 - This paper, investigates the feasibility of performing a robust numerical simulation of the dynamics of vortex cavitation. An equilibrium cavitation model is employed, which assumes local thermodynamic and mechanical equilibrium in the two-phase flow region. Furthermore, the phase transition does not depend on empirical constants in this model. The computational method assumes a compressible flow together with appropriate thermodynamic equations of state i.e. Tait's equation for the liquid phase, a perfect gas for the vapor phase, and an equilibrium model for the mixture phase. The unsteady compressible Euler equations are employed using a cell-centered structured multi-block finite volume scheme. The viscous terms are not taken into account, because the numerical issues encountered are typically caused by (the discretization of) the inviscid equations. The 3D vortex cavitation simulations using a MUSCL scheme on an Arndt's elliptic hydrofoil are presented. The results show that the common MUSCL schemes are not well-suited for such complex simulations. For an accurate representation of the cavitating flow, the higher-order accurate Weighted Essentially Non-Oscillatory (WENO) schemes are considered. In order to avoid negative density and/or internal energy, the scheme must fulfill the positivity-preserving property. The existing positivity-preserving approaches use limiter functions to preserve the monotonicity of the solution near the discontinuities. It is well-known that the limiter functions introduce considerable amount of artificial dissipation, which is highly undesirable in vortex cavitation simulations. We propose a non-limiting (no slope/flux limiters) positivity-preserving strategy for WENO schemes, which is rather simple and computationally low-cost. Some 1D test case simulations with or without cav-itation are presented to assess the developed positivity-preserving WENO aproach.

AB - This paper, investigates the feasibility of performing a robust numerical simulation of the dynamics of vortex cavitation. An equilibrium cavitation model is employed, which assumes local thermodynamic and mechanical equilibrium in the two-phase flow region. Furthermore, the phase transition does not depend on empirical constants in this model. The computational method assumes a compressible flow together with appropriate thermodynamic equations of state i.e. Tait's equation for the liquid phase, a perfect gas for the vapor phase, and an equilibrium model for the mixture phase. The unsteady compressible Euler equations are employed using a cell-centered structured multi-block finite volume scheme. The viscous terms are not taken into account, because the numerical issues encountered are typically caused by (the discretization of) the inviscid equations. The 3D vortex cavitation simulations using a MUSCL scheme on an Arndt's elliptic hydrofoil are presented. The results show that the common MUSCL schemes are not well-suited for such complex simulations. For an accurate representation of the cavitating flow, the higher-order accurate Weighted Essentially Non-Oscillatory (WENO) schemes are considered. In order to avoid negative density and/or internal energy, the scheme must fulfill the positivity-preserving property. The existing positivity-preserving approaches use limiter functions to preserve the monotonicity of the solution near the discontinuities. It is well-known that the limiter functions introduce considerable amount of artificial dissipation, which is highly undesirable in vortex cavitation simulations. We propose a non-limiting (no slope/flux limiters) positivity-preserving strategy for WENO schemes, which is rather simple and computationally low-cost. Some 1D test case simulations with or without cav-itation are presented to assess the developed positivity-preserving WENO aproach.

KW - Cavitation

KW - Positivity-preserving

KW - Vortex dynamics

KW - WENO

UR - http://www.scopus.com/inward/record.url?scp=84924011932&partnerID=8YFLogxK

M3 - Conference contribution

SP - 4765

EP - 4778

BT - 11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014

A2 - Huerta, Antonio

A2 - Onate, Eugenio

A2 - Oliver, Xavier

PB - International Center for Numerical Methods in Engineering

ER -