### Abstract

Richtmyer-Meshkov (RM) instability occurs when one fluid is impulsively accelerated into a second fluid, such that ρ_{1} ρ_{2}. This research numerically investigates RM instabilities between incompressible media, similar to the experiments reported by Niederhaus & Jacobs [1]. A two-dimensional, finite-volume numerical algorithm has been developed to solve the variable density Navier-Stokes equations explicitly on a Cartesian, co-located grid. In previous calculations, no physical viscosity was implemented; however, small scale fluctuations were damped by the numerical algorithm. In contrast, current simulations incorporate the physical viscosities reported by Niederhaus & Jacobs [1] and are explicitly used. Calculations of volume fraction and momentum advections are second-order accurate in space. Unphysical oscillations due to the higher-order advection scheme are minimized through the use of a Van Leer flux limiting algorithm. An initial velocity impulse [2] has been used to model the impulsive acceleration history found in the experiments of Niederhaus & Jacobs [1]. Both inviscid and viscous simulations result in similar growth rates for the interpenetration of one fluid into another. However, the inviscid simulations (i.e. no explicit viscosity) are unable to capture the full dynamics of the internal vortex structure that exists between the two fluids due to the absence of viscous effects.

Original language | English (US) |
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Title of host publication | American Society of Mechanical Engineers, Fluids Engineering Division (Publication) FED |

Pages | 109-118 |

Number of pages | 10 |

Volume | 261 FED |

DOIs | |

State | Published - 2005 |

Event | 2005 ASME International Mechanical Engineering Congress and Exposition, IMECE 2005 - Orlando, FL, United States Duration: Nov 5 2005 → Nov 11 2005 |

### Other

Other | 2005 ASME International Mechanical Engineering Congress and Exposition, IMECE 2005 |
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Country | United States |

City | Orlando, FL |

Period | 11/5/05 → 11/11/05 |

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### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*American Society of Mechanical Engineers, Fluids Engineering Division (Publication) FED*(Vol. 261 FED, pp. 109-118) https://doi.org/10.1115/IMECE2005-82723

**Numerical investigation of internal vortex structure in two dimensional, incompressible Richtmyer-Meshkov flows.** / Mueschke, Nicholas J.; Kraft, Wayne N.; Andrews, Malcolm J.; Jacobs, Jeffrey W.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*American Society of Mechanical Engineers, Fluids Engineering Division (Publication) FED.*vol. 261 FED, pp. 109-118, 2005 ASME International Mechanical Engineering Congress and Exposition, IMECE 2005, Orlando, FL, United States, 11/5/05. https://doi.org/10.1115/IMECE2005-82723

}

TY - GEN

T1 - Numerical investigation of internal vortex structure in two dimensional, incompressible Richtmyer-Meshkov flows

AU - Mueschke, Nicholas J.

AU - Kraft, Wayne N.

AU - Andrews, Malcolm J.

AU - Jacobs, Jeffrey W

PY - 2005

Y1 - 2005

N2 - Richtmyer-Meshkov (RM) instability occurs when one fluid is impulsively accelerated into a second fluid, such that ρ1 ρ2. This research numerically investigates RM instabilities between incompressible media, similar to the experiments reported by Niederhaus & Jacobs [1]. A two-dimensional, finite-volume numerical algorithm has been developed to solve the variable density Navier-Stokes equations explicitly on a Cartesian, co-located grid. In previous calculations, no physical viscosity was implemented; however, small scale fluctuations were damped by the numerical algorithm. In contrast, current simulations incorporate the physical viscosities reported by Niederhaus & Jacobs [1] and are explicitly used. Calculations of volume fraction and momentum advections are second-order accurate in space. Unphysical oscillations due to the higher-order advection scheme are minimized through the use of a Van Leer flux limiting algorithm. An initial velocity impulse [2] has been used to model the impulsive acceleration history found in the experiments of Niederhaus & Jacobs [1]. Both inviscid and viscous simulations result in similar growth rates for the interpenetration of one fluid into another. However, the inviscid simulations (i.e. no explicit viscosity) are unable to capture the full dynamics of the internal vortex structure that exists between the two fluids due to the absence of viscous effects.

AB - Richtmyer-Meshkov (RM) instability occurs when one fluid is impulsively accelerated into a second fluid, such that ρ1 ρ2. This research numerically investigates RM instabilities between incompressible media, similar to the experiments reported by Niederhaus & Jacobs [1]. A two-dimensional, finite-volume numerical algorithm has been developed to solve the variable density Navier-Stokes equations explicitly on a Cartesian, co-located grid. In previous calculations, no physical viscosity was implemented; however, small scale fluctuations were damped by the numerical algorithm. In contrast, current simulations incorporate the physical viscosities reported by Niederhaus & Jacobs [1] and are explicitly used. Calculations of volume fraction and momentum advections are second-order accurate in space. Unphysical oscillations due to the higher-order advection scheme are minimized through the use of a Van Leer flux limiting algorithm. An initial velocity impulse [2] has been used to model the impulsive acceleration history found in the experiments of Niederhaus & Jacobs [1]. Both inviscid and viscous simulations result in similar growth rates for the interpenetration of one fluid into another. However, the inviscid simulations (i.e. no explicit viscosity) are unable to capture the full dynamics of the internal vortex structure that exists between the two fluids due to the absence of viscous effects.

UR - http://www.scopus.com/inward/record.url?scp=33645989438&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33645989438&partnerID=8YFLogxK

U2 - 10.1115/IMECE2005-82723

DO - 10.1115/IMECE2005-82723

M3 - Conference contribution

AN - SCOPUS:33645989438

SN - 0791842193

SN - 9780791842195

VL - 261 FED

SP - 109

EP - 118

BT - American Society of Mechanical Engineers, Fluids Engineering Division (Publication) FED

ER -