### Abstract

The compressible Navier-Stokes equations for an ideal polytropic gas are considered in ℝ^{n}, n = 2,3. The question of possible vacuum formation, an open theoretical problem, is investigated numerically using highly accurate computational methods. The flow is assumed to be symmetric about the origin with a purely radial velocity field. The numerical results indicate that there are weak solutions to the Navier-Stokes system in two and three space dimensions, which display formation of vacuum when the initial data are discontinuous and sufficiently large. The initial density is constant, while the initial velocity field is symmetric, points radially away from the origin, and belongs to H_{loc}^{s} for all s < n/2. In addition, in the one-dimensional case, the numerical solutions are in agreement with known theoretical results.

Original language | English (US) |
---|---|

Pages (from-to) | 1675-1692 |

Number of pages | 18 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 67 |

Issue number | 6 |

DOIs | |

State | Published - Dec 1 2007 |

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### All Science Journal Classification (ASJC) codes

- Applied Mathematics

### Cite this

*SIAM Journal on Applied Mathematics*,

*67*(6), 1675-1692. https://doi.org/10.1137/060652713

}

*SIAM Journal on Applied Mathematics*, vol. 67, no. 6, pp. 1675-1692. https://doi.org/10.1137/060652713

**Numerical investigation of cavitation in multidimensional compressible flows.** / Devault, Kristen J.; Gremaud, Pierre A.; Jenssen, Helge Kristian.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Numerical investigation of cavitation in multidimensional compressible flows

AU - Devault, Kristen J.

AU - Gremaud, Pierre A.

AU - Jenssen, Helge Kristian

PY - 2007/12/1

Y1 - 2007/12/1

N2 - The compressible Navier-Stokes equations for an ideal polytropic gas are considered in ℝn, n = 2,3. The question of possible vacuum formation, an open theoretical problem, is investigated numerically using highly accurate computational methods. The flow is assumed to be symmetric about the origin with a purely radial velocity field. The numerical results indicate that there are weak solutions to the Navier-Stokes system in two and three space dimensions, which display formation of vacuum when the initial data are discontinuous and sufficiently large. The initial density is constant, while the initial velocity field is symmetric, points radially away from the origin, and belongs to Hlocs for all s < n/2. In addition, in the one-dimensional case, the numerical solutions are in agreement with known theoretical results.

AB - The compressible Navier-Stokes equations for an ideal polytropic gas are considered in ℝn, n = 2,3. The question of possible vacuum formation, an open theoretical problem, is investigated numerically using highly accurate computational methods. The flow is assumed to be symmetric about the origin with a purely radial velocity field. The numerical results indicate that there are weak solutions to the Navier-Stokes system in two and three space dimensions, which display formation of vacuum when the initial data are discontinuous and sufficiently large. The initial density is constant, while the initial velocity field is symmetric, points radially away from the origin, and belongs to Hlocs for all s < n/2. In addition, in the one-dimensional case, the numerical solutions are in agreement with known theoretical results.

UR - http://www.scopus.com/inward/record.url?scp=38049009613&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38049009613&partnerID=8YFLogxK

U2 - 10.1137/060652713

DO - 10.1137/060652713

M3 - Article

AN - SCOPUS:38049009613

VL - 67

SP - 1675

EP - 1692

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 6

ER -