Efficient Numerical Solution of Steady Free-Surface Navier–Stokes Flow
Numerical solution of flows that are partially bounded by a freely moving boundary is of great importance in practical applications such as ship hydrodynamics. The usual method for solving steady viscous free-surface flow subject to gravitation is alternating time integration of the kinematic condit...
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| Published in | Journal of computational physics Vol. 174; no. 1; pp. 120 - 137 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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Elsevier Inc
20.11.2001
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| Abstract | Numerical solution of flows that are partially bounded by a freely moving boundary is of great importance in practical applications such as ship hydrodynamics. The usual method for solving steady viscous free-surface flow subject to gravitation is alternating time integration of the kinematic condition, and the Navier–Stokes equations subject to the dynamic conditions, until steady state is reached. This paper shows that this time integration approach is often inefficient. It proposes an efficient iterative method for solving the steady free-surface flow problem. The new method relies on a different but equivalent formulation of the free-surface flow problem, involving a so-called quasi free-surface condition. The convergence behavior of the new method is shown to be asymptotically mesh-width independent. Numerical results are presented for two-dimensional flow over an obstacle in a channel. The results confirm the mesh-width independence of the convergence behavior, and comparison of the numerical results with measurements shows good agreement. |
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| AbstractList | Numerical solution of flows that are partially bounded by a freely moving boundary is of great importance in practical applications such as ship hydrodynamics. The usual method for solving steady viscous free-surface flow subject to gravitation is alternating time integration of the kinematic condition, and the Navier-Stokes equations subject to the dynamic conditions, until steady state is reached, This paper shows that this time integration approach is often inefficient. It proposes an efficient iterative method for solving the steady free-surface flow problem. The new method relies on a different but equivalent formulation of the free-surface flow problem, involving a so-called quasi-free-surface condition. The convergence behavior of the new method is shown to be asymptotically mesh-width independent. Numerical results are presented for two-dimensional flow over an obstacle in a channel. The results confirm the mesh-width independence of the convergence behavior, and comparison of the numerical results with measurements shows good agreement. (Author) Numerical solution of flows that are partially bounded by a freely moving boundary is of great importance in practical applications such as ship hydrodynamics. The usual method for solving steady viscous free-surface flow subject to gravitation is alternating time integration of the kinematic condition, and the Navier–Stokes equations subject to the dynamic conditions, until steady state is reached. This paper shows that this time integration approach is often inefficient. It proposes an efficient iterative method for solving the steady free-surface flow problem. The new method relies on a different but equivalent formulation of the free-surface flow problem, involving a so-called quasi free-surface condition. The convergence behavior of the new method is shown to be asymptotically mesh-width independent. Numerical results are presented for two-dimensional flow over an obstacle in a channel. The results confirm the mesh-width independence of the convergence behavior, and comparison of the numerical results with measurements shows good agreement. |
| Author | Koren, B. van Brummelen, E.H. Raven, H.C. |
| Author_xml | – sequence: 1 givenname: E.H. surname: van Brummelen fullname: van Brummelen, E.H. organization: CWI, P.O. Box 94079, Amsterdam, 1090 GB, The Netherlandsf1harald.van.brummelen@cwi.nl; barry.koren@cwi.nlf1 – sequence: 2 givenname: H.C. surname: Raven fullname: Raven, H.C. organization: Maritime Research Institute Netherlands, P.O. Box 28, Wageningen, 6700 AA, The Netherlandsf2h.c.raven@marin.nlf2 – sequence: 3 givenname: B. surname: Koren fullname: Koren, B. organization: CWI, P.O. Box 94079, Amsterdam, 1090 GB, The Netherlandsf1harald.van.brummelen@cwi.nl; barry.koren@cwi.nlf1 |
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| Cites_doi | 10.1002/fld.1650190404 10.1002/(SICI)1097-0363(19970915)25:5<567::AID-FLD577>3.0.CO;2-Q 10.1016/0021-9991(81)90232-1 10.1016/0021-9991(80)90091-1 10.1002/fld.1650210902 10.2514/6.1993-767 10.1016/0021-9991(87)90090-8 10.1016/0009-2509(60)87003-0 10.1006/jcph.1996.0081 |
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| Keywords | free-surface flows numerical solution methods incompressible Navier–Stokes equations |
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Ta'asan, Infinite dimensional preconditioners for optimal design problems, in, Inverse Design and Optimization Methods, edited by, R. A. van denBraembussche and M. Manna, VKI Lecture Series, Von Karman Institute for Fluid Dynamics, 1997, Vol, 5. – year: 1967 ident: RF3 – year: 1974 ident: RF7 – volume: 125 start-page: 83 year: 1996 ident: RF16 article-title: A Newton–Raphson pseudo-solid domain mapping technique for free and moving boundary problems: A finite element implementation publication-title: J. Comput. Phys – year: 1989 ident: RF25 – year: 1984 ident: RF5 – year: 1978 ident: RF12 – volume: 72 start-page: 393 year: 1987 ident: RF13 article-title: Difference solution of a viscous flow with free-surface wave about an advancing ship publication-title: J. Comput. Phys – reference: M. Vogt, A numerical investigation of the level set method for computing free surface waves, Tech. Rep. 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| Title | Efficient Numerical Solution of Steady Free-Surface Navier–Stokes Flow |
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