Single- to Double-Vortex Numerical Simulation in 2D Water Tanks Based on the Linearized Navier-Stokes Equations

HAN Hong-yang; LUO Zhi-qiang

doi:10.21656/1000-0887.370118

Volume 37 Issue 9

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HAN Hong-yang, LUO Zhi-qiang. Single- to Double-Vortex Numerical Simulation in 2D Water Tanks Based on the Linearized Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2016, 37(9): 953-968. doi: 10.21656/1000-0887.370118

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Single- to Double-Vortex Numerical Simulation in 2D Water Tanks Based on the Linearized Navier-Stokes Equations

doi: 10.21656/1000-0887.370118

Department of Mathematics, Kunming University of Science and Technology,Kunming 650500, P.R.China

Funds: The National Natural Science Foundation of China(11561037)

Received Date: 2016-04-14
Rev Recd Date: 2016-07-16
Publish Date: 2016-09-15

Abstract

Abstract

A predictor-corrector finite difference method based on the linearized Navier-Stokes equations was developed to numerically simulate the single- and double-vortex motions in 2D rectangular water tanks. Numerical results obtained with the present method were compared with the linearized analytical solution and previously published numerical results, and the agreements were pretty good. It is found that the free surface wave oscillates with a decaying amplitude in the case of viscous fluid, and as the Reynolds number increases, the free surface wave elevation decays more slowly. Under the short-period pitching excitation, a clear single vortex cycle occurs at different Reynolds numbers. However, the single vortex will change to double ones in the case of a long-period pitching excitation, only when the Reynolds number is small to some extent.
- linearized Navier-Stokes equations,
- predictor-corrector finite difference method,
- vortex,
- staggered grid,
- numerical simulation

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References(24)

References

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