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
 Citation: 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.

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

##### doi: 10.21656/1000-0887.370118
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
• 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.
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沈阳化工大学材料科学与工程学院 沈阳 110142

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