基于浅水方程的硇洲岛海域二维潮流数值模拟

2D numerical simulation of tidal current in the sea around Naozhou island based on shallow water equation

以浅水方程为控制方程,对硇洲岛海域潮汐潮流进行了数值模拟。采用有限单元法离散求解浅水方程,将底坡源项归并到压力方程,保证了数值解具有和谐性;在限制水深法的基础上进行水深梯度修正,保证动量守恒,准确模拟了干湿变化过程;根据特征线理论建立边界潮位和潮流流速的关系,使得边界变量满足相容条件。研究结果表明:硇洲岛海域潮流为往复流,临近东海岛处海域流向呈NE-SW向,临近雷州湾处海域流向呈NW-SE向。

The tidal current around Naozhou island is simulated with the shallow equation. The governing equations are discretized by a fractional finite element method using a characteristic-Galerkin procedure. In order to maintain the "well-balanced" property, the bottom slope source term was merged into the pressure equation. Moreover, a local bed slope modification technique is employed in drying-wetting interface treatments, the gradient of water depth was modified to ensure momentum conservation. Then the relationship between tidal level and velocity at the boundary was established based on the characteristic theory to ensure the accuracy of simulation. The results show that the tidal current around Naozhou island is the reciprocating-flow.The tidal current near the Donghai island flows along the NE-SW direction, while flows along the NW-SE direction near Leizhou bay.