非结构化网格下椭圆型缓坡方程的数值求解

Numerical simulation of elliptic mild-slope equation on unstructured grid

椭圆型缓坡方程是一种用线性波浪理论研究近岸波浪传播变形的有效波浪数学模型。非结构化网格下的有限容积法不仅对复杂边界的适应性好,还能保证迭代求解过程的守恒性。建立了非结构化网格下的椭圆型缓坡方程数值模型。在模型中采用非结构化网格下的有限容积法对椭圆型缓坡方程进行了数值离散,结合GPBiCG(m,n)算法求解离散方程。数值计算结果表明,该数值模型可有效地用于模拟近岸缓坡区域复杂边界下波浪的传播。

The elliptic mild-slope equation for linear water waves is an effective mathematic model for studying the water wave propagating in coastal mild-slope zones. The finite volume method on a unstructured grid system is adaptive well to complicated boundaries, and keeps conservation during the iterative calculation. The numerical model for the elliptic mild-slope equation on the unstructured grid is presented. In the presented model, the elliptic mild-slope equation is discredited based on the finite volume method on the unstructured grid, and the GPBiCG（m, n） algorithm is applied to solve the discredited equation. It is shown that the presented numerical model can be applicable to simulating the coastal wave propagation in complicated boundary conditions effectively.