求解浅水流动的分步有限元方法

A fractional step finite element method for shallow water flows

本文将分步有限元的计算方法引入到浅水方程组的求解中。该方法起源于Taylor Galerkin(T G)方法,但数值稳定性优于T G法并具有三阶精度。由于计算中没有引入高阶的空间导数项,实现起来比Taylor Galerkin方法简单,适用于非线性和多维问题的求解。计算模型中包含了零方程和双方程的紊流模型,可以根据需要选择。文中详细介绍了初始和边界条件的取法,并通过五个算例验证了计算模型的可靠性。

A fractional step finite element method is introduced to solve the shallow water flows. This method originates from Taylor-Galerkin method. It has third-order accuracy and better stability property than the T-G method. Compared with Taylor-Galerkin method, no higher order spacial derivative is involved in the present one, so it can be easily implemented and is suitable for solving nonlinear and multi-dimensional problems. Zero-equation and two-equation turbulence models are included in the solver. The implementation of initial and boundary conditions is discussed in detail in this paper. Five numerical experiments are used to verify the present method.