一个求解浅水波方程的时域分段展开算法

发展了一种时域分段展开自适应方法求解一维非线性浅水波方程。通过时域分段展开,将一个非线性的时空耦合初边值问题转化为一系列的线性空间边值问题,并采用有限元方法递推求解;通过展开阶数的递进,实现了分段时域的自适应计算,当不同步长时可保持稳定的计算精度。研究结果表明,当步长较大而Heun’s法、四阶Runge-Kutta法不能得到合理结果时,本文算法仍能保证足够的计算精度。

A temporally-piecewise adaptive algorithm to solve shallow water equations

A temporally-piecewise adaptive algorithm is developed to solve 1-D shallow water equations.By expanding variables at a discretized time interval,a nonlinear time and space coupled initial boundary value problem is converted into a series of recursive linear boundary value problems which are tackled by FEM,and no approximation and iteration related with non-linearity are required.An adaptive computation is conducted to maintain a steady computing accuracy for different step sizes.Numerical comparison shows that when the time step is relatively larger,a sufficient computing accuracy can be achieved by the proposed algorithm,while Heun's method and 4-order Runge-Kutta method lead to unreasonable results.