Euler方程有限差分方法数值模拟

Numerical Simulation of Euler Equations with a Finite Difference Method

研究了定义在二维水槽上带非线性自由面边界条件的Euler方程的数值解.通过合适的σ坐标变换对不规则的水槽液体区域变换为一个规则的正方形区域,建立流场变量的差分耦合迭代的算法,运用交错网格求解了无粘不可压缩的Euler方程的数值解,数值结果表明,与之前结果和解析解比较数值解较好,对水平激励和垂直激励下非线性的效果和波拍的现象非常明显.

The numerical solutions of Euler equation with a σ coordinate transformation are studied in a two-dimensional tank.A finite difference mehtod is used to solve Euler equation with a nonlinear boundary condition.The irregular tank is mapped onto a fixed square domain through a coordinate transformation,and a staggered mesh system is employed in two dimensional tank in order to evaluate the elevation of the transient fluid.The surge and heave motions are presented in this paper and the non-linear and beating phenomena are very clear.The numerical solution agree well with previously published results and analytic solution.