同位网格下平面二维水流数学模型的有限分析解法

Finite analytic numerical solution of plane 2-D water mathematical model with co-located grid

为避免在求解平面二维水流数学模型方程时,流速、水位分别采用有限分析法和有限差分法求解而导致运动方程和连续性方程的计算精度不匹配,进而降低模型整体的计算精度和收敛速度.参照SIMPLE算法,推导出了能够在同位网格下采用有限分析法求解的一般曲线坐标系中的水位控制方程,实现在同位网格下采用有限分析方法求解全部控制方程的同精度算法,避免了交错网格,提高了计算精度,加快了收敛速度.运用于实际工程,计算结果与实测值基本吻合.

When the finite analytic method（FAM） is used to solve the plane 2-D water mathematical model equations previously, the momentum equation is solved by FAM ; and the continuity equation is solved by finite difference method. Then the stagger grid scheme has to be used to avoid the bad water elevation result. However the stagger grid is inconvenient and less accurate. This paper presents a new continuity equation in body-fitted curvilinear coordinate system that can be solved with FAM based on co-located grid. So the whole numerical governing equations solved under the same accuracy arithmetic with FAM based on co-located grid are attained. Since the stagger scheme is avoided, the calculational accuracy and speed are improved.