TVD三阶和四阶格式求解渗流方程新方法

New Method to Solve Flow Equation using Total Variation Diminishing Schemes with Third and Fourth Order Accuracy

在使用显式格式计算含水率曲线过程中,如果空间步长太大,则会造成差分格式的不稳定。为了减弱空间步长带来的影响,建立了TVD三阶和四阶格式来计算两相流问题的含水率,与一点上游加权格式和两点上游加权格式进行比较,可以看出,用TVD格式计算的结果与实际结果更接近;该格式在稳定性方面也比上游加权格式稳定,Courant数的大小对格式的稳定性起决定作用。

When calculating water cut curves with explicit method, the exceedingly large spatial step will cause the instability of difference scheme. In order to decrease the effect of spatial step, the third order and fourth order accuracy total variation diminishing schemes were buiet to calculate the water cut of two phase flow. It is easy to find out that the result of these two schemes are much closer to the actual result when comparing with one point and two points upstream weighting schemes. Also, these two schemes are steadier than upstream weighting schemes, and the Courant number is critical to the stability of these schemes.