基于迎风差分格式的TVD聚合物驱数学模拟

聚合物驱替过程中存在饱和度和聚合物质量浓度2个间断,在2个间断之间有"油墙"形成。文中分别运用特征线法(MOC)、一阶迎风差分(SPU)方法和显式全变差递减差分(TVD)方法对聚合物驱替过程进行求解,通过与特征线解进行对比,考察了SPU方法和TVD方法的数值模拟效果。研究表明:SPU方法的精度低,数值耗散严重,对2个间断特别是聚合物质量浓度间断的捕捉能力较差;高阶精度TVD方法分辨力高,但在"油墙"处会产生非物理"振荡"。利用迎风的思想,对传统TVD方法进行了改进。数值实验表明,改进的TVD方法在保持高精确度的同时,还能有效地防止非物理"振荡"的产生,具有较好的稳定性。

Mathematical simulation of polymer flooding with upstream-TVD solution

For polymer flooding,there are two discontinuities of saturation and concentration,between which "oil bank" exists.The polymer flooding was investigated with method of characteristics(MOC),single point upstream(SPU) finite difference method and explicit total variation diminishing(TVD) finite difference method respectively.Based on the solution of MOC,performance of simulation results of both SPU and TVD were evaluated.It is suggested TVD exhibits a better numerical performance while the SPU scheme suffers numerical diffusion badly.The conventional TVD method is modified on the calculation of numerical flux,so that non-physical oscillation can be prevented on the "oil bank" between the two discontinuities.Numerical tests demonstrate that the upstream-TVD can achieve better stability than the conventional TVD method.