不可压缩可混溶驱动问题迎风区域分裂差分方法(英文)

Domain Decomposition with the Upwind Difference Method for Incompressible Miscible Displacement in Porous Media

结合区域分裂思想,本文给出了一维不可压缩可混溶驱动问题两种非重叠区域分裂迎风差分格式。由于饱和度的计算规模远大于压力方程,因此饱和度方程采用了迎风区域分裂差分法,内边界处和各子区域分别对应显隐格式。在稳定性条件下,给出了 l2 模误差估计,最后给出数值算例验证了理论结果。

Basing on the upwind difference method, we present domain decomposition schemes for 1-D incompressible miscible flow in porous media with nonoverlapping domain. Since the scale of solver for the saturation is much larger than that for the pressure, the saturation equation is treated by domain decomposition schemes, which apply an upwind approximation to the first derivative and rely on implicit procedures in subdomains and explicit calculation on inter-domain boundaries. Convergence in l^2-norm is analyzed under suitable assumptions. Numerical results illustrate the theoretical results and their accuracy.