油水资源数值模拟中分数步长法和算子分裂法

Fractional Steps and Operator-splitting Methods of Numerical Simulation in the Resources of Oil and Water

作者应用计算数学、渗流力学及其理论分析来研究海水入侵和防治、油田勘探和开发中数值模拟的分数步长法和算子分裂法。数学模型是一类耦合非线性偏微分方程组的初边值问题。考虑三维问题大规模科学与工程计算的特征 ,重点研究三维迎风分数步长差分方法、特征分数步长差分方法和算子分裂特征有限元法及其数值分析。

For the three-dimensional nonlinear partial differential equation with initial-boundary problem we put forward the upwind finite difference fractional steps method, the characteristic finite difference fractional steps method and the characteristic finite element operator-splitting method. Optimal order estimates in L2 norm are derived for the error in the approximation solution.