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本文使用双水平集函数逼近油藏模型特征,构造出Uzawas算法进行数值模拟.对于两相流渗透率的数值求解问题,可以通过测量油井数据和地震波数据来实现.将构造出来的带限制的最优化问题使用变异的Lagrange方法求解.如果使用双水平集函数逼近渗透率函数,则需要对Lagrange函数进行修正,从而将带限制的最优化问题转化成无限制的最优化问题.由于双水平集函数的优越性,进一步构造出最速梯度下降Uzawas算法和算子分裂格式Uzawas算法进行求解对应的最优化子问题.数值算例表明设计的算法是高效的、稳定的.
In this paper, the bi-level set function is used to approximate the reservoir model characteristics and the Uzawas algorithm is constructed for numerical simulation.The numerical solution to the permeability of two-phase flow can be achieved by measuring well data and seismic wave data.The constructed band limit The optimization problem is solved using the Lagrange method of variation. If the permeability function is approximated by a bi-level set function, the Lagrange function needs to be modified to transform the restricted optimization problem into an infinite optimization problem. Since the bi-level set function The Uzawas algorithm and Uzawas algorithm are further constructed to solve the corresponding optimization subproblem.The numerical examples show that the proposed algorithm is efficient and stable.