A projected Newton algorithm based on chemically allowed interval for chemical equilibrium computations  

作　　者：Hongbin Lu Shaohui Tao Xiaoyan Sun Li Xia Shuguang Xiang 

机构地区：[1]Institute of Process Systems Engineering,College of Chemical Engineering,Qingdao University of Science and Technology,Qingdao,266042,China

出　　处：《Frontiers of Chemical Science and Engineering》2024年第3期25-37,共13页化学科学与工程前沿（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.22178190 and 22008129).

摘　　要：The chemical equilibrium equations utilized in reactive transport modeling are complex and nonlinear,and are typically solved using the Newton-Raphson method.Although this algorithm is known for its quadratic convergence near the solution,it is less effective far from the solution,especially for ill-conditioned problems.In such cases,the algorithm may fail to converge or require excessive iterations.To address these limitations,a projected Newton method is introduced to incorporate the concept of projection.This method constrains the Newton step by utilizing a chemically allowed interval that generates feasible descending iterations.Moreover,we utilize the positive continuous fraction method as a preconditioning technique,providing reliable initial values for solving the algorithms.The numerical results are compared with those derived using the regular Newton-Raphson method,the Newton-Raphson method based on chemically allowed interval updating rules,and the bounded variable least squares method in six different test cases.The numerical results highlight the robustness and efficacy of the proposed algorithm.

关 键 词：chemical equilibrium reactive transport modeling numerical methods projected Newton method 

分 类 号：O17[理学—数学]