一种稀疏矩阵算法及其在燃烧室传热计算中的应用

摘要

依据温度刚度矩阵为稀疏矩阵的特点,提出了一种基于链表数据结构的存储方法来构建整体刚度矩阵,并对该方法进行了优化,提高了检索效率.此外,改进了传统的高斯消去法,提出了沿对角线按局部长操作数最少的方法选主元的策略,该策略在确保计算稳定性的前提下,既可以保证消元过程中剩余矩阵的稀疏性,又可以减小因选主元带来过大的额外计算量.将该方法应用于内燃机燃烧室耦合系统瞬态传热计算,计算结果表明,与传统方法相比,该算法能够显著提高求解效率.%Taking the temperature stiffness matrix as sparse matrix, the construction method of whole stiffness matrix with a linked list data structure was put forward and optimized to improve the searching efficiency. In addition, the Gauss elimination method was improved and the strategy of choosing principal element according to the least step operands along the diagonal line was proposed. The strategy not only ensured the residual matrix to be sparse during eliminating element but also cut the extra burden from choosing principal element at the premise of stable calculation. The algorithm was applied to the transient heat transfer calculation of combustion chamber coupled system. The results show that the improved method is more efficient in solving process.