Optimization of Numerical Simulation Algorithm for Spontaneous Combustion in Goaf via a Compression Storage and Solution Method of Coefficient Matrix

In coal mine engineering, numerical software is used to analyze the behavior of coal rock damage and fluid migration. The order of the coefficient matrix used in numerical calculations is increasing, and this increases the computation steps in obtaining the coefficient matrix solution. The storage and solution of the coefficient matrix are key factors influencing the efficiency of the numerical software. Therefore, to save storage space and reduce the computation steps, the coefficient matrix must be effectively compressed and stored. In this work, the structural characteristics of different coefficient matrices are analyzed in detail, and we find that for different computational regions, as long as the nodes are numbered according to certain rules, the corresponding coefficient matrices will have similar structural characteristics. The nonzero elements are symmetrically distributed in the diagonal band, and all the elements on both sides outside the band are zero. Based on this, the coefficient matrix is compressed by a pivoting scheme, and the compressed matrix is directly eliminated by dislocation Gaussian elimination. Thus, a compressed storage method that integrates the compression and solution of the coefficient matrix is established. The compressed storage and calculation module is incorporated into our self-developed simulation software COMBUSS-3D to simulate the evolution of the temperature field in the goaf of Luling Coal Mine. Compared with the conventional method, the compressed storage module can significantly improve the computing rate of the simulation, by approximately 80%