GMRES及变型方法在水动力分析中的应用

Application of GMRES and its variant methods in hydrodynamic analysis

为了提高时域水动力分析的计算效率,基于三维常数Rankine源建立了时域水动力模型,研究了广义最小残量(GMRES)算法及其变型方法在时域水动力模型求解的适用性.以三维圆柱为研究对象,计算其在不同垂荡强迫震荡频率下的辐射力,通过计算结果对比,研究了GMRES方法的在基于Rankine源的时域水动力计算上的适用性.在此基础上,研究了变型算法重启GMRES方法和简单重启GMRES方法的计算精度和计算效率,并针对计算过程中出现的计算不收敛问题,提出了线性方程右端项单位化优化方法.研究表明:优化后的简单重启GMRES方法收敛性更好,计算效率相比于GMRES方法提升了近3倍.

To improve the computational efficiency of hydrodynamic analysis in the time domain,the time-domain hydrodynamic numerical model was established based on the three-dimensional Rankine source method,and the applicability of generalized minimal residual(GMRES) method and its variant methods in solving the time-domain hydrodynamic numerical model was studied.By taking a three-dimensional cylinder as the subject of study,its radiation force under different heave forced oscillation frequencies was calculated.By comparing the calculation results,the applicability of the GMRES method in time-domain hydrodynamic calculations based on the Rankine source was studied.On this basis,the calculation accuracy and efficiency of the modified algorithm,which were restarted GMRES and simpler restarted GMRES,were discussed on this issue.Corresponding optimization methods based on unitization of the right-hand-side of the linear equation were proposed to solve the non-convergence problem in the time-domain calculation process.Research results show that the optimized simpler restarted GMRES algorithm converges better,and the computational efficiency is improved by nearly 3 times compared to GMRES.