Study Of Curve Grid Finite Difference Method In Rupture Dynamics And High Performance Computing

Large earthquakes usually occur on active faults,and their high-speed rupture pro-cesses will lead to strong ground motions,causing casualties and property losses.The study of earthquake dynamics can deepen our understanding of disaster mechanism caused by strong ground motions,so as to better mitigate and prevent earthquake dis-aster.Numerical simulation is an effective method to study seismic dynamics.Among them,the curved-grid finite difference method(CGFDM,Zhang et al.(2014a))has be-come a mature method to simulate the rupture dynamics of non planar faults due to its flexibility in describing complex boundaries and its high efficiency.We improve the original CGFDM method,by modifying the method of apply-ing fault boundary conditions,the numerical instability problem in the original scheme which needs filtering is avoid.The CGFDM method is based on the first-order velocity-stress equation,in which the numerical treatment of fault boundary conditions includes two aspects:(1)the calculation of stress spatial derivatives,in this paper,the traction image method is combined with the trial traction method to avoid the order reduction problem in the original CGFDM method;(2)the caculation of the velocity spatial deriva-tive.We use the known fault traction to deal with the difficult-to-solve velocity spatial derivative at the fault boundary.We use the improved CGFDM method to simulate the dynamic rupture processes of rough faults and compare the results with the original CGFDM's.The results show that the improved CGFDM method can solve the nu-merical instability problem in the simulation of the rough fault rupture process without applying filtering.The process of fault rupture is controlled by friction laws.Therefore,different fric-tion laws have a great influence on fault rupture styles.Compared with the simpler slip weakening friction law,the rate-and-state friction laws can not only describe the rup-ture process of the fault with high-speed instability,but also give the recovery process of the fault friction,which is very important for understanding the complete periodic process of an earthquake.We extend the existing CGFDM method to the simulation under the control of rate-and-state friction laws,and validate our method by comparing our results with the results calculated by other numerical methods.Although the CGFDM method is very efficient compared to many finite element methods,it is still very inefficient to simulate the large-scale 3D dynamic rupture pro-cess even with FDM methods,which limits the development of many studies of rupture dynamics.To this end,we developed a rupture dynamics program based on the GPU architecture.Our GPU program has two orders of magnitude speedup compared with single-core CPU program while ensuring correctness.Even compared to the multi-core CPU program,the GPU program still has huge advantages in computational efficiency,which greatly facilitates the research related to dynamics rupture simulations.It is important to accurately simulate the strong ground motion caused by the fault rupture process for earthquake disaster analysis.We have implemented the high-resolution,high-frequency simulation of strong ground motion on the Sunway Taihu-Light supercomputer.Taking the Tangshan Earthquake as an example,the influence of spatial grid resolution on the simulation of strong ground motion under complex sedi-mentary basins is analyzed.We find that the coarse grid cannot accurately resolve the low-frequency components of synthetic seismograms in areas with complex basin struc-tures.Our work emphasizes the important role of supercomputers in the simulation of complex large earthquakes,and is also a reference for research work using numerical methods to calculate the distribution of earthquake damage under complex sedimentary basins.We have further improved the reliability and efficiency of the numerical simulation method of rupture dynamics through the in-depth development of CGFDM method and its high-performance computing.Using our extended high-efficiency CGFDM method,researchers can more conveniently carry out research work such as scenario earthquake simulation for statistical prediction of earthquake damage in active fault areas,which will be of great significance to earthquake disaster prevention and mitigation.