Modeling Wave Propagation In Fluid-solid Configurations With Coupled LBM-LSM

Implementing irregular fluid-solid coupled interfaces in seismic wave simulation is a hot research subject in geophysical exploration field.Due to the limitations of the continuous assumptions of wave equations,existing macroscopic wave equation based numerical simulation methods(e.g.,finite difference method and finite element method)may fail when dealing with such complex fluid-solid interface coupled problems.Therefore,in this thesis,two numerical simulation methods(lattice Boltzmann method and lattice spring model)based on mesoscopic mechanical models without depending on wave equations are adopted to solve the problems of seismic wave in fluid and solid phases,respectively,and appropriate fluid-solid interaction boundaries are developed to address the seismic wave propagation process in the whole two-phase media.The lattice Boltzmann method is a numerical simulation tool for solving the Navier-Stokes equation in a simplified way.By describing the interaction between fluid particles on the mesoscopic level,it can simulate the wave propagation and other complex physical phenomena on the macroscopic level.Lattice spring model is a relatively novel mesoscopic method to study the elastic and plastic properties of media.The method discretizes the media into a series of elastic elements connected by springs and mass points,and simulates the macroscopic elastic properties of media,such as elasticity and fracture property,by studying the micro-mechanical action mechanism between the elastic elements.Based on the combination of lattice Boltzmann model and lattice spring model,the momentum exchange algorithm can be used to realize the mutual transfer of wavefield at the fluid-solid interface.A quantitative relationship model between relaxation time in the lattice Boltzmann model and quality factors in the Kelvin-Voigt model was found and established,which was verified through a mass of numerical simulations and strict theoretical derivation.The thesis studies and tests the application effects of the lattice Boltzmann model with single relaxation time and multiple relaxation times in the forward modeling of viscous acoustic wave in fluid media,and finds that the multi-relaxation times lattice Boltzmann model is superior to the single relaxation time model,while the calculation consume of the two models are not much different.Since the existing lattice spring model mainly employs square grid and triangle grid for discretization,a rectangular grid based lattice spring model is further developed in this thesis,and a variety of complex media models are used to test the reliability.At the same time,a uniform three-dimensional lattice spring model is proposed,and the wavefield simulation results of the three typical discrete models are tested and compared by several different geological models.On this basis,by adopting the standard bounce back boundary condition,mirror bounce back boundary condition and the hybrid boundary condition,the coupled lattice Boltzmann model and lattice spring model scheme could be an effective simulation technology to calculate wave propagation in complex two-phase media.The coupled scheme was employed to solve wavefield numerical problems in the fluid saturated cavity model,porous media and complex marine seismic exploration model,and reasonable wavefield simulation results were obtained.In conclusion,the lattice Boltzmann model coupled with the lattice spring model can be developed to solve the forward simulation problem of seismic wavefield in complex two-phase media.Compared with traditional methods such as finite difference method,the coupled scheme studied in this thesis has better adaptability and flexibility to deal with irregular interface.Through further development,this method is expected to be used to simulate the seismic wave propagation problem in realistic geological models.