PML and CFS-PML boundary conditions for a mesh-free finite difference solution of the elastic wave equation

Mesh-free finite difference(FD)methods can improve the geometric flexibility of modeling without the need for lattice mapping or complex meshing process.Radial-basisfunction-generated FD is among the most commonly used mesh-free FD methods and can accurately simulate seismic wave propagation in the non-rectangular computational domain.In this paper,we propose a perfectly matched layer(PML)boundary condition for a meshfree FD solution of the elastic wave equation,which can be applied to the boundaries of the non-rectangular velocity model.The performance of the PML is,however,severely reduced for near-grazing incident waves and low-frequency waves.We thus also propose the complexfrequency-shifted PML(CFS-PML)boundary condition for a mesh-free FD solution of the elastic wave equation.For two PML boundary conditions,we derive unsplit time-domain expressions by constructing auxiliary differential equations,both of which require less memory and are easy for programming.Numerical experiments demonstrate that these two PML boundary conditions effectively eliminate artificial boundary reflections in mesh-free FD simulations.When compared with the PML boundary condition,the CFS-PML boundary condition results in better absorption for near-grazing incident waves and evanescent waves.

Large eddy simulation study of 3D wind field in a complex mountainous area under different boundary conditions

Large eddy simulations generally are used to predict 3D wind field characteristics in complex mountainous areas.Certain simulation boundary conditions,such as the height and length of the computational domain or the characteristics of inflow turbulence,can significantly impact the quality of predictions.In this study,we examined these boundary conditions within the context of the mountainous terrain around a long-span cable-stayed bridge using a wind tunnel experiment.Various sizes of computational domains and turbulent incoming wind velocities were used in large eddy simulations.The results show that when the height of the computational domain is five times greater than the height of the terrain model,there is minimal influence from the top wall on the wind field characteristics in this complex mountainous area.Expanding the length of the wake region of the computational domain has negligible effects on the wind fields.Turbulence in the inlet boundary reduces the length of the wake region on a leeward hill with a low slope,but has less impact on the mean wind velocity of steep hills.