Abstract
To provide a simple numerical formulation based on fixed grids, a wavelet element method for fluid–solid modelling is introduced in this work. Compared with the classical wavelet finite element method, the presented method can potentially handle more complex shapes. Considering the differences between the solid and fluid regions, a damping-like interface based on wavelet elements is designed, in order to ensure consistency between the two parts. The inner regions are constructed with the same wavelet function in space. In the time and spatial domains, a partitioned approach based on Jacobi iteration is combined with the pseudo-parallel calculation method. Numerical convergence analyses show that the method can serve as an alternative choice for fluid–solid coupling modelling.
Highlights
In the context of structural health monitoring, as well as seismic and acoustic exploration, the numerical modelling and analyses of fluid–solid interfaces and coupling have been considered crucial issues, due to the complexity of the related physical phenomena
For waves propagating in a single medium, most types of numerical methods can be used, such as the finite difference method [1,2] and its derivative formulations [3], boundary element methods [4], spectral element methods [5,6], pseudo-spectral element methods [7], wavelet spectral methods [8,9,10], and mixed formulations based on spectral methods [11]
The numerical primary wave (P-wave) wavefront in fluid qualitatively agreed with the theoretical wavefront
Summary
In the context of structural health monitoring, as well as seismic and acoustic exploration, the numerical modelling and analyses of fluid–solid interfaces and coupling have been considered crucial issues, due to the complexity of the related physical phenomena. The numerical properties of the immersed boundary method mean that it is straightforward to determine the type of the boundary conditions for the fluid grid, if the fluid surrounds the structure, while some non-physical boundary conditions are required for the interface Another fixed grid technique is the fictitious domain method. Considering the difference between solid and fluid regions, in terms of their degrees of freedom, a damping-like interface based on wavelet elements is designed. The inner regions, both for the fluid and the solid, are constructed using the same wavelet function in the spatial domain.
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