Superposition method for modelling boundaries between media in viscoelastic finite difference time domain simulations

Abstract

Finite-difference time domain (FDTD) techniques are widely used to model the propagation of viscoelastic waves through complex and heterogeneous structures. However, in the specific case of media mixing liquid and solid, attempts to model continuous media onto a Cartesian grid produces errors when the liquid-solid interface between different media do not align precisely with the Cartesian grid. The increase in spatial resolution required to eliminate this grid staircasing effect can be computationally prohibitive. Here, a modification to the Virieux staggered-grid FDTD scheme called the superposition method is presented. This method is intended to reduce this staircasing effect while keeping a manageable computational time. The method was validated by comparing low-spatial-resolution simulations against simulations with sufficiently high resolution to provide reasonably accurate results at any incident angle. The comparison of the root-mean-square of the stress amplitude maps showed that the amplitude of artifactual waves could be reduced by several orders of magnitude when compared to the Virieux staggered-grid FDTD method and that the superposition method helped to significantly reduce the staircasing effect in FDTD simulations.

Benchmark problems for transcranial ultrasound simulation: Intercomparison of compressional wave models

“…36 Optional reduction of staircasing artifacts can be enabled using a superposition operator. 37 A perfectly matched layer (PML) condition for viscoelastic propagation is used to absorb waves at the boundaries. 38 All benchmarks were computed using a resolution of 12 grid PPW.…”

Numerical modeling of mechanical wave propagation

“…Another extension is given by the rotated staggered grids [131], which have shown to be useful to anisotropic media, especially in the study of shear-wave splitting [132]. Staggered grids handle more easily boundary conditions and interfaces [117,119,[133][134][135], in addition that their numerical error is less sensitive to Poisson's ratio [119]. They also provide a natural framework for implementing non-uniform or discontinuous grids [136][137][138][139].…”

“…In addition to the algebraic form (135), the approximate diagonal mass matrix may be obtained through reduced integration [450]. For high-order finite elements, the natural choice is to employ a Gauss-Lobatto-Legendre quadrature and shift the degrees of freedom so that they coincide with the quadrature nodes [239].…”

Dynamic Modelling and Control of Flexible Link Manipulators: Methods and Scope - Part 2

“…But, the method is computationally intensive. Configuration space method [Hammami et al, 2016] (36) ; [Yamamoto, 2017] (37) ; [Jiang et al, 2017] (38) ; [Zeng et al, 2017] (39) ; [Mehnert et al, 2018] (40) ; [Drainville, 2019] (41) ; [Goryacheva and Miftakhova, 2019] (42) ; [Jamshidi et al, 2020] (43) ; [Kromer and Roubicek, 2020] (44) ; [Brighenti et al, 2021] (45) ;…”