Eulerian simulation of complex suspensions and biolocomotion in three dimensions

We present a numerical method specifically designed for simulating three-dimensional fluid–structure interaction (FSI) problems based on the reference map technique (RMT). The RMT is a fully Eulerian FSI numerical method that allows fluids and large-deformation elastic solids to be represented on a single fixed computational grid. This eliminates the need for meshing complex geometries typical in other FSI approaches and greatly simplifies the coupling between fluid and solids. We develop a three-dimensional implementation of the RMT, parallelized using the distributed memory paradigm, to simulate incompressible FSI with neo-Hookean solids. As part of our method, we develop a field extrapolation scheme that works efficiently in parallel. Through representative examples, we demonstrate the method’s suitability in investigating many-body and active systems, as well as its accuracy and convergence. The examples include settling of a mixture of heavy and buoyant soft ellipsoids, lid-driven cavity flow containing a soft sphere, and swimmers actuated via active stress.

An analysis of axisymmetric Sezawa waves in elastic solids

The wave propagation in elastic solids covered by a thin layer has received significant attention due to the existence of Sezawa waves in many applications such as medical imaging. With a Helmholtz decomposition in cylindrical coordinates and subsequent solutions with Bessel functions, it is found that the velocity of such Sezawa waves is the same as the one in Cartesian coordinates, but the displacement will be decaying along the radius with eventual conversion to plane waves. The decaying with radius exhibits a strong contrast to the uniform displacement in the Cartesian formulation, and the asymptotic approximation is accurate in the range about one wavelength away from the origin. The displacement components in the vicinity of origin are naturally given in Bessel functions which can be singular, making it more suitable to analyze waves excited by a point source with solutions from cylindrical coordinates. This is particularly important in extracting vital wave properties and reconstructing the waveform in the vicinity of source of excitation with measurement data from the outer region.

Reflection and transmission of P-waves at a very rough interface between two isotropic elastic solids

This paper deals with the reflection and transmission of P-waves at a very rough interface between two isotropic elastic solids. The interface is assumed to oscillate between two straight lines. By mean of homogenization, this problem is reduced to the reflection and transmission of P-waves through an inhomogeneous orthotropic elastic layer. It is shown that a P incident wave always creates two reflected waves (one P wave and one SV wave), however, there may exist two, one or no transmitted waves. Expressions in closed-form of the reflection and transmission coefficient have been derived using the transfer matrix of an orthotropic elastic layer. Some numerical examples are carried out to examine the reflection and transmission of P-waves at a very rough interface of tooth-comb type, tooth-saw type and sin type. It is found numerically that the reflection and transmission coefficients depend strongly on the incident angle, the incident wave frequency, the roughness and the type of interfaces.