Study of Spurious Wave Reflection at the Interface of Peridynamics and Finite Element Regions

Peridynamics ability to model crack as a material response removes deficiencies associated with using classical continuum-based methods in modeling discontinuities. Due to its nonlocal formulation, however, peridynamics is computationally more expensive than the classical continuum-based numerical methods such as finite element method. To reduce the computational cost, peridynamics can be coupled with finite element method. In this method, peridynamics is used only in critical areas such as the vicinity of crack tip and finite element method is used everywhere else. The main issue associated with such coupling methods is the spurious wave reflections occurring at the interface of peridynamics and finite elements. High frequency waves traveling from peridynamics to finite element spuriously reflect back at the interface and the amplitude of transmitted waves also alter. In this paper, we take an analytical approach to study this phenomenon of spurious reflections. We study the impact of factors such as horizon size of peridynamic formulation, discretization, and change in mesh size on the amplitude of spuriously reflected waves. Finally, we present a method to reduce these spurious reflections by using Arlequin method.

The virtual refraction: Useful spurious energy in seismic interferometry

Seismic interferometry is rapidly becoming an established technique to recover the Green’s function between receivers, but practical limitations in the source-energy distribution inevitably lead to spurious energy in the results. Instead of attempting to suppress all such energy, we use a spurious wave associated with the crosscorrelation of refracted energy at both receivers to infer estimates of subsurface parameters. We named this spurious event the virtual refraction. Illustrated by a numerical two-layer example, we found that the slope of the virtual refraction defines the velocity of the faster medium and that the stationary-phase point in the correlation gather provides the critical offset. With the associated critical time derived from the real shot record, this approach includes all of the necessary information to estimate wave speeds and interface depth without the need of inferences from other wave types.

Limitations of Hall MHD as a model for turbulence in weakly collisional plasmas

The limitations of Hall MHD as a model for turbulence in weakly collisional plasmas are explored using quantitative comparisons to Vlasov-Maxwell kinetic theory over a wide range of parameter space. The validity of Hall MHD in the cold ion limit is shown, but spurious undamped wave modes exist in Hall MHD when the ion temperature is finite. It is argued that turbulence in the dissipation range of the solar wind must be one, or a mixture, of three electromagnetic wave modes: the parallel whistler, oblique whistler, or kinetic Alfvén waves. These modes are generally well described by Hall MHD. Determining the applicability of linear kinetic damping rates in turbulent plasmas requires a suite of fluid and kinetic nonlinear numerical simulations. Contrasting fluid and kinetic simulations will also shed light on whether the presence of spurious wave modes alters the nonlinear couplings inherent in turbulence and will illuminate the turbulent dynamics and energy transfer in the regime of the characteristic ion kinetic scales.