James R. Kamm

A New Approach for a Nonlocal, Nonlinear Conservation Law

We describe an approach to nonlocal, nonlinear advection in one dimension that extends the usual pointwise concepts to account for nonlocal contributions to the flux. The spatially nonlocal operators we consider do not involve derivatives. Instead, the spatial operator involves an integral that, in a distributional sense, reduces to a conventional nonlinear advective operator. In particular, we examine a nonlocal inviscid Burgers equation, which gives a basic form with which to characterize properties associated with well-posedness, and to examine numerical results for specific cases. We describe the connection to a nonlocal viscous regularization, which mimics the viscous Burgers equation in an appropriate limit. We present numerical results that compare the behavior of the nonlocal Burgers formulation to the standard local case. The developments presented in this paper form the preliminary building blocks upon which to build a theory of nonlocal advection phenomena consistent within the peridynamic theo...

The Gas Curtain Experimental Technique And Analysis Methodologies

The qualitative and quantitative relationship of numerical simulation to the physical phenomena being modeled is of paramount importance in computational physics. If the phenomena are dominated by irregular (i. e., nonsmooth or disordered) behavior, then pointwise comparisons cannot be made and statistical measures are required. The problem we consider is the gas curtain Richtmyer-Meshkov (RM) instability experiments of Rightley et al. (13), which exhibit complicated, disordered motion. We examine four spectral analysis methods for quantifying the experimental data and computed results: Fourier analysis, structure functions, fractal analysis, and continuous wavelet transforms. We investigate the applicability of these methods for quantifying the details of fluid mixing.

FLAG Simulations of the Elasticity Test Problem of Gavrilyuk et al.

This report contains a description of the impact problem used to compare hypoelastic and hyperelastic material models, as described by Gavrilyuk, Favrie & Saurel. That description is used to set up hypoelastic simulations in the FLAG hydrocode.