Hypervelocity Richtmyer–Meshkov instability

The Richtmyer-Meshkov instability is numerically investigated for strong shocks, i.e., for hypervelocity cases. To model the interaction of the flow with non-equilibrium chemical effects typical of high-enthalpy flows, the Lighthill-Freeman ideal dissociating gas model is employed. Richtmyer's linear theory and the impulse model are extended to include equilibrium dissociation chemistry. Numerical simulations of the compressible Euler equations indicate no period of linear growth even for amplitude to wavelength ratios as small as one percent. For large Atwood numbers, dissociation causes significant changes in density and temperature, but the change in growth of the perturbations is small. A Mach number scaling for strong shocks is presented which holds for frozen chemistry at high Mach numbers. A local analysis is used to determine the initial baroclinic circulation generation for interfaces corresponding to both positive and negative Atwood ratios

Numerical Calculation of Three-Dimensional Interfacial Potential Flows Using the Point Vortex Method

An application of the point vortex method to the singular Biot--Savart integrals used in water wave calculations is presented. The error for this approximation is shown to be a series in odd powers of h. A method for calculating the coefficients in the series is presented

Vortex simulations of the Rayleigh–Taylor instability

A vortex technique capable of calculating the Rayleigh–Taylor instability to large amplitudes in inviscid, incompressible, layered flows is introduced. The results show the formation of a steady‐state bubble at large times, whose velocity is in agreement with the theory of Birkhoff and Carter. It is shown that the spike acceleration can exceed free fall, as suggested recently by Menikoff and Zemach. Results are also presented for instability at various Atwood ratios and for fluids having several layers

Selection of steady states in the two-dimensional symmetric model of dendritic growth

Selection of steady needle crystals in the full nonlocal symmetric model of dendritic growth is considered. The diffusion equation and associated kinematic and thermodynamic boundary conditions are recast into a nonlinear integral equation which is solved numerically. For the range of Peclet numbers and capillarity lengths considered it is found that a smooth solution exists only if anisotropy is included in the capillarity term of the Gibbs-Thomson condition. The behavior of the selected velocity and tip radius as a function of undercooling is also examined

Critical indices from perturbation analysis of the Callan-Symanzik equation

Recent results giving both the asymptotic behavior and the explicit values of the leading-order perturbation-expansion terms in fixed dimension for the coefficients of the Callan-Symanzik equation are analyzed by the the Borel-Leroy, Padé-approximant method for the n-component φ^4 model. Estimates of the critical exponents for these models are obtained for n=0, 1, 2, and 3 in three dimensions with a typical accuracy of a few one thousandths. In two dimensions less accurate results are obtained

Integrating Task and Data Parallelism with the Collective Communication Archetype

A parallel program archetype aids in the development of reliable, efficient parallel applications with common computation/communication structures by providing stepwise refinement methods and code libraries specific to the structure. The methods and libraries help in transforming a sequential program into a parallel program via a sequence of refinement steps that help maintain correctness while refining the program to obtain the appropriate level of granularity for a target machine. The specific archetype discussed here deals with the integration of task and data parallelism by using collective (or group) communication. This archetype has been used to develop several applications

Calculation of steady three-dimensional deep-water waves

Steady three-dimensional symmetric wave patterns for finite-amplitude gravity waves on deep water are calculated from the full unapproximated water-wave equations as well as from an approximate equation due to Zakharov. These solutions are obtained as bifurcations from plane Stokes waves. The results are in good agreement with the experimental observations of Su