J. A. Viecelli

A computing method for incompressible flows bounded by moving walls

Abstract A modified type of Marker and Cell computing method is presented for solving problems in incompressible hydrodynamics. The method is applicable to time dependent problems in two spatial dimensions or three spatial dimensions with axial symmetry. Details are presented for calculation of arbitrarily shaped curved wall boundaries and flexible moving wall boundaries. Example problems with moving walls and free surfaces are given.

A method for including arbitrary external boundaries in the MAC incompressible fluid computing technique

A method is proposed which treats the fluid boundary at an arbitrarily curved wall or obstacle as if it were a free surface, to which a pressure is applied such that the particles at the boundary line move tangent to it. The pressure can be determined by replacing the conventional MAC relaxation iteration with one in which the pressure in boundary cells is adjusted by an amount proportional to the scalar product of the particle velocity at the boundary and a unit normal defining the boundary.

Phase transformations of nanometer size carbon particles in shocked hydrocarbons and explosives

Estimates for the displacement of the phase equilibrium lines for small carbon particles containing from several hundred to several tens of thousands of atoms are made, and an error analysis of the uncertainties in these estimates is derived and evaluated using available experimental data. Hugoniot calculations for methane, benzene, polyethylene, and polybutene, based on a carbon particle surface energy adjusted equation of state, are in better agreement with shock pressure-volume and temperature data than those obtained with a bulk carbon equation of state. The results suggest that carbon particles, of order 103–104 atoms, can exist in the liquid state at lower temperatures than bulk carbon.

Kinetics and thermodynamic behavior of carbon clusters under high pressure and high temperature

Physical processes that govern the growth kinetics of carbon clusters at high pressure and high temperature are: (a) thermodynamics and structural sp ?-to- sp ? bonding) changes and (b) cluster diffusion. Our study on item (a) deals with ab initio and semi-empirical quantum mechanical calculations to examine effects of cluster size on the relative stability of graphite and diamond clusters and the energy barrier between the two. We have also made molecular dynamics simulations using the Brenner bond order potential. Kesults show that the melting line of diamond based on the Brenner potential is reasonable and that the liquid structure changes from mostly sp -bonded carbon chains to mostly sp ?-bonding over a relatively narrow density interval. Our study on item (b) uses the time-dependent clustor size distribution function obtained from the relevant Smoluchowski equations. The resulting surface contribution to the Gibbs free energy of carbon clusters was implemented in a thermochemical code.

A carbon cycle model with latitude dependence

A two-dimensional carbon cycle model is divided into three zones representing equatorial, middle and high latitude regions. The three zones are coupled together by a deep ocean meridional convective cell and atmospheric transport terms. The model is applied to the calculation of the dispersion of radiocarbon and tritium from nuclear weapons tests, to the calculation of the atmospheric record of bomb radiocarbon and to the calculation of the Mauna Loa record of atmospheric CO2. Calibrating on the basis of the Northern hemisphere bomb test data yields a model which has approximately twice the CO2 ocean uptake of the one-dimension box diffusion models calibrated on the basis of deep water equilibrium carbon 14.

Exponential difference operator approximation for the sixth order Onsager equation

An accurate, easy to program, method of solving the one-dimensional form of the sixth order Onsager equation is presented. Boundary conditions are included naturally. (AIP)

Structure of Lagrangian turbulence

A structure function describing the geometrical properties of Lagrangian turbulence is proposed. This function yields the asymptotic mixing properties of inertial range turbulence. The form of the structure function is deduced from Richardson’s particle dispersion law. Scaling relationships for the mixing volume fraction, the surface area of boundaries between materials, and the chord lengths defined by the intersection points of a ray with material boundaries are obtained. Scaling laws are also deduced for the area fraction, perimeter length, and chord lengths in a two‐dimensional section, and for the trajectory of a single particle. The predictions for the two‐dimensional case have been verified in several examples of mixing, using data obtained from numerical integration of the Navier–Stokes equations.

Statistical mechanics and correlation properties of a rotating two‐dimensional flow of like‐sign vortices

The Hamiltonian flow of a set of point vortices of like sign and strength has a low‐temperature phase consisting of a rotating triangular lattice of vortices, and a normal temperature turbulent phase consisting of random clusters of vorticity that orbit about a common center along random tracks. The mean‐field flow in the normal temperature phase has similarities with turbulent quasi‐two‐dimensional rotating laboratory and geophysical flows, whereas the low‐temperature phase displays effects associated with quantum fluids. In the normal temperature phase the vortices follow power‐law clustering distributions, while in the time domain random interval modulation of the vortex orbit radii fluctuations produces singular fractional exponent power‐law low‐frequency spectra corresponding to time autocorrelation functions with fractional exponent power‐law tails. Enhanced diffusion is present in the turbulent state, whereas in the solid‐body rotation state vortices thermally diffuse across the lattice. Over the e...

Functional representation of power-law random fields and time series

Abstract Current methods of generating stationary random fields having power-law spectra are based on fast Fourier transforming an array of random numbers with zero mean and unit variance to wave space. Multiplication by the desired spectrum weight function, followed by inverse transformation to physical space then yields the sample field. We show that the desired spectral weightings can be generated directly in physical space, using the successive random addition methods previously employed for graphical display of random fractals, and derive expressions for the constants of the process in terms of the spectrum amplitude and exponent. A formula for the random number call sequence can be derived for the random addition process, eliminating the need for field array storage. This makes representation of random fields by a single computational function of the physical coordinates possible. Correspondingly, the scale range and dimension covered by the field function is limited only by machine word length. The same method can be used to represent time series with power-law frequency spectra functional form, or to include time-dependence in random field problems.

Dynamics of two-dimensional turbulence

Mixing of Lagrangian particles by a vortex singularity is shown to correspond to a continuous curdling process with the Lipschitz–Holder exponent equal to (4)/(3) , demonstrating that Richardson’s l4/3 scaling is derivable from the two‐dimensional kinematics of the vortex singularity. Scaling relationships describing the Lagrangian geometry of two‐dimensional turbulence are linked to the rate of enhanced diffusion. The value of the two‐dimensional intermittency exponent μ= (2)/(3) , derived from the author’s Lagrangian structure function theory [Phys. Fluids A 1, 1836 (1989)], when used in the Levy flight theory of enhanced diffusion developed by Shlesinger et al. [Phys. Rev. Lett. 58, 1100 (1987)] predicts 〈R2〉∝t2.6 for the time rate of separation of labeled pairs of vortices in two dimensions. This is found to be in good agreement with the rate of dispersion measured in numerical simulations of inviscid two‐dimensional turbulence. Kinetic theory arguments, supplemented by the previously derived Lagrangi...