The practical importance of two-dimensional (2D) immiscible two-phase turbulence is well known. Although the physics of 2D single-phase turbulence has been studied extensively, it is very difficult to apply the same methodology to study the 2D immiscible two-phase flows. Lattice Boltzmann (LB) method has many advantages on treating realistic boundary conditions and immiscible interfacial dynamics. Furthermore, LB computations are purely local and very appropriate for large-scale parallel implementation. In this paper, we will study many fundamental aspects of 2D immiscible two-phase flows such as the scaling properties of the energy, pressure, and order parameter, as well as the physical structures. In particular, we will demonstrate that high resolution LB computations can be a powerful tool in studying the effects of interfacial dynamics.
[Q3.02] Second Order Godunov Schemes for 2D and 3D Supersonic MHD Flows
Wenlong Dai, Paul Woodward, Dennis Dinge, David Porter, Kevin Edger (University of Minnesota)
One outstanding difficult in numerical simulations for supersonic MHD flows is to exactly maintain the divergence-free constraint and conservation laws simultaneously. One typical approach used in the existing Godunov schemes is to add a ``cleaning-up'' procedure, i.e., to solve a Poisson equation, after each time step. But, to solve the Poisson equation needs global information, and the cleaning-up destroys the conservative property of a scheme. We have spent many years in developing numerical schemes for supersonic MHD flows, and recently, we have developed a scheme for two- and three-dimensional supersonic MHD flows, in which both the conservation laws for mass, momentum, energy and three components of magnetic field, and the divergence-free constraint are exactly maintained. The scheme is second order accurate in both space and time. Compared with existing numerical schemes, our scheme is very simple, and no global solver is needed. Numerical examples will be shown to demonstrate the features of the scheme.
[Q3.03] Angular Momentum Redistribution in Turbulent Compressible Convection
Neal Hurlburt (Lockheed Martin ATC), Nicholas Brummell, Juri Toomre (University of Colorado)
We consider the dynamics of turbulent compressible convection within a curved local segment of a rotating spherical shell. We aim to understand the disparity between the observed solar differential rotation and previous numerical simulations. The angular extent of the curved domain is limited to a small solid angle in order to exploit fully the available spatial degrees of freedom on current supercomputers and attain the highest possible Reynolds numbers. Here we present simulations with Rayleigh numbers in excess of 10^7, and Prandtl numbers less than 0.1. This computational domain takes the form of a curved, periodic channel in longitude with stress-free sidewalls in latitude and radius. The numerical solutions are obtained using high-order accuracy explicit code. It evaluates spatial derivatives using sixth-order compact finite differences in radius and latitude and psuedospectral methods in longitude and advances the solutions in time using a fourth-order Bulirsch-Stoer integrator. The surface flows form broad, laminar networks which mask the much more turbulent flows of the interior. The dynamics within this turbulent region is controlled by the interactions of a tangled web of strong vortex tubes. These tubes and their interactions redistrubute the angular momentum, generating azimuthal flows with strong shear in both radius and latitude. Lockheed Martin Solar and Astrophysics Lab
[Q3.04] High-Resolution Three-Dimensional Simulations of Compressible Rayleigh-Taylor Instability and Turbulent Mixing
A. M. Dimits, R. H. Cohen, W. P. Dannevik, D. E. Eliason, A. A. Mirin, O. Schilling (Lawrence Livermore National Laboratory), D. H. Porter, P. R. Woodward (University of Minnesota), S. A. Orszag, I. A. Staroselsky (Cambridge Hydrodynamics Incorporated)
The results of 3D simulations of compressible Rayleigh-Taylor (RT) instability and turbulence in an ideal gas using the piecewise-parabolic (PPM) method, both with and without Navier-Stokes terms, are presented. Spatial resolutions of up to 512^3 are used. The formation of bubbles and spikes, their subsequent growth and merger, and the evolution of the mean fields towards a stably-stratified equilibrium are observed. The dependence of mixing rates on dimensionless parameters such as the Atwood number and the degree of compressibility is studied. The relationship between the level of molecular dissipation and the spatial resolution needed for the simulations to be converged with respect to spatial resolution is investigated. The question of whether PPM simulations reproduce fully-resolved Navier-Stokes simulations with molecular dissipation is also addressed. Finally apriori analyses using the simulation data that address the applicability to RT turbulence of various subgrid-scale models and Reynolds-averaged Navier-Stokes (RANS) models in common use are presented.
This abstract was not submitted electronically.
[Q3.06] Fully threaded tree for adaptive mesh fluid dynamics simulations
Alexei Khokhlov (Naval Research Laboratory)
A fully threaded tree (FTT) for adaptive refinement of regular meshes is described. By using a tree threaded at all levels, tree traversals for finding nearest neighbors are avoided. All operations on a tree including tree modifications are \cal O(N), where N is a number of cells, and are performed in parallel. An efficient implementation of the tree is described that requires 2N words of memory. A filtering algorithm for removing high-frequency noise during mesh refinement is described.
A FTT can be used in various numerical applications. In this paper, it is applied to the integration of the Euler equations of fluid dynamics. An adaptive-mesh time stepping algorithm is described in which different time steps are used at different levels of the tree. Time stepping and mesh refinement are interleaved to avoid extensive buffer layers of fine mesh which were otherwise required ahead of moving shocks. Test examples are presented, and the FTT performance is evaluated. The three-dimensional simulation of the interaction of a shock wave and a spherical bubble is carried out that shows the development of azimuthal perturbations on the bubble surface.
Full text of the paper can be found on this ftp URL.
[Q3.07] Overlay of Arbitrarily Shaped Material Regions onto Hexahedral Meshes
Jeffrey Grandy (Lawrence Livermore National Laboratory)
In Eulerian and ALE hydrodynamics simulations, zones contain a mixture of materials when mesh boundaries do not conform with material boundaries. In problem generation at initial time, three-dimensional regions containing assigned material properties are specified as shapes, with a limited number of parameters describing the volume of the region. In the shape overlay procedure, the mesh is initialized with a background material in each zone, and the background material is replaced with the assigned material within each region. Zones intersecting the surface of the shape become mixed, and the essential requirement is to compute the volume of intersection between the shape and each zone on the mesh. We demonstrate, using meshes containing up to 10^6 nonorthogonal, nonuniform hexahedral zones, that shape overlays are a practical means of accurately and efficiently generating hydrodynamics problems on currently available workstations.
[Q3.08] Accurate, Finite-Volume Methods for 3D MHD and Applications
D. C. Barnes, J. E. Morel, Tom Oliphant, Mikhail Shaskov, Chris Rousculp (Los Alamos National Laboratory)
Recently developed algorithms for 3D MHD calculations on a structured, Lagrangian, hexahedral mesh are described. The magnetic field B is described in terms of the magnetic flux through each hex face. Vertex forces are derived by the variation of magnetic energy with respect to vertex positions. This assures symmetry, magnetic flux, momentum, and energy conservation, as well as maintaining an exact vanishing divergence of B. It is shown that the form of the ideal dispersion relation may be preserved by an appropriate choice of volume, and volume averages, so that the well known stiffness is resolved without pollution of the low-frequency modes. Resistive diffusion is calculated using the support operator method, to obtain an energy conservative, symmetric method on an arbitrary mesh. Implicit time difference equations are solved by preconditioned, conjugate gradient methods. Results of convergence tests are presented. Initial results of a liner implosion problem illustrate the application of these methods to multi-material problems. Applications to electromagnetism on arbitrary 3D hex meshes are also discussed.
[Q3.09] Second Order Godunov Schemes for Multidimensional Radiation Hydrodynamics
Wenlong Dai, Paul Woodward, Dennis Dinge, David Porter, Kevin Edger (University of Minnesota)
Radiation hydrodynamical equations play an important role in astrophysics. In the diffusion limit, the radiation hydrodynamical equations may be written as a set of conservation laws plus radiative heat transfer. The existing approach for the set of conservation laws is to solve Euler equations first and then to update momentum and energy due to radiation. Therefore, the conservation laws are satisfied only to the accuracy of a scheme. The truncation error in the conservation laws may be O if strong shocks are involved. Recently, we proposed a Godunov scheme for multidimensional radiation hydrodynamical equations in the diffusion limit. Both linear and nonlinear Riemann solvers are developed in the scheme. The nonlinear Riemann solver works very well for any left and right states, and therefore, the scheme is robust even for the problems involving very strong radiation hydrodynamical shocks. The scheme is second order accurate in both space and time. Numerical examples will be given to show the features of the scheme.