Donald Eliason

Three-dimensional simulation of a Richtmyer-Meshkov instability with a two-scale initial perturbation

Three-dimensional high-resolution simulations (up to 8 billion zones) have been performed for a Richtmyer–Meshkov instability produced by passing a shock through a contact discontinuity with a two-scale initial perturbation. The setup approximates shock-tube experiments with a membrane pushed through a wire mesh. The simulation produces mixing-layer widths similar to those observed experimentally. Comparison of runs at various resolutions suggests a mixing transition from unstable to turbulent flow as the numerical Reynolds number is increased. At the highest resolutions, the spectrum exhibits a region of power-law decay, in which the spectral flux is approximately constant, suggestive of an inertial range, but with weaker wave number dependence than Kolmogorov scaling, about k−6/5. Analysis of structure functions at the end of the simulation indicates the persistence of structures with velocities largest in the stream-wise direction. Comparison of three-dimensional and two-dimensional runs illustrates th...

Very High Resolution Simulations of Compressible, Turbulent Flows

The steadily increasing power of supercomputing systems is enabling very high resolution simulations of compressible, turbulent flows in the high Reynolds number limit, which is of interest in astrophysics as well as in several other fluid dynamical applications. This paper discusses two such simulations, using grids of up to 8 billion cells. In each type of flow, convergence in a statistical sense is observed as the mesh is refined. The behavior of the convergent sequences indicates how a subgrid-scale model of turbulence could improve the treatment of these flows by high-resolution Euler schemes like PPM. The best resolved case, a simulation of a Richtmyer-Meshkov mixing layer in a shock tube experiment, also points the way toward such a subgrid-scale model. Analysis of the results of that simulation indicates a proportionality relationship between the energy transfer rate from large to small motions and the determinant of the deviatoric symmetric strain as well as the divergence of the velocity for the large-scale field.

VALIDATION OF NUMERICAL SHALLOW WATER MODELS FOR STRATIFIED SEICHES

SUMMARY A new analytical solution is presented for the case of a stratified seiche. This solution, especially its energetics, is useful for the validation of numerical shallow water models under stratified conditions. The utility of the analytical solution for validation is shown by using it to validate a simple finite difference numerical model. A comparison of the energetics of the numerical and analytical solutions reveals that the model results converge rapidly to the analytical solution with increasing resolution, such that a grid size of 30 30 would appear adequate for validation. In addition to properly resolving the spatial features, good temporal resolution is also necessary for validation, i.e use of a Courant number (Cr) less than one. For example, owing to the numerical dispersion of the present model, using Cr 5/4 rather than Cr 1/4 for the 50 50 grid resulted in 3 6 times larger RMS errors of model versus analytical barotropic available potential energy. This new analytical solution should be applied to a test suite of such validation tools before using such numerical models to simulate the more realistic geophysical flows encountered in lakes, bays, harbours and semienclosed seas under stratified conditions. 1997 by John Wiley & Sons, Ltd.

An analytical solution for stratified tidal lagoons: Application to the validation of a numerical open boundary condition

An analytical solution is presented for the case of a stratified, tidally forced lagoon. This solution, especially its energy and mass balances, is useful for the validation of numerical shallow water models under stratified, tidally forced conditions. The utility of the analytical solution for validation is demonstrated for a simple finite difference numerical model. The energy, mass, and their balances from the numerical model are shown to converge to the analytical solution with a power law dependence as spatial and temporal resolution are increased. The power law convergence of the numerical results to the analytical solution validates both the finite difference scheme and the open boundary conditions used for the tidal forcing. The open boundary conditions work well because they are consistent with the characteristics of the analytical solution.