Research Interests
Numerical Approach
Computational Resources
Research Project Descriptions

RESEARCH INTERESTS:

Dr. Miller's research involves the large scale simulation and modeling of turbulent air-hydrocarbon mixing and reaction at both atmospheric pressure and supercritical pressures relevant to modern and forthcoming gas turbines and diesel engines. The research is directed at fundamental studies of single-phase and multiphase flows involving complex physics in relatively simplified geometries such as homogeneous turbulence, mixing layers and jets. The preferred research approach is computational fluid dynamics (CFD); in particular, the direct numerical simulation technique. Results obtained from the simulations are used both to study the flow physics and to aid in the development and testing of mathematical and stochastic models relevant to future engineering applications. Models used in large eddy simulations (LES) and probability density function (PDF) methods are of particular interest.

Direct numerical simulation, or `DNS', is an advanced computational technique in which all of the length and time scales of the governing equations are completely resolved, without resort to modeling. When conducted with high order accurate numerical algorithms, DNS therefore yields very nearly the exact solution to the problem. In this case, the results contain all of the information describing a flow at nearly all points in both time and space. This is incontrast to experiments in which information is known only where data gathering probes are installed in the flow. However, due to computational limitations DNS is a valid approach only for relatively moderate to low Reynolds number turbulence for which the range of length and time scales remains resolvable by available computer resources.

NUMERICAL APPROACH:

As mentioned above, DNS is performed using highly accurate computational algorithms in order to achieve desired levels of resolution and accuracy. The approach presently employed in Dr. Miller's research program is that of high accuracy finite difference schemes due to their relative ease of use on parallel computing architectures (as opposed to spectral methods or finite element algorithms). In particular, we employ several of the schemes detailed by Kennedy and Carpenter (1994) including both third and fourth order accurate Runge-Kutta time integration schemes, eighth order accurate explicit central finite differences, and fourth order accurate compact (tridiagonal) finite differences. For multiphase flow simulations a fourth order accurate Lagrange interpolation procedure is used to determine gas phase flow variables at droplet or particle locations.

COMPUTATIONAL RESOURCES:

All computational codes presently employed by Dr. Miller's research group are conducted on parallel processing architectures. All parellelization is based on the Message Passing Interface (MPI) subroutines based on full three dimensional domain decomposition. Partial computational support has been provided by the following:

The National Science Foundation through the National Computational Science Alliance (NCSA) under Grant CTS990040N utilizing the NCSA SGI/Origin 2000 (1024 processors).

The California Institute of Technology's Center for Advanced Computing Research (CACR) utilizing the Hewlett-Packard V2500 (128 processors).

Clemon University's Division of Computing and Information Technology utilizing a SUN Microsystems HPC 6000 (16 processors).

The Department of Mechanical Engineering's beowulf cluster of Pentium based PCs (48 processors).

RESEARCH PROJECT EXAMPLES:

The support of the National Science Foundation through the Faculty Early Career Development (CAREER) young investigator award, Grant CTS-9983762, is gratefully acknowledged.

REFERENCES:

C.A. Kennedy and M.H. Carpenter, `Several New Numerical Methods for Compressible Shear-Layer Simulations,' Applied Numerical Mathematics, 14, 397-433, 1994.