Design of ‘mimetic’ numerical methods that capture the physics of partial differential equations exactly.

• Mimetic Methods
• Particle and Moving Mesh Methods
• Error estimation
• Unstructured Staggered Mesh Methods
• Secondary Conservation
• Fractional Step Methods (Classical, Exact, Large Timestep)

Supported by DARPA – Polyplexus, Stanford University,

Use of novel hardware accelerators to increase the performance of parallel supercomputers by at least an order of magnitude.

• Cluster Design and Build
• Scientific Computing with GPUs
• Tilera Pro64 (64 core processor) performance
• Memristor Analog Computing
• Smith-Waterman (GEMS)
• Interactive CFD
• Desktop Supercomputer

Supported by: Office of Naval Research, Oak Ridge National Laboratory, Nvidia, UMass.

Direct Numerical Simulation of basic turbulent flows using physically realistic initial conditions and mimetic methods.

• Rotating Decay
• Return-to-Isotropy
• Plane Strain
• Axisymmtric Strain
• Isotropic Decay
• Superhydrophobic Surfaces
• Shear-Free Turbulent Boundary Layers

Supported by NSF.

Development of equation systems which mimic Navier-Stokes equations but which are computationally tractable on a PC.

• Turbulent Potential Model
• Oriented-Eddy Collision Model
• Universal RANS/LES (k/eps, RST)
• Dissipation Tensor
• Decay Rate
• Transition

Supported by AFOSR, ONR, NSF.

Systems requiring advanced numerical methods.

• Fast Smith-Waterman sequence matching (DNA, RNA, Proteins)
• Micro-mixers
• Droplet free-surface collision.
• Droplet Dynamics
• Drag on Sea Turtles

Supported by DOE, NSF.

Wind Turbines Aerodynamics and Wakes.

• Full rotating blade CFD
• Wake reduction
• Offshore platform dynamics

Supported by DOE.

Discovery and explanation of super-hydrophobic drag reduction.

• Early experiments (2000)
• Laminar mechanism discovery.
• Turbulent simulations and analysis

Supported by ONR.