THE CRUNCH GROUP

RESEARCH

Research Areas:

• I. Multiscale Simulation of Arterial Blood Flow
• II. Ultrascale parallel paradigms and High-order Spectral/hp Element Methods
• III. Stochastic Simulations and Uncertainty quantification.
• IV. Data Assimilation & Low-Dimensional Modeling.

Multiscale Simulation of Arterial Blood Flow

The human vascular system is very complex, with five liters of blood traveling through the vascular network of 60,000 miles in just one minute. Interactions of blood ow in the human body occur between dierent scales, in which the large-scale flow features are being coupled to cellular and sub-cellular biology, or at similar scales in different regions of the vascular system.

We propose to develop and validate an integrated model of the cerebrovasculature characterized by three distinct spatial length scales:

• The macrovascular network (MaN) consisting of large arteries, down to diameter of 0.5 mm, which are patient-specific and can be reconstructed from MRA imaging.
• The mesovascular network (MeN) consisting of small arteries and arterioles, from 0.5mm down to 0.01 mm, which follow a tree-like structure governed by specific fractal laws.
• The microvascular network (MiN) consisting of the capillary bed, which follows a net-like structure.

More comprehensively, we propose to separate the simulations into two regimes: The first one involves all arteries that can be accurately imaged clinically at the present time, whereas the second regime involves the “subpixel” dynamics (MeN and MiN).

Specifically, we focus on the following projects:

• Modeling 3D Unsteady Flow in the Brain
• Modeling 1D Unsteady Flow in the Brain
• Modeling Blood Flow in Arteries with Aneurysm
• Collaborative Research: Scalable Multiscale Models for Cerbrovasculature Algorithms: Software and Petaflop Simulation(Grant NSF OCI-0904288)
• Multiscale Modeling and Parallel Simulations of Blood Flow in Cerebral Malaria and Sickle Cell Diseases(Grant NIH R01HL094270)
• Multiscale Modeling of Flow over Functionalized Surfaces: Algorithms and Applications(Grant NSF CBET-0852948)

Ultrascale parallel paradigms and High-order Spectral/hp Element Methods

• Two-level Domain Decomposition Method(Grant NSF OCI-0904288)
• Time- Space-window POD Analyzis of Intermittent Laminar-Turbulent Flow

Stochastic Simulations and Uncertainty Quantification

• A Multi-element Generalized Polynomial Chaos Method for Modeling Uncertainty in Flow Simulations (Grant NSF DMS-0510799)
• Multi-scale Fusion of Information for Uncertainty Quantification and Management in Large Scale Simulations(Grant OSD/AFOSR/MURI FA-9550-09-1-0613)
• Overcoming the Bottlenecks in Polynomial Chaos: Algorithms and Applications to Systems Biology and Fluid Mechanics(Grant NSF DMS-0915077)

Data Assimilation & Low-Dimensional Modeling

• Stochastic Nonlinear Data-Reduction Methods with Detection & Prediction of Critical Rare Events(Grant DOE DE-SC0002542)
• Stochastic Analysis of Advection-Diffusion-Reactive Systems with Applications to Reactive Transport in Porous Media(Grant DOE/PNNL - DE-FG02-07ER25818)