This project combines simulations of pyroclastic flows and surges and related gravity currents based on meshfree methods, together with modeling and analysis, all tested against lab and field data. The Least Squares Meshfree Method forms the core of a proposed particle-based computational method for simulations. Adaptivity - injecting new particle basis functions, increasing basis function order of approximation - will be introduced, allowing accurate resolution of free surfaces and other fundamental structures within the flows. Mathematical and computational modeling will extend the current Least Squares methodology to flows which are composed of a mixture of gas and grains, and to flows with significant thermal content. Mathematical analysis will elucidate the smoothing properties of the method, to ensure a robust and accurate simulation technology, and to enable translation of the method to other geophysical mass flow systems. Simulations will be validated against laboratory experiments, and its predictive efficacy tested against field results. In this way, mathematical theory and geological experiment together can develop a new approach to the mathematical modeling of geophysical flow systems.

Pyroclastic flows are heavier-than-air gas-particle mixtures resulting from volcanic activity. Pyroclastic flows can travel at velocities from 10-100 m/sec, and can attain temperatures upwards of 1000 degrees C. Pyroclastic flows can have high density, and move down mountainsides and under water, or they can be of low density, and lift over mountains and across water. Because of their speed, temperature and volume, pyroclastic flows pose an enormous risk to populations within miles of the volcanic source. Evidence of their destructive power can be seen Mount St. Helens, WA, USA, Soufriere Hills Volcano, Montserrat, Mount Pinatubo, Phillipines, and Colima Volcano, Mexico, among other sites. Although pyroclastic flows and surges (basically a dilute pyroclastic flow) are carefully studied, a detailed understanding of the dynamics of the stratified, flowing material over natural topography is not in hand; predictive capability a scientifically-based assessment of what regions are at high risk is lacking. As scientists, it is important to be able to rationally assess risk and communicate the nature of that risk to local public safety officials. An interaction between science and society based on a clear understanding of the phenomenology leading to the construction of reasonable hazard risk maps will, hopefully, save lives. This program of mathematical and computational research, coupled with laboratory and field study, will better predict the speed and extent of pyroclastic flows and surges. These results will serve the public interest by aiding the production of trustworthy hazard risk maps.

Project Report

Free surfaces and/or stratified flows arise in many geophysical contexts. This project examined so-called sediment gravity flows (or, more generally, a geophysical mass flow) both experimentally and computationally. In the field, a large mass flow contains millimeter-centimeter sized particles, comprising flow features at the O(m)-scale, and running out over many kilometers. So one immediate and obvious difficulty in studying mass flows is the problem of multiple scales of interest. Flows run over varying terrain, and the composition of the flow itself can change as larger particles migrate up through the deforming mass, as fine particles are lifted off the basal surface and into a more turbulent airflow, as interstitial fluid liquefies the flowing mass, and as new solid and fluid material is entrained into the flow. A detailed description of all the active physical processes may not be possible. Cleaver experiments have provided insight into the behavior of these flows, but much remains to be discovered. There is a tremendous need for an improved understanding of these flows, to aid civil protection authorities who are charged with hazard assessment and risk mitigation. To construct scientifically sound models and to create successful simulation tools to aid in the hazard analysis of gravity and pyroclastic density currents, three principal challenges must be confronted: The challenge of scales; The challenge of phases; The challenge of methods. No single modeling approach will adequately capture the dynamics across the entire span of length and time scales operating in mass flow problems. At the same time, coarse and fine particles at high temperature mix with air, creating internal dynamics of particle migration and fluid entrainment. Finally, the difficulties of accurately simulating free surface flows over the length scales of importance, and accurately accounting for erosion and deposition, make for difficult computational and modeling choices. Traditionally, a depth-averaging procedure, akin to the shallow water equations, has been used to compute geophysical mass flows. This approach has met with several successes in recent years. But there are fundamental limitations to the methodology. Principal among these limitations is that the depth averaging approach is a long wavelength approach – that is, the approach only resolves features that change slowly over the terrain. Mathematically, if we let H be the typical thickness of a mass flow, and L a typical length scale along the basal surface, the thin layer method ignores terms that are on the order of ε=H/L. Mesh-free, particle-based methods have been developed as alternatives to standard mesh-based methods. This project began a program of numerical analysis and simulation, using particle-based methods, coupled with lab-scale experiments, to simulate geophysical flows. Three principal activities have been completed: Data were taken on approximately 275 runs of granular material flows. These different runs explored different sized granular materials (usually glass beads of differing sizes) down a quasi-two dimensional inclined plane flume, approximately 15 feet long, 8 inches wide. Semi-circular and rectanglar obstacles were inserted into the flow path. High speed video and PIV instruments record flows. Data such as the mass that surmounts the barrier, and propagation of bore waves upstream from the obstacle, have been recorded. How the several parameters influence the behavior of the system has being analyzed. After extensive numerical experimentation and analysis of various approaches pseudo-particle methods, the Smooth Particle Hydrodynamics methodology was adapted to solve the governing mass and momentum balance laws. Classical SPH does not robustly solve flow equations without the addition of additional, non-physical terms that stabilize the numerical computations. We have adapted new ideas for solving the SPH equations, approaches growing out of work during the last 25 years on numerical solvers for gas dynamics. With this Godunov-SPH approach, computations can be performed reliably in realistic settings. Based on the G-SPH methodology, a mathematical analysis of the initial-boundary value problem has been performed, demonstrating the foundational soundness of the approach. A parallel G-SPH code has been developed in 2 space dimensions, for flows over simple geometries. Simulations of cannonical problems have been performed. Comparisons with the 275 runs are currently underway.

Agency
National Science Foundation (NSF)
Institute
Division of Earth Sciences (EAR)
Type
Standard Grant (Standard)
Application #
0620991
Program Officer
Robin Reichlin
Project Start
Project End
Budget Start
2006-09-01
Budget End
2011-08-31
Support Year
Fiscal Year
2006
Total Cost
$488,956
Indirect Cost
Name
Suny at Buffalo
Department
Type
DUNS #
City
Buffalo
State
NY
Country
United States
Zip Code
14260