Computational Challenges in the Geosciences (The IMA Volumes in Mathematics and its Applications Book 156)

**__Computational Challenges in the Geosciences__** addresses a cross-section of grand challenge problems arising in geoscience applications, including groundwater and petroleum reservoir simulation, hurricane storm surge, oceanography, volcanic eruptions and landslides, and tsunamis. Each of these applications gives rise to complex physical and mathematical models spanning multiple space-time scales, which can only be studied through computer simulation. The data required by the models is often highly uncertain, and the numerical solution of the models requires sophisticated algorithms which are mathematically accurate, computationally efficient and yet must preserve basic physical properties of the models. This volume summarizes current methodologies and future research challenges in this broad and important field. Front Matter....Pages i-ix Physical and Computational Issues in the Numerical Modeling of Ocean Circulation....Pages 1-23 Modeling Hazardous, Free-Surface Geophysical Flows with Depth-Averaged Hyperbolic Systems and Adaptive Numerical Methods....Pages 25-48 Real-Time Forecasting and Visualization of Hurricane Waves and Storm Surge Using SWAN+ADCIRC and FigureGen....Pages 49-70 Methane in Subsurface: Mathematical Modeling and Computational Challenges....Pages 71-100 Fast Algorithms for Bayesian Inversion....Pages 101-142 Modeling Spatial and Structural Uncertainty in the Subsurface....Pages 143-167