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Joint Applied Math and Stanford SIAM Students Chapter Seminar
High-Resolution Finite Volume Methods with Application to Volcano and Tsunami Modeling
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Hyperbolic systems of partial differential equations often arise when modeling phenomena involving wave propagation or advective flow. Finite volume methods are a natural approach for conservation laws of this form since they are based directly on integral formulations and are applicable to problems involving shock waves and other discontinuities. High-resolution shock-capturing methods developed originally for compressible gas dynamics can also be applied to many other hyperbolic systems. A general formulation of these methods has been developed in the CLAWPACK software that allows application of these methods, with adaptive mesh refinement, to a variety of problems in fluid and solid dynamics. I will describe these methods in the context of some recent work on modeling geophysical flow problems, particularly in the study of volcanos and tsunamis. Volcanos generate many challenging flow problems, and accurate simulation is required both to further scientific understanding and to aid in hazard assessment and mitigation. The initial blast wave can cause devastation in a large region around the volcano, the continuing eruption leads to lava flows or pyroclastic flows on the flanks of the volcano and ash plumes that are a danger to aircraft far away. Melting glaciers on snow-capped volcanos can lead to debris flows endangering nearby cities. Tsunamis generated by earthquakes or underwater landslides can cause damage and loss of life far away from the source, and accurate prediction of their propagation through the ocean and interaction with coastal topography is essential in issuing early warnings. |