CMG: Studies of Sediment Gravity Flows

该项目结合了基于无网格方法的火山碎屑流和涌流以及相关重力流的模拟，以及建模和分析，所有这些都针对实验室和现场数据进行了测试。最小二乘无网格法是一种基于粒子的模拟计算方法的核心。自适应-注入新的粒子基函数，增加基函数的近似阶数-将被引入，允许精确地分辨流动中的自由表面和其他基本结构。数学和计算建模将把目前的最小二乘方法扩展到由气体和颗粒混合物组成的流动，以及具有显著热含量的流动。数学分析将阐明该方法的平滑特性，以确保鲁棒和准确的模拟技术，并使该方法能够转化为其他地球物理质量流系统。模拟将通过实验室实验验证，并根据现场结果测试其预测效果。这样，数学理论与地质实验相结合，为地球物理流动系统的数学建模开辟了一条新的途径。火山碎屑流是由火山活动产生的比空气重的气体颗粒混合物。火山碎屑流可以以10-100米/秒的速度移动，温度可以达到1000摄氏度以上。火山碎屑流可以高密度，沿着山坡和水下移动，也可以低密度，越过山脉和水面上升。由于其速度、温度和体积，火山碎屑流对火山源附近数英里内的居民构成了巨大的威胁。其破坏力的证据可以在美国西澳的圣海伦斯火山、蒙特塞拉特的苏弗里埃尔山火山、菲律宾的皮纳图博火山和墨西哥的科利马火山等地看到。虽然火山碎屑流和浪涌（基本上是一种稀释的火山碎屑流）被仔细研究，但对自然地形上分层流动物质的动力学的详细了解还没有到手；缺乏预测能力，即对哪些地区处于高风险的科学评估。作为科学家，重要的是能够理性地评估风险，并向当地公共安全官员传达风险的性质。基于对现象学的清晰理解，科学与社会之间的互动将导致构建合理的危害风险地图，这将有望拯救生命。这个数学和计算研究项目，加上实验室和实地研究，将更好地预测火山碎屑流和涌流的速度和程度。这些结果将有助于制作可靠的灾害风险地图，从而为公众利益服务。

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.