在本論文中，我們應用於地形座標系統所建立的深度平均動力學模型來模擬2010年Merapi火山噴發時的礫石流動，透過流量、深度分佈和流速等流場的重要資訊來探討防災、減災等災害管理相關議題。在數值計算中，地形的資料仰賴現有的數位地形地圖(DEM)。數位地形地圖的建立乃依據現實的地形，難免會有不可避免的劇烈崎嶇起伏，以至於無法直接適用於地形座標。妥協的方法就是將劇烈崎嶇起伏的地形平滑化(濾波法)，然而平滑化之後也改變了真實地形。為了解決這個問題，我們在平滑化的曲面地形上建立子地形(sub-topography)來重塑真實的地形。在情境模擬的部分，我們透過引入火山口的礫石湧出量來控制數值模擬中的礫石分佈與總量。此外，論文中也進一步探討理論模型中的摩擦係數和動量校正因子對於礫石流動與動態分部的影響。藉由過往的流變分析研究，歷史記錄和衛星圖像驗證理論，獲得非常好的相關性。

In this thesis, a depth-averaged model in a terrain-fitted coordinate system is applied to simulate the pyroclastic flows during the eruption of Mt. Merapi in 2010. Through the numerical simulation we are able to obtain more precise flow information, such as the local flow fluxes, the distributions of flow depth and velocity as well as the deposits, for the goal of hazard mitigation or hazard management. In the numerical computation, the terrain-fitted coordinate system is based on the digital elevation model (DEM). Because of the fact that the real topography might consists of highly varying elevation, e.g. obstacles or cliffs, which is not applicable in the terrain-fitted coordinate, a compromised treatment is to smooth (filter) the topographic surface. However, the employment of the smooth basal surface might introduce deviation because of the lack of the sudden change of topography. In this study, we introduce the so-call “sub-topography” over the smoothed topographic surface, to mimic the real topography.
In the simulations, we also introduce the “Upwelling” to mimic the exploded material, especially by the multiple eruptions, so that we may have a more reasonable spreading/supply of flow material. In addition, we also investigate the impacts of the key parameters on the flow behaviors, such as the friction coefficient, momentum correction factor and the amount of upwelling. Besides, the Voellmy rheology has also been taken into account. The results of these tests were compared to theoretical findings of rheological analysis presented in previous studies as well as historical records, and satellite images to figure out the representative values of the relevant parameters.

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