利用理查森外插法應用於土石流計算

Abstract

台灣地區土石流災害頻繁，一般事前預警的方法之中，土石流計算模擬是其中常見的一種方法，本文根據前人開發出來的模式，藉由粗細兩種網格的操作，計算後進行外插處理，而外插的根據來自於數值離散方式的誤差推導，旨在希望外插後的結果能夠優於原本粗細兩種網格計算的結果。本文先藉由基礎理論的章節，利用三大方程式來進行誤差推導與外插應用，說明方法進行的實際作用，進入土石流相關章節後，詳細推導出模式本身計算上的誤差，再經由不同組實驗，觀察理論與實際結果的吻合程度，來驗證外插法使用的結果。

In this paper, according to the pattern developed by the predecessors, the operation of the two kinds of grids is calculated and the extrapolation is applied to after the calculation of the two kinds of meshes. The extrapolation is based on the error derived from the numerical discretization method, and it is intended that the results after extrapolation be better than the results of the two coarse grid calculations. This paper first uses the three different equations to carry out the error derivation and extrapolation application, illustrating the practical effect of the method. About the relevant sections of the debris flow, the calculation of the error of the model itself is derived. Then by different groups of experiments, Observe the degree of agreement between the theory and the actual results, to verify the results of the use of extrapolation.