以特徵消散有限元素形貌動力模式模擬粒徑篩化現象

Abstract

河川形貌動力學（River morphology）之知識乃為河岸工程建設與淡水環境棲地復育之基礎。許多特別之現象如河床甲護化（Armoring）及下游顆粒細化（Downstream fining）等，均顯著地影響了河川生物棲地之品質。因此，瞭解中尺度河川地形貌（Meso-scale bedforms）之演變及其底床顆粒之組成變化乃為一重要之課題；然而河川之水流水理、底床之非均勻粒徑組成及輸砂運移事件此三者間複雜之交互作用使得形貌動力之問題非常難以處理。本研究中，吾人發展了一套二維水深平均（Depth-averaged 2D）能夠處理多粒徑輸砂（Mixed-size sediment transport）之有限元素（Finite element）形貌動力模式，並研發了垂直方向連續篩化（Vertical continuous sorting）之演算機制─虛擬質量法（Virtual mass），以試圖瞭解天然河川中常見之區塊動力（Patch dynamics）等問題其形貌與粒徑組成之演變；模式中應用特徵消散有限元素上風方法（Characteristic dissipative Galerkin, CDG scheme）於乾溼演算水理模組（Wetting and drying module）及床貌演變模組（Bed evolution module）以處理傳遞主導（Advection dominated）之砂洲遷移問題中常見之數值不穩定性問題（Numerical instability）。

The knowledge of river morphology is fundamental and useful information for engineering and habitat restoration purposes. Many interesting phenomena such as armoring and downstream fining significantly affect the quality of riverine habitats. Therefore, the development of meso-scale bedforms and the change in their sediment composition have become important topics of study. However, the complex interactions between flood flow, nonuniform particles and sediment transport make these problems difficult to tackle. In this study, we develop a 2D (two-dimensional) many-fraction FE (finite element) morphodynamic model which is capable of dealing with mixed-size sediment transport problems. We also present a new type of vertical sorting scheme, the virtual mass method, to investigate the common phenomenon such as patch dynamics that could occurs in most natural rivers. The proposed model adopts the characteristic dissipative Galerkin (CDG) scheme in the wetting and drying module and bed evolution module such that the convection dominated bar evolution can be computed without numerical instabilities.