耦合與分離河道輸砂模式之比較研究

Abstract

本文擬藉由參數敏感度分析探討耦合和分離演算法模式對非均勻沈滓輸砂模式之差異性和適用性。分離演算法乃假設在單位計算時間距內，泥砂輸送所造成的底床高程變動量對水流部分的影響可忽略，將控制方程式分成泥砂和水流兩部分分別計算;耦合演算法則在單位計算時間間距同時解所有的控制方程式。 本研究比較之耦合與分離模式具有相同之控制方程式、數值差分法與輸砂公式。首先選定交換層厚度與普立斯曼四點法的加權因子，控制方程式無因次化後得到之無因次參數，經數值試驗並以平均絕對差定義底床變化偏移量與中值粒徑偏移量，如此可量化無因次參數的影響程度，將測試所得偏移量經複迴歸分析可得冪次形式關係式，並藉由關係式來探討耦合與分離模式對無因次參數之敏感度。 就測試結果顯示，分離模式有穩定性的問題，需同時考慮多個參數才能確保模擬結果的穩定性和精確性，耦合模式則沒有穩定性的顧慮。複迴歸關係式顯示耦合模式的模擬結果受到無因次參數變化的影響比分離模式較為敏感，較能反應出參數變化之影響，但於實際應用上耦合模式需特別注意無因次參數值變化的程度，以確保模擬結果的精確性。

This study investigates the differences and restrictions of coupled and uncoupled alluvial-channel sediment transport models through sensitivity and stability analyses. The uncoupled model assumes the change of sediment variables is small enough during a computational time step, so that its effect on variables can be ignored. Therefore, the flow and sediment equations can be solved separately in one time step. The coupled model solves all of the governing equations simultaneously, and the mutual iteration of the flow and sediment variables are considered. The coupled and uncoupled models used in this study have the same governing equations, sediment transport formula and the numerical scheme. First, the effect caused by numerical weighting factor and mixing layer thickness is analyzed. The numerical dimensionless parameters are derived from governing equations. The influence of the dimensionless parameters to the deviation of bed change and mean particle size has been quantified by numerical experiments. The relation between the deviations and the dimensionless parameters has been constructed as a base function for the sensitivity test of both of the coupled and uncoupled models. The results indicate that there exists an instability problem for the uncoupled model. While the simulation is progressed, one has to consider several parameters simultaneously to ensure the accuracy and stability of the results. From the dimensionless parameters multi-regression relation, one can observe that the sensitivity of simulation results of the coupled model is higher than the uncoupled model.