On an Improved Finite-Volume-Difference Method in Fluids Computation

有限體積方法之改進與實踐

李天佑(Daniel Lee) ； 游輝宏(Mulder Yu)

《中國航空太空學會學刊》 33卷3期 (2001/09) Pp. 171-179

https://doi.org/10.6124/TAASRC.200109_33(3).04

摘要

本文利用前所發展之定積分解析式四階逼近，設計一個四階有限體積差分方法，並將此一演算法推廣及於一般之CN算則。並針對三維非線性Burgers方程，推廣具體之演算法與嚴道之收斂性與穩定性定理。本文也展示包含NS方程之相關數值資料，充分體現此一四階演算法之可行性與實用性。

關鍵字

有限體積－有限差分方法 ； CN方法 ； 線性穩定

並列摘要

We make use of an analytic approximation to definite integrals frequently arising in the study of finite volume method, to derive for three-dimensional fluids computation an improved Finite-Volume-Difference method. The scheme is of first order in the temporal and fourth order in the spatial variables. When combined with the generalized Crank-Nicolson (CN) approach, the scheme is unconditionally stable for CN parameter in the range 1/2 to 1, and of second order in time for CN parameter equal to 1/2. Theoretical results in accuracy and linear stability are proved here. Exhibited are also some numerical results that justify the theory. Various applications of the idea are shown to achieve successful results.

並列關鍵字

Finite-Volume-Difference Methods ； Crank-Nicolson Approach ； Linear Stability