摘要
沉浸邊界與移動邊界問題在近幾年來引起很大的發展研究，透過數值模擬的方式計算此類行的物理問題是本文的目的。本文提出以非交錯的直角坐標網格系統解移動邊界問題且在時間微分項選用隱式的差分方法。如此一來就不用因為配合物體外觀而選用不同的網格座標進行計算，可大大降低網格所需要的計算，加上時間微分項選用隱式的差分方法使用，所以時間的網格大小將不受限制，進而減少計算時所需要的次數。
本文中使用了虛擬邊界的概念，配合虛擬點與強制點，並提出新的強制力方法，去設置物體邊界的固體點與液體點之計算方法。使整套系統在計算時能滿足物體邊界的條件。本文實際應用了此方法去解均勻流流過圓柱與圓柱在靜止流場中行簡諧運動之物理問題，與其他數值方法相比，本文的方法計算頗佳，希望將此方法獻給各位研究者參考。

參考文獻
[1] C.S. Peskin, Flow patterns around heart valves; a numerical method, J. Comput. Phys 10 (1972) 252-271
[2] S.L. Lee, D.W. Lin, Transient conjugate heat transfer on a niturally cooled boby of arbitrary shape, International Journal of Heat and Mass Transfer, Vol. 40(1997), pp. 2133-2145
[3] J. Mohd-Yusof, Combined immersed boundary/B-spline methods for simulation of flows in complex geometries, in: Annual Research Briefs, NASA Ames Research Center/Stanford University Center for Turbulence Research, Stanford, CA,1997,pp.317-327
[4] Y.H. Tseng, J.H. Ferziger, A ghost-cell immersed boundary method flow in complex geometry, Journal of Computational Physics 192 (2003) 593-6230
[5] Jianming Yang, E. Balaras , An embedded-boundary formulation for large-eddy simulation of turbulent flows interacting with moving boundaries, Journal of Computational Physics 215 (2006) 12-40
[6] S. L. Lee, R. Y. Tzong, Aritifical pressure for pressure-linked equation, International Journal of Heat and Mass Transfer, Vol. 35, pp. 2705-2716
[7] S. L. Lee, Weighting function scheme and its application on multidimensional conservation equations, International Journal of Heat and Mass Transfer, Vol. 32 (1989), pp. 2065-2073
[8] S. L. Lee, A strongly implicit solver for 2-diemensional elliptic differential equations. Numerical Heat Transfer, 16 (1989), pp. 161-178
[9] S. Majumdar, G. Iaccarino, P. Durbin, RANS solvers with adaptive structured boundary non-conforming grids, in: Annual Research Briefs, NASA Ames Research Center/Stanford Uinversity Center for Turbulence Research, Standfor, CA,2001, pp.353-366
[10] H. Dutsch, F. Dorst, S. Becker, H. Lienhart, Low-Reynolds-number flow around an oscillating circular cylinder at low Keulegan-Carperter number, J. Fluid Mech. 360 (1998) 249-271