過去以有限元素方法計算多孔彈性力學問題時，在不可壓縮流體與低滲透率的條件下，模擬結果存在著孔隙壓力數值震盪的問題，該現象不符合真實的物理現象。因此，為了消除此一非物理性的震盪現象(即偽震盪)，本研究提供了一種簡易且基於有限體積的質量守恆與動量守恆概念下的交錯演算法，此方法是將位移變數與孔隙壓力變數在空間上交錯配置進行求解。接著，為了驗證此一方法的可行性，本研究亦對此方法進行收斂分析與探討各項無因次係數對系統穩定性的影響，並針對與其他的數值模擬結果進行相互比較。透過三種不同的物理問題，分析此一交錯方法對數值上的偽震盪現象消除效果。 生物組織可以被視為被流體滲透的多孔、可滲透和可變形的介質。將交錯方法運用於多重網絡彈性理論(MPET)中以研究此類生物系統中的傳輸現象。並且利用一個模擬大腦的案例，探討其方法之可行性。 ;It is well-known that, under the conditions of incompressible fluid and low permeability, the finite element method results would cause non-physical oscillations in the discrete pressure solution. The oscillations doesn’t correspond to a real physical phenomenon. In order to eliminate the non-physical oscillation, this study propose a staggered finite volume method based on the conservation of mass and the conservation of momentum. This method is solved by method in which the displacement and pore pressure unknowns are located in a staggered configuration. Then, in order to verify the feasibility of this method, this study carried out a convergence analysis of this method. And discuss the influence of each dimensionless coefficients on the system stability, Furthermore, through three different physical problems, analyze the effect of this staggered method on the numerical value of non-physical oscillation elimination. Biological tissue can be viewed as a porous, permeable and deformable medium penetrated by fluids. The staggered method has been developed based on the Multiple-Network Poroelastic Theory (MPET) to study transport phenomena in such biological systems. We proposed a case of simulating cerebral environment to explore the feasibility of its method.
