基于传递矩阵的两相介质波动问题时域显式有限元方法稳定性研究

Study of stability of explicit finite element method for wave motion of two-phase medium based on transfer matrix

饱和两相介质波动问题的时域显式有限元方法具有条件稳定性。这类方法的稳定性可通过方法中动力反应时域递推计算格式传递矩阵传递因子的数值进行评估,传递因子的数值越小,方法的稳定性越好。针对饱和两相介质波动问题的两种时域显式有限元方法,基于其动力反应时域递推计算格式的传递矩阵的性质,在两相介质体系物理参数取值不同的条件下,对两种方法稳定性性质的差异进行了对比研究。结果表明:渗透系数的取值对两种时域显式有限元方法稳定性性质的差异具有较为显著的影响。当渗透系数取值较大时,两种方法的稳定性性质没有明显的差异;当渗透系数的取值较小时,两种方法的稳定性性质将表现出明显的差异,方法1的稳定性要优于方法2。

The time-domain explicit finite element method for the wave motion of saturated two-phase medium is conditionally stable,and the stability of this kind of method can be evaluated by the transfer factor of transfer matrix of calculating formula. The smallerthe value of transfer factor is, the better the stability of the explicit finite element method is. The stability of two time-domain explicitfinite element methods for the wave motion of saturated two-phase medium is compared based on the transfer matrix of thecalculating formula of the method, as various values of physical parameters of saturated two-phase medium are adopted. Calculatingresults show that the value of permeability coefficient has a remarkable effect on the distinction between the stability characteristic ofthe two methods. When a large value of permeability coeff-cient is adopted, the stability characteristic of the two methods does notdistinguish obviously from each other. On the other hand, when a small value of permeability coefficient is adopted, the stabilitycharacteristic of the two methods will have a remarkable difference from each other. One method has more ascendant stabilitycharacteristic than that of the other method.