X Ma N.Zabares/Joumal of Computational Physics 27(0)844-471 8455 d-宫4-名名新m (48) such that 4-22am (49 =0.u==0 0=1 u=v=0 Free fluid Porous Medium Fg.Schematic of atural saturated variable porous medium .Comparison of th d ¼ XP m¼0 dmWm ¼ XP i¼0 XP l¼0 ^lvn i WiWl; ð48Þ such that dm ¼ XP i¼0 XP l¼0 ^lvn i elim: ð49Þ Free fluid Porous Medium = 1 u = v =0 = 0 u = v =0 θ θ = 0, u = v =0 n ∂ θ ∂ = 0, u = v =0 n ∂ θ ∂ l ε =1 w ε Fig. 1. Schematic of natural convection in a fluid saturated variable porous medium. 0. 0 1 .2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 -1.73 -1.73 -1.73 -0.09 -0.09 -0.09 -0.09 -0.01 -0.01 -0.01 -0.01 -0.01 -5.48 -9 -8 -7 -6 -5 -4 -4 -3 -3 -2 -2 -1 -1 1 1 2 2 3 4 5 Fig. 2. Comparison of the streamlines (left) and isotherms (right). Top row: first-order projection method. Bottom row: second-order projection method. X. Ma, N. Zabaras / Journal of Computational Physics 227 (2008) 8448–8471 8455