One-, two-, and three-dimensional solutions for counter-current steady-state two-phase subsurface flow

摘要: Abstract This paper derives analytical solutions for steady-state one-dimensional (1-D), two-dimensional (2-D), and three-dimensional (3-D) two-phase immiscible subsurface flow a counter-current problem. Since the governing equations are highly nonlinear, 2-D 3-D derivations generally difficult to obtain. The primary purpose is test finite difference/volume/element computer programs accuracy scalability using architectures ranging from PCs parallel high performance computers. derivation accomplished by first solving saturation of water in terms function that solution Laplace’s equation achieve set partial differential allows some degree latitude choice boundary conditions. Separation variables Fourier series used obtain final solution. problem consists rectangular block soil where specified pressure applied at top bottom sample, no-flow conditions imposed on sides. sample step testing adaptive meshing or concentration grid points action zones.