An improved CE/SE scheme for incompressible multiphase flows and its applications

Abstract

Abstract:A new space-time conservation element-solution element (CE/SE) scheme, which is based on the hexahedron mesh, is proposed by constructing a new structure of solution elements (SEs) and conservation elements (CEs) and extended to two-dimensional incompressible multiphase flows. This scheme is applied to several incompressible flow problems, such as lid-driven cavity flow, dam break flow, motions of falling droplets, flow instability and water-kerosene interaction. The numerical results and their comparison with lecture results and experimental data are presented. The comparisons demonstrate that the computational scheme developed currently is clear in physical concept, easy to be implemented and highly accurate and efficient for the above-mentioned problems. The highlight is that the pretreatment method is proposed, transforming the elliptic-parabolic equations to the hyperbolic equations, which can be directly simulated by the improved CE/SE scheme. Thus, the improved CE/SE scheme can be applied to incompressible multiphase flows widely.

Green functions of mass diffusion waves in porous media

“…Diffusion waves arise from the classical parabolic diffusion equation with an oscillatory force function in homogeneous media [9]. Diffusion-wave methods have been developed in the study of heat transfer [10], diffusive neutron waves [11], diffusive viscosity waves [12], pressure diffusion in porous media [13][14][15][16] and mass transport [17]. Diffusion waves are heavily damped with relatively slow velocity and short wavelength.…”

Numerical analysis of confined flow past permeable square cylinder with CE/SE method

“…The CE/SE method has been widely applied in compressible (Wang et al, 2008;Zhang and Wang, 2009) and incompressible multiphase flows by using the preconditioned method (Yang et al, 2012;Yang and Zhang, 2013), as well as poromechanical problems (Yang et al, 2014) governed by hyperbolic equations. Yang et al (2010) applied the above method to incompressible multiphase flows in porous media, including the contact interface of dual porous medium, lid-driven cavity flows, dual layer lid-driven cavity flow, which expanded the CE/SE method to the field of fluid mechanics in porous media.…”

“…The relation between the independent physical variables and their derivatives are derived by the continuity condition of flow variables on a staggered grid. The detailed CE/SE method was referred in the literature (Yang and Zhang, 2013). The generalised N-S equation set (Yang et al, 2012) was applied for flows in porous media.…”

“…The Brinkman and Forchheimer effects were considered in the flow mechanism. The preconditioned procedure (Yang and Zhang, 2013) was applied for transforming the parabolic equations, which govern incompressible viscous flows in porous media, into the hyperbolic ones, which can be directly solved by CE/SE method. A staggered mesh was applied for the calculations in order to avoid a pressure shift phenomenon.…”