Modified two-grid method for solving coupled Navier-Stokes/Darcy model based on Newton iteration

A new decoupled two-gird algorithm with the Newton iteration is proposed for solving the coupled Navier-Stokes/Darcy model which describes a fluid flow filtrating through porous media. Moreover the err...     

Coupling nonlinear Stokes and Darcy flow using mortar finite elements

We study a system composed of a nonlinear Stokes flow in one subdomain coupled with a nonlinear porous medium flow in another subdomain. Special attention is paid to the mathematical consequence of the shear-dependent fluid viscosity for the Stokes flow and the velocity-dependent effective viscosity for the Darcy flow. Motivated by the physical setting, we consider the case where only flow rates are specified on the inflow and outflow boundaries in both subdomains. We recast the coupled Stokes–Darcy system as a reduced matching problem on the interface using a mortar space approach. We prove a number of properties of the nonlinear interface operator associated with the reduced problem, which directly yield the existence, uniqueness and regularity of a variational solution to the system. We further propose and analyze a numerical algorithm based on mortar finite elements for the interface problem and conforming finite elements for the subdomain problems. Optimal a priori error estimates are established for the interface and subdomain problems, and a number of compatibility conditions for the finite element spaces used are discussed. Numerical simulations are presented to illustrate the algorithm and to compare two treatments of the defective boundary conditions.     

Spatial decay in a double diffusive convection problem in Darcy flow

This paper deals with a model of time-dependent double diffusive convection in Darcy flow. In particular it is concerned with the spatial decay of solutions when the flow is confined to a semi-infinite cylinder. Decay bounds for an energy expression are derived.     

Convective Flows on Reactive Surfaces in Porous Media

A model for the convective flow in a fluidsaturated porous medium containing a reactive component is considered. This component undergoes an exothermic reaction (modelled by a first order mechanism) on an impermeable bounding surface, the resulting heat released driving the convective flow. Large Rayleigh number flow near a stagnation point is treated in detail by first considering the steady states. Multiple solution branches and critical points arising from a hysteresis bifurcation are identified. The form that these solution branches take depends on whether or not the effects of reactant consumption are included. An initialvalue problem is then discussed. This shows that both the lower (slow reaction) and upper (fast reaction) solution branches are stable (and the ultimate state of the system). When the parameter values are such that there is no steady state, the solution develops a finitetime singularity, the nature of which is analysed.     

Optimal error estimates of a decoupled scheme based on two-grid finite element for mixed Stokes–Darcy model

Although the numerical results suggest the optimal convergence order of the two-grid finite element decoupled scheme for mixed Stokes–Darcy model with Beavers–Joseph–Saffman interface condition in literatures, the numerical analysis only gets the optimal error order for porous media flow and a non-optimal error order that is half order lower than the optimal one in fluid flow. The purpose of this paper is to fill in the gap between the numerical results and the theoretical analysis.     

On hydraulic permeability of random packs of monodisperse spheres: Direct flow simulations versus correlations

Hydraulic permeability is studied in porous media consisting of randomly distributed monodisperse spheres by means of computational fluid dynamics (CFD) simulations. The packing of spheres is generated by inserting a certain number of nonoverlapping spherical particles inside a cubic box at both low and high packing fractions using proper algorithms. Fluid flow simulations are performed within the interparticulate porous space by solving Navier-Stokes equations in a low-Reynolds laminar flow regime. The hydraulic permeability is calculated from the Darcy equation once the mean values of velocity and pressure gradient are calculated across the particle packing. The simulation results for the pressure drop across the packing are verified by the Ergun equation for the lower range of porosities (<0.75), and the Stokes equation for higher porosities (∼1). Using the results of simulations, the effects of porosity and particle diameters on the hydraulic permeability are investigated. Simulations precisely specified the range of applicability of empirical or semi-empirical correlations for hydraulic permeability, namely the Carman-Kozeny, Rumpf-Gupte, and Howells-Hinch formulas. The number of spheres in the model is gradually decreased from 2000 to 20 to discover the finite-size effect of pores on the hydraulic permeability of spherical packing, which has not been clearly addressed in the literature. In addition, the scale dependence of hydraulic permeability is studied via simulations of the packing of spheres shrunk to lower scales. The results of this work not only reveal the validity range of the aforementioned correlations, but also show the finite-size effect of pores and the scale-independence of direct CFD simulations for hydraulic permeability.     

CFETR TF 线圈 VPI 充模数值模拟

真空压力浸渍(Vacuum Pressure Impregnation, VPI)是大型超导线圈绝缘制造的关键技术. 传统 VPI 工艺中的关键参数需要依靠长期积累的经验和不断的试验得到, 对于 TF(Toroidal Field) 线圈 VPI 工艺参数的获得需要投入更多的时间、人力和物力, 采用计算机模拟优化 VPI 工艺参数是一种有效节约成本的方法. 基于Darcy 定律对全尺寸的TF 线圈充模过程进行了数值模拟, 采用不同注胶方案, 优化注胶口数量, 获得最佳的 VPI 注胶口数量和位置. 优化后的 VPI 注胶参数极大地提高了注胶时间, 为CFETR TF 线圈绝缘制造提供理论依据.     

多孔介质中相互作用的Brinkman方程组与Darcy方程组解的收敛性

研究了在有界区域内多孔介质中相互作用的Brinkman流体方程组与Darcy流体方程组解的收敛性。假设在中,流体速度较慢满足Brinkman方程组,而在中,饱和流体满足Darcy方程组,借助温度的最大值以及其他界,构造了能量表达式,得到了满足该能量表达式的微分不等式和Brinkman-Darcy流体方程组的解对边界系数的收敛性结果。