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2016年 第37卷 第11期    刊出日期：2016-11-01

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论文

Simulation of incompressible multiphase flows with complex geometry using etching multiblock method

Haoran LIU, Kai MU, Hang DING

2016, 37(11):  1405-1418.  doi:10.1007/s10483-016-2101-8

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The incompressible two-phase flows are simulated using combination of an etching multiblock method and a diffuse interface (DI) model,particularly in the complex domain that can be decomposed into multiple rectangular subdomains.The etching multiblock method allows natural communications between the connected subdomains and the efficient parallel computation.The DI model can consider two-phase flows with a large density ratio,and simulate the flows with the moving contact line (MCL) when a geometric formulation of the MCL model is included.Therefore,combination of the etching method and the DI model has potential to deal with a variety of two-phase flows in industrial applications.The performance is examined through a series of numerical experiments.The convergence of the etching method is firstly tested by simulating single-phase flows past a square cylinder,and the method for the multiphase flow simulation is validated by investing drops dripping from a pore.The numerical results are compared with either those from other researchers or experimental data.Good agreement is achieved.The method is also used to investigate the impact of a droplet on a grooved substrate and droplet generation in flow focusing devices.



Continuous adjoint-based error estimation and its application to adaptive discontinuous Galerkin method

Huiqiang YUE, Tiegang LIU, V. SHAYDUROV

2016, 37(11):  1419-1430.  doi:10.1007/s10483-016-2102-6

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An adaptive mesh refinement algorithm based on a continuous adjoint approach is developed.Both the primal equation and the adjoint equation are approximated with the discontinuous Galerkin (DG) method.The proposed adaptive algorithm is used in compressible Euler equations.Numerical tests are made to show the superiority of the proposed adaptive algorithm.

Dissipative particle dynamics simulation of flow through periodic arrays of circular micropillar

Lüwen ZHOU, Yuqian ZHANG, Xiaolong DENG, Moubin LIU

2016, 37(11):  1431-1440.  doi:10.1007/s10483-016-2091-9

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Flow through arrays of micropillar embedded inside microfluidic chip systems is important for various microfluidic devices.It is critical to accurately predict the mass flow rate through pillar arrays based on the pillar design.This work presents a dissipative particle dynamics (DPD) model to simulate a problem of flow across periodic arrays of circular micropillar and investigates the permeability of two types of micropillar arrays.The flow fields including horizontal and vertical velocity fields,the number density field,and the streamline of the flow are analyzed.The predicted solid volumes by the presented DPD simulation of both types of arrays are quite close to the actual counterparts.These quantitative agreements show usefulness and effectiveness of the DPD model in simulating arrays of micropillar.By comparing two types of micropillar arrangement patterns,we find that the arrangement pattern of micropillar does not have significant influence on the permeability of the array.

A Newton multigrid method for steady-state shallow water equations with topography and dry areas

Kailiang WU, Huazhong TANG

2016, 37(11):  1441-1466.  doi:10.1007/s10483-016-2108-6

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A Newton multigrid method is developed for one-dimensional (1D) and twodimensional (2D) steady-state shallow water equations (SWEs) with topography and dry areas.The nonlinear system arising from the well-balanced finite volume discretization of the steady-state SWEs is solved by the Newton method as the outer iteration and a geometric multigrid method with the block symmetric Gauss-Seidel smoother as the inner iteration.The proposed Newton multigrid method makes use of the local residual to regularize the Jacobian matrix of the Newton iteration,and can handle the steadystate problem with wet/dry transition.Several numerical experiments are conducted to demonstrate the efficiency,robustness,and well-balanced property of the proposed method.The relation between the convergence behavior of the Newton multigrid method and the distribution of the eigenvalues of the iteration matrix is detailedly discussed.

Numerical simulation based on two-directional freeze and thaw algorithm for thermal diffusion model

Junqiang GAO, Zhenghui XIE, Aiwen WANG, Zhendong LUO

2016, 37(11):  1467-1478.  doi:10.1007/s10483-016-2106-8

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Freeze-thaw processes significantly modulate hydraulic and thermal characteristics of soil.The changes in the frost and thaw fronts (FTFs) affect the water and energy cycles between the land surface and the atmosphere.Thus,the frozen soil comprising permafrost and seasonally frozen soil has important effects on the land surface hydrology in cold regions.In this study,a two-directional freeze and thaw algorithm is incorporated into a thermal diffusion equation for simulating FTFs.A local adaptive variable-grid method is used to discretize the model.Sensitivity tests demonstrate that the method is stable and FTFs can be tracked continuously.The FTFs and soil temperature at the Qinghai-Tibet Plateau D66 site are simulated hourly from September 1,1997 to September 22,1998.The results show that the incorporated model performs much better in the soil temperature simulation than the original thermal diffusion equation,showing potential applications of the method in land-surface process modeling.

Anisotropic adaptive finite element method for magnetohydrodynamic flow at high Hartmann numbers

Jikun ZHAO, Shipeng MAO, Weiying ZHENG

2016, 37(11):  1479-1500.  doi:10.1007/s10483-016-2107-9

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This paper presents an anisotropic adaptive finite element method (FEM) to solve the governing equations of steady magnetohydrodynamic (MHD) duct flow.A residual error estimator is presented for the standard FEM,and two-sided bounds on the error independent of the aspect ratio of meshes are provided.Based on the Zienkiewicz-Zhu estimates,a computable anisotropic error indicator and an implement anisotropic adaptive refinement for the MHD problem are derived at different values of the Hartmann number.The most distinguishing feature of the method is that the layer information from some directions is captured well such that the number of mesh vertices is dramatically reduced for a given level of accuracy.Thus,this approach is more suitable for approximating the layer problem at high Hartmann numbers.Numerical results show efficiency of the algorithm.

Improving microwave brightness temperature predictions based on Bayesian model averaging ensemble approach

Binghao JIA, Zhenghui XIE

2016, 37(11):  1501-1516.  doi:10.1007/s10483-016-2103-6

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The choices of the parameterizations for each component in a microwave emission model have significant effects on the quality of brightness temperature (Tb) simulation.How to reduce the uncertainty in the Tb simulation is investigated by adopting a statistical post-processing procedure with the Bayesian model averaging (BMA) ensemble approach.The simulations by the community microwave emission model (CMEM) coupled with the community land model version 4.5(CLM4.5) over mainland China are conducted by the 24 configurations from four vegetation opacity parameterizations (VOPs),three soil dielectric constant parameterizations (SDCPs),and two soil roughness parameterizations (SRPs).Compared with the simple arithmetical averaging (SAA) method,the BMA reconstructions have a higher spatial correlation coefficient (larger than 0.99) than the C-band satellite observations of the advanced microwave scanning radiometer on the Earth observing system (AMSR-E) at the vertical polarization.Moreover,the BMA product performs the best among the ensemble members for all vegetation classes,with a mean root-mean-square difference (RMSD) of 4 K and a temporal correlation coefficient of 0.64.

Harten-Lax-van Leer-contact (HLLC) approximation Riemann solver with elastic waves for one-dimensional elasticplastic problems

Junbo CHENG

2016, 37(11):  1517-1538.  doi:10.1007/s10483-016-2104-9

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A Harten-Lax-van Leer-contact (HLLC) approximate Riemann solver is built with elastic waves (HLLCE) for one-dimensional elastic-plastic flows with a hypoelastic constitutive model and the von Mises' yielding criterion.Based on the HLLCE,a third-order cell-centered Lagrangian scheme is built for one-dimensional elastic-plastic problems.A number of numerical experiments are carried out.The numerical results show that the proposed third-order scheme achieves the desired order of accuracy.The third-order scheme is used to the numerical solution of the problems with elastic shock waves and elastic rarefaction waves.The numerical results are compared with a reference solution and the results obtained by other authors.The comparison shows that the presented high-order scheme is convergent,stable,and essentially non-oscillatory.Moreover,the HLLCE is more efficient than the two-rarefaction Riemann solver with elastic waves (TRRSE).

Strain-stress relation in macromolecular microsphere composite hydrogel

Hui ZHANG

2016, 37(11):  1539-1550.  doi:10.1007/s10483-016-2110-9

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This paper investigates the strain-stress relation for the macromolecular microsphere composite (MMC) hydrogel.The novel point is to present the strain-stress model,which is based on the microscopic mixed entropy set up in the previous work and the Flory-Rehner elastic energy.Then,the numerical result of the strain-stress model is shown,which is completely consistent with the chemical experiment.Moreover,the theoretical relation of the strain-stress depends on the microscopic parameters of the MMC hydrogel.Therefore,it is a way to investigate the relation of macroscopic properties and microscopic structures of soft matters.This approach can be extended to other soft matters.

Entropy convergence of new two-value scheme with slope relaxation for conservation laws

Yue WANG, Jiequan LI

2016, 37(11):  1551-1570.  doi:10.1007/s10483-016-2109-8

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This paper establishes the entropy convergence of a new two-value high resolution finite volume scheme with slope relaxation for conservation laws.This scheme,motivated by the general method of high resolution schemes that have high-order accuracy in smooth regions of solutions and are free of oscillations near discontinuities,unifies and evolves slopes directly with a slope relaxation equation that governs the evolution of slopes in both smooth and discontinuous regions.Proper choices of slopes are realized adaptively via a relaxation parameter.The scheme is shown to be total-variation-bounded (TVB) stable and satisfies cell-entropy inequalities.

Comparisons of some difference forms for compressible flow in cylindrical geometry on arbitrary Lagrangian and Eulerian framework

Zhijun SHEN, Xiao LI, Jian REN

2016, 37(11):  1571-1586.  doi:10.1007/s10483-016-2105-8

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The study of cylindrically symmetric compressible fluid is interesting from both theoretical and numerical points of view.In this paper,the typical spherical symmetry properties of the numerical schemes are discussed,and an area weighted scheme is extended from a Lagrangian method to an arbitrary Lagrangian and Eulerian (ALE) method.Numerical results are presented to compare three discrete configurations,i.e.,the control volume scheme,the area weighted scheme,and the plane scheme with the addition of a geometrical source.The fact that the singularity arises from the geometrical source term in the plane scheme is illustrated.A suggestion for choosing the discrete formulation is given when the strong shock wave problems are simulated.