Effects of element order and interface reconstruction in FEM/volume‐of‐fluid incompressible flow simulation

In previous studies, the moment‐of‐fluid interface reconstruction method showed dramatic accuracy improvements in static and pure advection tests over existing methods, but this did not translate into an equivalent improvement in volume‐tracked multimaterial incompressible flow simulation using low‐order finite elements. In this work, the combined effects of the spatial discretization and interface reconstruction in flow simulation are examined. The mixed finite element pairs, Q₁Q₀ (with pressure stabilization) and Q₂P _{? 1} are compared. Material order‐dependent and material order‐independent first and second‐order accurate interface reconstruction methods are used. The Q₂P _{? 1} elements show significant improvements in computed flow solution accuracy for single material flows but show reduced convergence using element‐average piecewise constant density and viscosity in volume‐tracked simulations. In general, a refined Q₁Q₀ grid, with better material interface resolution, provided an accuracy similar to the Q₂P _{? 1} element grid with a comparable number of degrees of freedom. Moment‐of‐fluid shows more benefit from the higher‐order accurate flow simulation than the LVIRA, Youngs', and power diagram interface reconstruction methods, especially on unstructured grids, but does not recover the dramatic accuracy improvements it has shown in advection tests. Published 2012. This article is a US Government work and is in the public domain in the USA.     

Numerical investigation of natural convection heat transfer of nanofluids in a Γ shaped cavity

This paper analyzes the heat transfer and fluid flow of natural convection in a Γ shaped enclosure filled with Al₂O₃/Water nanofluid that operates under differentially heated walls. The Navier–Stokes and energy equations are solved numerically. Heat transfer and fluid flow are examined for parameters of non-uniform nanoparticle size, mean nanoparticle diameter, nanoparticle volume fraction, Grashof number and different geometry of enclosure. Finite volume method is used for discretizating positional expressions, and the forth order Rung-Kuta is used for discretizating time expressions. Also an artificial compressibility technique was applied to couple continuity to momentum equations. Results indicate that using nanofluid causes an increase in the heat transfer and the Nusselt number so that for R = 0.001 in Gr = 10³, the Nusselt number 25%, in Gr = 10⁴ 26%, and in Gr = 10⁵ 28% increases. Furthermore; by decreasing the mean diameters of nanoparticles, Nusselt number increases. By increasing R parameter (d_p,min/d_p,max) and nano particle volume fraction, Nusselt number increases.     

数值模拟二维高速碰撞问题的拉格朗日任意三角形网格有限体积法

描述了一个数值模拟二维高速碰撞问题的拉格朗日任意三角形网格有限体积法,方法考虑了材料的弹性和塑性性质。文中给出两个计算例题。     

DFT Study on Some Properties of Polybrominated Phenoxathiin 10-Oxides

With the B3LYP calculation method of density functional theory(DFT)and the 6-31G* basis set,full optimization calculation was made for phenoxathiin10-oxide(PTO)and 135 polybromine phenoxathiin 10-oxides(PBPTOs)with the Gaussian 03 program and molar heat capacity in constant volume(CVθ)value of each molecule in the standard state was obtained.The relation between CVθ and the substitution position and number of bromine atom(NPBS)was studied,and the results indicated good correlation(R2 = 1.000)between CVθ and NPBS of PBPTO compounds.Based on the output file of Gaussian 03 program,molar heat capacity at constant pressure(Cp,m)of PBPTO compounds from 200 to 1,000 K was calculated with the statistical thermodynamics program,and the correlation equation between Cp,m and temperature(T,T-1 and T-2)was obtained with the least-squares method,and the correlation coefficient of the correlation equation(R2)was 1.000.In addition,based on the partition function of each molecule calculated by vibration analysis,the relative rate constant of formation of each molecule was calculated.     

On the discretization of gradient and curl in atmospheric models using height‐based terrain‐following coordinates

Different discretizations of the gradient and curl operators are considered for a staggered grid in a height‐based terrain‐following coordinate system. A combination of discrete operators is identified that guarantees the mimetic property that the curl of the gradient of any scalar vanishes identically. The result is illustrated with some numerical examples. Copyright © 2010 John Wiley & Sons, Ltd.     

Mobile and immobile fluid transport: Coupling framework

We introduce a solver method for mobile and immobile transport regions. The motivation is driven by transport processes in porous media (e.g. waste disposal, chemical deposition processes). We analyze the coupled transport‐reaction equation with mobile and immobile areas. We apply analytical methods, such as Laplace‐transformation, and for the numerical methods we apply Godunov's scheme, see (Mat. Sb. 1959; 47 :271–306; Finite Volume Methods for Hyperbolic Problems. Cambridge University Press: Cambridge, 2002). The method is based numerically on flux‐based characteristic methods and is an attractive alternative to the classical higher‐order TVD methods, see (J. Comput. Phys. 1993; 49 :357–393). In this paper, we will focus on the derivation of analytical solutions for general and special solutions of the characteristic methods that are embedded in a finite‐volume method. At the end of the paper, we illustrate the higher‐order method for different benchmark problems. Copyright © 2010 John Wiley & Sons, Ltd.     

An accurate and efficient semi‐implicit method for section‐averaged free‐surface flow modelling

An accurate, efficient and robust numerical method for the solution of the section‐averaged De St. Venant equations of open channel flow is presented and discussed. The method consists in a semi‐implicit, finite‐volume discretization of the continuity equation capable to deal with arbitrary cross‐section geometry and in a semi‐implicit, finite‐difference discretization of the momentum equation. By using a proper semi‐Lagrangian discretization of the momentum equation, a highly efficient scheme that is particularly suitable for subcritical regimes is derived. Accurate solutions are obtained in all regimes, except in presence of strong unsteady shocks as in dam‐break cases. By using a suitable upwind, Eulerian discretization of the same equation, instead, a scheme capable of describing accurately also unsteady shocks can be obtained, although this scheme requires to comply with a more restrictive stability condition. The formulation of the two approaches allows a unified implementation and an easy switch between the two. The code is verified in a wide range of idealized test cases, highlighting its accuracy and efficiency characteristics, especially for long time range simulations of subcritical river flow. Finally, a model validation on field data is presented, concerning simulations of a flooding event of the Adige river. Copyright © 2009 John Wiley & Sons, Ltd.     

Explicit characteristic‐based finite volume element method for level set equation

Accurate modeling of interfacial flows requires a realistic representation of interface topology. To reduce the computational effort from the complexity of the interface topological changes, the level set method is widely used for solving two‐phase flow problems. This paper presents an explicit characteristic‐based finite volume element method for solving the two‐dimensional level set equation. The method is applicable for the case of non‐divergence‐free velocity field. Accuracy and performance of the proposed method are evaluated via test cases with prescribed velocity fields on structured grids. By given a velocity field, the motion of interface in the normal direction and the mean curvature, examples are presented to demonstrate the performance of the proposed method for calculating interface evolutions in time. Copyright © 2010 John Wiley & Sons, Ltd.     

A high-order finite volume method for systems of conservation laws—Multi-dimensional Optimal Order Detection (MOOD)

In this paper, we investigate an original way to deal with the problems generated by the limitation process of high-order finite volume methods based on polynomial reconstructions. Multi-dimensional Optimal Order Detection (MOOD) breaks away from classical limitations employed in high-order methods. The proposed method consists of detecting problematic situations after each time update of the solution and of reducing the local polynomial degree before recomputing the solution. As multi-dimensional MUSCL methods, the concept is simple and independent of mesh structure. Moreover MOOD is able to take physical constraints such as density and pressure positivity into account through an “a posteriori” detection. Numerical results on classical and demanding test cases for advection and Euler system are presented on quadrangular meshes to support the promising potential of this approach.