Integrated numerical model for vegetated surface and saturated subsurface flow interaction

The construction of an integrated numerical model is presented in this paper to deal with the interactions between vegetated surface and saturated subsurface flows. A numerical model is built by integrating the previously developed quasi-three-dimensional (Q3D) vegetated surface flow model with a two-dimensional (2D) saturated groundwater flow model. The vegetated surface flow model is constructed by coupling the explicit finite volume solution of 2D shallow water equations (SWEs) with the implicit finite difference solution of Navier-Stokes equations (NSEs) for vertical velocity distribution. The subsurface model is based on the explicit finite volume solution of 2D saturated groundwater flow equations (SGFEs). The ground and vegetated surface water interaction is achieved by introducing source-sink terms into the continuity equations. Two solutions are tightly coupled in a single code. The integrated model is applied to four test cases, and the results are satisfactory.     

SOLUTION OF MULTIPLE CRACKS IN A FINITE PLATE OF AN ELASTIC ISOTROPIC MATERIAL WITH THE DISTRIBUTED DISLOCATION METHOD

This paper presents a numerical solution to model multiple cracks in a finite plate of an elastic isotropic material. Both the boundaries and the cracks are modeled by distributed dislocations. This method results in a system of singular integral equations with Cauchy kernels which can be solved by Gauss-Chebyshev quadrature method. Four examples are provided to assess the capability of this method.     

A new model for dissipative particle dynamics boundary condition of walls with different wettabilities

The implementation of solid-fluid boundary condition has been a major challenge for dissipative particle dynamics(DPD)method.Current implementations of boundary conditions usually try to approach a uniform density distribution and a velocity profile close to analytical solution.The density oscillations and slip velocity are intentionally eliminated,and different wall properties disappear in the same analytical solution.This paper develops a new wall model that combines image and frozen particles and a new strategy to emphasize different wall properties especially wettabilities.The strategy first studies the realistic wall-fluid system by molecular dynamics(MD)simulation depending on physical parameters.Then,a DPD simulation is used to match the density and velocity profiles with the new wall model.The obtained DPD parameters can simulate the systems with the same wall and fluid materials.With this method,a simulation of the Poiseuille flow of liquid argon with copper walls is presented.Other walls with super-hydrophilic,hydrophilic,and hydrophobic wettabilities are also simulated.The limitations of the analytical solution and the effect of the wall-fluid interaction are discussed.The results show that the method suggested in this paper can simulate the mesoscale behavior of the microchannel flow related to realistic systems.     

VIBRATION ANALYSIS OF A ROD WITH COMPLEX BOUNDARY CONDITIONS

This paper deals with the forced longitudinal vibration ora rod carrying a concentrated mass and supported by a spring at one end. The vibration of the rod is excited by the motion of the support point at the other end Since the boundary conditions of the problem are complex and it is necessary to consider the damping, we determine only the steady state periodic solution. First the linear system is analysed, then the material nonlinearity is considered and the approximate analytic solution of nonlinear partial differential equation with nonlinear boundary conditions is obtained by the perturbation method.     

THEORETIC SOLUTION OF RECTANGULAR THIN PLATE ON FOUNDATION WITH FOUR EDGES FREE BY SYMPLECTIC GEOMETRY METHOD

The theoretic solution for rectangular thin plate on foundation with four edges free is derived by symplectic geometry method. In the analysis proceeding, the elastic foundation is presented by the Winkler model. Firstly, the basic equations for elastic thin plate are transferred into Hamilton canonical equations. The symplectic geometry method is used to separate the whole variables and eigenvalues are obtained simultaneously. Finally, according to the method of eigen function expansion, the explicit solution for rectangular thin plate on foundation with the boundary conditions of four edges frees are developed. Since the basic elasticity equations of thin plate are only used and it is not need to select the deformation function arbitrarily. Therefore, the solution is theoretical and reasonable. In order to show the correction of formulations derived, a numerical example is given to demonstrate the accuracy and convergence of the current solution.     

Attractive fixed-point solution study of shell model for homogeneous isotropic turbulence

The attractive fixed-point solution of a nonlinear cascade model is studied for the homogeneous isotropic turbulence containing a parameter C, introduced by Desnyansky and Novikov. With a traditional constant positive external force added on the first shell equation, it can be found that the attractive fixed-point solution of the model depends on both the parameter C and the external force. Thus, an explicit force is introduced to remove the effects of the external force on the attractive fixed-point solution. Furthermore, two groups of attractive fixed-point solutions are derived theoretically and studied numerically. One of the groups has the same scaling behavior of the velocity in the whole inertial range and agrees well with those observed by Bell and Nelkin for the nonnegative parameters. The other is found to have different scaling behaviors of the velocity at the odd and even number shells for the negative parameters. This special characteristic may be used to study the anomalous scaling behavior of the turbulence.     

Thermomagnetic viscoelastic responses in a functionally graded hollow structure

This paper presents an analytical solution for the interaction of electric potentials,electric displacements,elastic deformations,and thermoelasticity,and describes electromagnetoelastic responses and perturbation of the magnetic field vector in hollow structures(cylinder or sphere),subjected to mechanical load and electric potential.The material properties,thermal expansion coefficient and magnetic permeability of the structure are assumed to be graded in the radial direction by a power law distribution.In the present model we consider the solution for the case of a hollow structure made of viscoelastic isotropic material,reinforced by elastic isotropic fibers,this material is considered as structurally anisotropic material.The exact solutions for stresses and perturbations of the magnetic field vector in FGM hollow structures are determined using the infinitesimal theory of magnetothermoelasticity,and then the hollow structure model with viscoelastic material is solved using the correspondence principle and Illyushin’s approximation method.Finally,numerical results are carried out and discussed.     

Diffraction of elastic waves in the plane multiply-connected region and dynamic stress concentration

This paper deals with the problem of diffraction of elastic waves in the plane multiply-connected regions by the theory of complex functions. The complete function series which approach the solution of the problem and general expressions for boundary conditions are given.’ Then the problem is reduced to the solution to infinite series of algebraic equations and the solution can be directly obtained by using electronic computer. In particular, for the case of weak interaction, an asymptotic method is presented here, by which the problem ofp waves diffracted by a circular cavities is discussed in detail. Based on the solution of the diffracted wave field the general formulas for calculating dynamic stress concentration factor for a cavity of arbitrary shape in multiply-connected region are given.     

A numerical approach for pressure transient analysis of a vertical well with complex fractures

A new well test model for a vertical fractured well is developed based on a discrete-fracture model in which the fractures are discretized as one dimensional (1-D) entities. The model overcomes the weakness of complex meshing, a large number of grids, and instability in conventional stripe-fracture models. Then, the discrete-fracture model is implemented using a hybrid element finite-element method. Triangular elements are used for matrix and line elements for the fractures. The finite element formulation is validated by comparing with the semi-analytical solution of a single ver-tical fractured well. The accuracy of the approach is shown through several examples with different fracture apertures, fracture conductivity, and fracture amount. Results from the discrete-fracture model agree reasonably well with the stripe-fracture model and the analytic solutions. The advantages of the discrete-fracture model are presented in mesh gen-eration, computational improvement, and abilities to handle complex fractures like wedge-shaped fractures and fractures with branches. Analytical results show that the number of grids in the discrete-fracture model is 10%less than stripe-fracture model, and computational efficiency increases by about 50%. The more fractures there are, the more the com-putational efficiency increases.     

Computational model for short-fiber composites with eigenstrain formulation of boundary integral equations

A computational model is proposed for short-fiber reinforced materials with the eigenstrain formulation of the boundary integral equations （BIE） and solved with the newly developed boundary point method （BPM）. The model is closely derived from the concept of the equivalent inclusion Of Eshelby tensors. Eigenstrains are iteratively determined for each short-fiber embedded in the matrix with various properties via the Eshelby tensors, which can be readily obtained beforehand either through analytical or numerical means. As unknown variables appear only on the boundary of the solution domain, the solution scale of the inhomogeneity problem with the model is greatly reduced. This feature is considered significant because such a traditionally time-consuming problem with inhomogeneity can be solved most cost-effectively compared with existing numerical models of the FEM or the BEM. The numerical examples are presented to compute the overall elastic properties for various short-fiber reinforced composites over a representative volume element （RVE）, showing the validity and the effectiveness of the proposed computational modal and the solution procedure.     

Heat transfer in vertical annular laminar flow of two immiscible liquids

The paper investigates heat transfer in annular laminar undisturbed flow of two immiscible liquids, with constant heat-flux generated at the wall of the tube. It presents an analytical solution for the fully developed temperature field. This is used to obtain a more general solution from a model, describing the temperature field as a superposition of the fully developed and the developing fields. This superposition model is solved by an orthogonal collocation method. An asymptotic model for short entry lengths is also described. Calculations for a kerosene-water system, show that the superposition solution converges to the entrance solution below 100 diameters and converges asymptotically to the solution of the fully developed temperature field beyond 5000 diameters. The effect of the wavy interface is assessed experimentally for annular kerosene-water flow, by comparing predicted and measured temperature profiles. It is found that experimental profiles are considerably flatter and measured Nusselt numbers for the kerosene phase are accordingly higher by 40–320% as compared to the undisturbed flow analyses.     

Two Nonlinear Models of Brittle Fracture for Solids

This paper considers isotropic and orthotropic nonlinear constitutive relations for brittle materials in the case of plane stresses. Numerical solution algorithms based on the finite-element method are developed. The resulting material models are incorporated in the PIONER software. The correctness of crack path determination is examined by solving a test problem of crack propagation. The isotropic model gives mesh-dependent results, whereas the orthotropic model provides an adequate solution. It is shown that solutions obtained for the isotropic model are close to those obtained by eliminating failed elements.     

On the need of mode interpolation for data-driven Galerkin models of a transient flow around a sphere

We present a low-dimensional Galerkin model with state-dependent modes capturing linear and nonlinear dynamics. Departure point is a direct numerical simulation of the three-dimensional incompressible flow around a sphere at Reynolds numbers 400. This solution starts near the unstable steady Navier–Stokes solution and converges to a periodic limit cycle. The investigated Galerkin models are based on the dynamic mode decomposition (DMD) and derive the dynamical system from first principles, the Navier–Stokes equations. A DMD model with training data from the initial linear transient fails to predict the limit cycle. Conversely, a model from limit-cycle data underpredicts the initial growth rate roughly by a factor 5. Key enablers for uniform accuracy throughout the transient are a continuous mode interpolation between both oscillatory fluctuations and the addition of a shift mode. This interpolated model is shown to capture both the transient growth of the oscillation and the limit cycle.     

Numerical calculation of Reynolds stresses in a square duct with secondary flow

A new model for the Reynolds stress equations is presented. This model is used to obtain a theoretical solution for the problem of fully developed turbulent flow in a square duct. Nine governing equations for the axial velocity, lateral vorticity, lateral stream function and six components of the Reynolds stresses are simultaneously solved, by a finite-difference technique. To ensure numerical stability of the solution a special linearised implicit representation of the source terms is proposed, and simultaneous solution of the equations at each.mesh point is obtained. Near the wall a special procedure is used, by which the Reynolds stress equations are assumed to be in local equilibrium, and the velocity profile is assumed to be logarithmic. However, due to the secondary motion the logarithmic velocity profile is inclined to the axial direction. The results bear reasonable agreement with experimental data. Computer time requirements are moderate.     

A mode split,Godunov‐type model for nonhydrostatic,free surface flow

A previously developed model for nonhydrostatic, free surface flow is redesigned to improve computational efficiency without sacrificing accuracy. Both models solve the Reynolds averaged Navier–Stokes equations in a fractional step manner with the pressure split into hydrostatic and nonhydrostatic components. The hydrostatic equations are first solved with an approximate Riemann solver. The hydrostatic solution is then corrected by including the nonhydrostatic pressure and requiring the velocity field to obey the incompressibility constraint. The original model requires the solution of a Riemann problem at every cell face for each vertical layer of cells, which is computationally expensive. The redesigned model instead solves the shallow water (long wave) equations for the hydrostatic solution. Vertical shear is computed by subtracting the shallow water equations from the full three dimensional equations, which removes the hydrostatic thrust terms. Therefore, the required fluxes may be more efficiently computed with velocity based upwind differencing rather than solving a Riemann problem in each vertical layer of cells. This approach is termed mode splitting and has been used in hydrostatic coastal and ocean circulation models, but not surf zone models. Numerical predictions are compared with analytical solutions and experimental data to show that the mode split model is as accurate as the original model, but requires significantly less computational effort especially for large numbers of cell layers. Published 2014. This article is a U.S. Government work and is in the public domain in the USA.     

Exact expressions for transient forced internal gravity waves and spatially-localized wave packets in a Boussinesq fluid

We re-examine a simple model describing the propagation of transient forced internal gravity waves in a Boussinesq fluid with constant horizontal mean velocity which was previously studied by Nadon and Campbell (Wave Motion, 2007). The waves are generated by a horizontally-periodic lower boundary condition and propagate upwards. We derive an alternative exact expression for the solution which more readily gives insight into the behaviour of the solution at high altitude. Some special cases of lower boundary conditions are considered to illustrate the features of the solution. This form of the solution allows us to use a Fourier transform to derive the solution for the more general situation where a wave packet is generated by a horizontally-localized lower boundary condition, comprising a continuous spectrum of horizontal wavenumbers or Fourier modes. This is a more realistic representation of internal gravity waves in the atmosphere and can be used as a starting point for investigating waves generated by an obstacle of finite horizontal extent such as an isolated mountain or a mountain range.     

Convergence acceleration of continuous adjoint solvers using a reduced‐order model

A novel acceleration technique using a reduced‐order model is presented to speed up convergence of continuous adjoint solvers. The acceleration is achieved by projecting to an improved solution within an iterative process solely using early solution results. This is achieved by forming basis vectors from early iteration adjoint solutions to perform model order reduction of the adjoint equations. The reduced‐order model of the adjoint equations is then substituted into the full‐order discretized governing equations to determine weighting coefficients for each basis vector. With these coefficients, a linear combination of the basis vectors is used to project to an improved solution. The method is applied to 3 inviscid quasi‐1D nozzle flow cases including fully subsonic flow, subsonic inlet to supersonic outlet flow, and transonic flow with a shock. Significant cost reductions are achieved for a single application as well as repeated applications of the convergence acceleration technique.     

关于一类电-力振动模型的建模与分析

从电学、力学的基本原理出发,通过数学方法建立和分析了一种电-力振动模型。这是一种较复杂的电力混合作用的线性振动系统,由模型的特殊结构(类扬声器结构)作者确立了两种磁场,即感生磁场和外磁场两者正交独立,并规定了电学、力学两种不同物理量的坐标取向关系。该模型需要求得三阶正系数常微分方程的收敛解,再求得包含暂态、稳态项的完整解。另外,文章从能量和做功的角度,通过对电压电流间的相位差分析,对所建模型的正确性作了论证,同时也为这类建模引荐了一种论证手段。     

Prediction of oscillating thick cambered aerofoil aerodynamics by a locally analytic method

A complete first-order model and locally analytic solution method are developed to analyse the effects of mean flow incidence and aerofoil camber and thickness on the incompressible aerodynamics of an oscillating aerofoil. This method incorporates analytic solutions, with the discrete algebraic equations which represent the differential flow field equations obtained from analytic solutions in individual grid elements. The velocity potential is separated into steady and unsteady harmonic parts, with the unsteady potential further decomposed into circulatory and non-circulatory components. These velocity potentials are individually described by Laplace equations. The steady velocity potential is independent of the unsteady flow field. However, the unsteady flow is coupled to the steady flow field through the boundary conditions on the oscillating aerofoil. A body-fitted computational grid is then utilized. Solutions for both the steady and the coupled unsteady flow fields are obtained by a locally analytic numerical method in which locally analytic solutions in individual grid elements are determined. The complete flow field solution is obtained by assembling these locally analytic solutions. This model and solution method are shown to accurately predict the Theodorsen oscillating flat plate classical solution. Locally analytic solutions for a series of Joukowski aerofoils demonstrate the strong coupling between the aerofoil unsteady and steady flow fields, i.e. the strong dependence of the oscillating aerofoil aerodynamics on the steady flow effects of mean flow incidence angle and aerofoil camber and thickness.     

基于卷积非粘滞阻尼模型的超高层结构风效应分析

有限元方法中相对于对结构质量与刚度特性的描述,结构阻尼的描述仍具有较大的模糊性。随着新型建筑材料与复杂结构体系的发展,以及对计算机模拟要求的提高,阻尼作用的机理与相应阻尼模型的研究成为值得关注的问题。基于一种阻尼力与质点速度历程相关的卷积非粘滞阻尼模型,采用微分求积求解算法,对一个大型复杂超高层建筑结构的风振响应进行了分析,并与常用的比例粘滞阻尼模型进行了对比。对卷积非粘滞阻尼力模型系统的响应特征进行了分析,特别是该模型的松弛效应对结构响应的影响。另外,作为将这种新阻尼模型应用于实际工程的一次探索,本文采用微分求积算法,建立了一套可将该阻尼模型及其求解算法嵌入通用有限元软件的求解系统,可用于复杂结构的动力响应分析。