一种基于多矩的有限体积浸入边界法

基于多矩VSIAM3格式及浸入边界法,提出一套在复杂计算区域内求解不可压缩流动的数值格式.不可压N-S方程使用VSIAM3格式进行离散,引入浸入边界法处理复杂、移动边界,使用虚拟网格方法计算动量方程修正项,同时还考虑了对连续方程的修正.使用标准算例对数值模式进行验证.     

Sound propagation in street canyons: comparison between diffusely and geometrically reflecting boundaries

This paper systematically compares the sound fields in street canyons with diffusely and geometrically reflecting boundaries. For diffuse boundaries, a radiosity-based theoretical/computer model has been developed. For geometrical boundaries, the image source method has been used. Computations using the models show that there are considerable differences between the sound fields resulting from the two kinds of boundaries. By replacing diffuse boundaries with geometrical boundaries, the sound attenuation along the length becomes significantly less; the RT30 is considerably longer; and the extra attenuation caused by air or vegetation absorption is reduced. There are also some similarities between the sound fields under the two boundary conditions. For example, in both cases the sound attenuation along the length with a given amount of absorption is the highest if the absorbers are arranged on one boundary and the lowest if they are evenly distributed on all boundaries. Overall, the results suggest that, from the viewpoint of urban noise reduction, it is better to design the street boundaries as diffusely reflective rather than acoustically smooth.     

非结构网格的并行生成

研究了非结构网格的并行生成方法.改进了R.Lohner的"波阵面"区域分裂算法以使子网格及其边界更有益于网格并行生成,提出了边界并行优化策略,改善了边界的光滑性;完善了子区域内生成网格时接受新点及新单元的条件,在界面网格生成过程中提出只接受新单元而拒绝新点的策略,节省了机时.     

Effect of reflecting modes on combined heat transfer within an anisotropic scattering slab

Under various interface reflecting modes, different transient thermal responses will occur in the media. Combined radiative-conductive heat transfer is investigated within a participating, anisotropic scattering gray planar slab. The two interfaces of the slab are considered to be diffuse and semitransparent. Using the ray tracing method, an anisotropic scattering radiative transfer model for diffuse reflection at boundaries is set up, and with the help of direct radiative transfer coefficients, corresponding radiative transfer coefficients (RTCs) are deduced. RTCs are used to calculate the radiative source term in energy equation. Transient energy equation is solved by the full implicit control-volume method under the external radiative-convective boundary conditions. The influences of two reflecting modes including both specular reflection and diffuse reflection on transient temperature fields and steady heat flux are examined. According to numerical results obtained in this paper, it is found that there exits great difference in thermal behavior between slabs with diffuse interfaces and that with specular interfaces for slabs with big refractive index.     

Influence of boundary conditions on the ordering of elastic dipoles

We consider elastic dipoles in several two-dimensional geometries. Using Cauchy integral techniques and the image method, the state of elastic equilibrium under different boundary conditions can be determined. The results are used to find the ground state of systems of anisotropic dipoles via the simulated annealing method. Only in the case of fixed boundaries the ordering depends on the boundary condition.     

γ-α相变中不同晶界特征下铁素体生长形貌的相场模拟

利用多相场模型模拟了奥氏体(γ)-铁素体(α)相变过程中不同晶界特征下铁素体晶粒的形貌与生长动力学.模型中通过能量梯度系数和耦合项系数的协同变化定量表达晶界能与晶界迁移率的各向异性,同时固定相场界面宽度来保证计算精度.模拟结果显示:随着原奥氏体晶界能与铁素体-奥氏体晶界能比值σ_(γ,γ)/σ_(α,γ)的增加,三叉相界面处的平衡角β减小,铁素体晶粒沿原奥氏体晶界与垂直于奥氏体晶界方向的生长速率差变大.铁素体与奥氏体晶粒间的晶粒取向越接近,铁素体生长越缓慢.模拟结果可描述铁素体晶粒生长形貌的多样性,与实验结果符合.     

A Cartesian grid embedded boundary method for solving the Poisson and heat equations with discontinuous coefficients in three dimensions

We present a method for solving Poisson and heat equations with discontinuous coefficients in two- and three-dimensions. It uses a Cartesian cut-cell/embedded boundary method to represent the interface between materials, as described in Johansen and Colella (1998). Matching conditions across the interface are enforced using an approximation to fluxes at the boundary. Overall second order accuracy is achieved, as indicated by an array of tests using non-trivial interface geometries. Both the elliptic and heat solvers are shown to remain stable and efficient for material coefficient contrasts up to 10⁶, thanks in part to the use of geometric multigrid. A test of accuracy when adaptive mesh refinement capabilities are utilized is also performed. An example problem relevant to nuclear reactor core simulation is presented, demonstrating the ability of the method to solve problems with realistic physical parameters.     

Numerical modeling of the sound fields in urban squares

This paper studies the basic characteristics of sound fields in urban squares surrounded by reflecting building fa?ades and the effectiveness of architectural changes and urban design options. A radiosity model and an image source model are developed, and a parametric study is carried out in hypothetical squares. The results show that the reverberation time (RT) is rather even in a square, whereas the early decay time (EDT) is very low in the near field, and then becomes close to RT after a rapid increase. Compared to diffuse boundaries, with geometrical boundaries the RT and EDT are significantly longer and the sound pressure level (SPL) attenuation with distance is generally smaller unless the height/side ratio is high. With a boundary diffusion coefficient of 0.2, the sound field is already close to that resulting from purely diffusely reflecting boundaries. The SPL in far field is typically 6-9 dB lower if the square side is doubled; 8 dB lower if the height of building fa?ades is decreased from 50 m to 6 m (diffuse boundaries); 5 dB (diffuse boundaries) or 2 dB (geometrical boundaries) lower if the length/width ratio is increased from 1 to 4; and 10-12 dB lower if the boundary absorption coefficient is increased from 0.1 to 0.9.     

Relaxation of sound fields in rooms of diffusely reflecting boundaries and its application in acoustical radiosity simulation

The acoustical radiosity method is a computationally expensive acoustical simulation algorithm that assumes an enclosure with ideal diffuse reflecting boundaries. Miles observed that for such an enclosure, the sound energy decay of every point on the boundaries will gradually converge to exponential manner with a uniform decay rate. Therefore, the ratio of radiosity between every pair of points on the boundaries will converge to a constant, and the radiosity across the boundaries will approach a fixed distribution during the sound decay process, where radiosity is defined as the acoustic power per unit area leaving (or being received by) a point on a boundary. We call this phenomenon the "relaxation" of the sound field. In this paper, we study the relaxation in rooms of different shapes with different boundary absorptions. Criteria based on the relaxation of the sound field are proposed to terminate the costly and unnecessary radiosity computation in the later phase, which can then be replaced by a fast regression step to speed up the acoustical radiosity simulation.     

Fourier spectral embedded boundary solution of the Poisson’s and Laplace equations with Dirichlet boundary conditions

A Fourier spectral embedded boundary method, for solution of the Poisson’s equation with Dirichlet boundary conditions and arbitrary forcing functions (including zero forcing function), is presented in this paper. This iterative method begins by transformation of the Dirichlet boundary conditions from the physical boundaries to some corresponding regular grid points (which are called the numerical boundaries), using a second order interpolation method. Then the transformed boundary conditions and the forcing function are extended to a square, smoothly and periodically, via multiplying them by some suitable error functions. Instead of direct solution of the resulting extended Poisson’s problem, it is suggested to define and solve an equivalent transient diffusion problem on the regular domain, until achievement of the steady solution (which is considered as the solution of the original problem). Without need of any numerical time integration method, time advancement of the solution is obtained directly, from the exact solution of the transient problem in the Fourier space. Consequently, timestep sizes can be chosen without stability limitations, which it means higher rates of convergence in comparison with the classical relaxation methods. The method is presented in details for one- and two-dimensional problems, and a new emerged phenomenon (which is called the saturation state) is illustrated both in the physical and spectral spaces. The numerical experiments have been performed on the one- and two-dimensional irregular domains to show the accuracy of the method and its superiority (from the rate of convergence viewpoint) to the other classical relaxation methods. Capability of the method, in dealing with complex geometries, and in presence of discontinuity at the boundaries, has been shown via some numerical experiments on a four-leaf shape geometry.     

Observation of a superfluid He-3 A- B phase transition in silica aerogel

A lattice-Boltzmann method has been developed to incorporate solid-fluid boundary conditions on length scales less than the grid spacing. By introducing a continuous parameter, specified at each node and representing the fluid volume fraction associated with that node, we obtain second-order accuracy for boundaries at arbitrary positions and orientations with respect to the grid. The method does not require surface normals, and can therefore be applied to irregular geometries such as porous media. The new rules conserve mass and momentum, and reduce to the link bounce-back rule at aligned interfaces.     

An efficient and stable spectral method for electromagnetic scattering from a layered periodic structure

The scattering of acoustic and electromagnetic waves by periodic structures plays an important role in a wide range of problems of scientific and technological interest. This contribution focuses upon the stable and high-order numerical simulation of the interaction of time-harmonic electromagnetic waves incident upon a periodic doubly layered dielectric media with sharp, irregular interface. We describe a boundary perturbation method for this problem which avoids not only the need for specialized quadrature rules but also the dense linear systems characteristic of boundary integral/element methods. Additionally, it is a provably stable algorithm as opposed to other boundary perturbation approaches such as Bruno and Reitich’s “method of field expansions” or Milder’s “method of operator expansions”. Our spectrally accurate approach is a natural extension of the “method of transformed field expansions” originally described by Nicholls and Reitich (and later refined to other geometries by the authors) in the single-layer case.     

Simulation of surface tension in 2D and 3D with smoothed particle hydrodynamics method

The methods for simulating surface tension with smoothed particle hydrodynamics (SPH) method in two dimensions and three dimensions are developed. In 2D surface tension model, the SPH particle on the boundary in 2D is detected dynamically according to the algorithm developed by Dilts [G.A. Dilts, Moving least-squares particle hydrodynamics II: conservation and boundaries, International Journal for Numerical Methods in Engineering 48 (2000) 1503–1524]. The boundary curve in 2D is reconstructed locally with Lagrangian interpolation polynomial. In 3D surface tension model, the SPH particle on the boundary in 3D is detected dynamically according to the algorithm developed by Haque and Dilts [A. Haque, G.A. Dilts, Three-dimensional boundary detection for particle methods, Journal of Computational Physics 226 (2007) 1710–1730]. The boundary surface in 3D is reconstructed locally with moving least squares (MLS) method. By transforming the coordinate system, it is guaranteed that the interface function is one-valued in the local coordinate system. The normal vector and curvature of the boundary surface are calculated according to the reconstructed boundary surface and then surface tension force can be calculated. Surface tension force acts only on the boundary particle. Density correction is applied to the boundary particle in order to remove the boundary inconsistency. The surface tension models in 2D and 3D have been applied to benchmark tests for surface tension. The ability of the current method applying to the simulation of surface tension in 2D and 3D is proved.     

A high order moving boundary treatment for compressible inviscid flows

We develop a high order numerical boundary condition for compressible inviscid flows involving complex moving geometries. It is based on finite difference methods on fixed Cartesian meshes which pose a challenge that the moving boundaries intersect the grid lines in an arbitrary fashion. Our method is an extension of the so-called inverse Lax–Wendroff procedure proposed in [17] for conservation laws in static geometries. This procedure helps us obtain normal spatial derivatives at inflow boundaries from Lagrangian time derivatives and tangential derivatives by repeated use of the Euler equations. Together with high order extrapolation at outflow boundaries, we can impose accurate values of ghost points near the boundaries by a Taylor expansion. To maintain high order accuracy in time, we need some special time matching technique at the two intermediate Runge–Kutta stages. Numerical examples in one and two dimensions show that our boundary treatment is high order accurate for problems with smooth solutions. Our method also performs well for problems involving interactions between shocks and moving rigid bodies.     

Boundary element method for bandgap computation of photonic crystals

A boundary element method for computing bandgap structures of two-dimensional photonic crystals is developed. For photonic crystals composed of a square or triangular lattice of parallel cylinders with arbitrarily shaped cross-sections, the boundary integral equations are formulated for a unit cell. Constant boundary elements are adopted to discretize the boundaries. Applying the periodic boundary conditions and the interface conditions, we obtain a linear eigenvalue equation with relatively small matrices. The solution of the eigenvalue equation yields the Bloch wave vectors for given frequencies. The convergence of the method for the desired accuracy and efficiency is examined by some typical numerical examples. It is shown that the present method is efficient and accurate and thus provides a flexible treatment of electromagnetic waves in periodic structures with inclusions of arbitrary shape.     

An Eulerian method for multi-component problems in non-linear elasticity with sliding interfaces

This paper is devoted to developing a multi-material numerical scheme for non-linear elastic solids, with emphasis on the inclusion of interfacial boundary conditions. In particular for colliding solid objects it is desirable to allow large deformations and relative slide, whilst employing fixed grids and maintaining sharp interfaces. Existing schemes utilising interface tracking methods such as volume-of-fluid typically introduce erroneous transport of tangential momentum across material boundaries. Aside from combatting these difficulties one can also make improvements in a numerical scheme for multiple compressible solids by utilising governing models that facilitate application of high-order shock capturing methods developed for hydrodynamics. A numerical scheme that simultaneously allows for sliding boundaries and utilises such high-order shock capturing methods has not yet been demonstrated. A scheme is proposed here that directly addresses these challenges by extending a ghost cell method for gas-dynamics to solid mechanics, by using a first-order model for elastic materials in conservative form. Interface interactions are captured using the solution of a multi-material Riemann problem which is derived in detail. Several different boundary conditions are considered including solid/solid and solid/vacuum contact problems. Interfaces are tracked using level-set functions. The underlying single material numerical method includes a characteristic based Riemann solver and high-order WENO reconstruction. Numerical solutions of example multi-material problems are provided in comparison to exact solutions for the one-dimensional augmented system, and for a two-dimensional friction experiment.     

Pomraning-Eddington approximation for radiative transfer in a spherical turbid medium

Abstract

The Pomraning-Eddington approximation is used to solve the radiative transfer problem for anisotropic scattering in a spherical homogeneous turbid medium with diffuse and specular reflecting boundaries. This approximation replaces the radiative transfer integro-differential equation by a second-order differential equation which has an analytical solution in terms of the modified Bessel function. Here, we calculate the partial heat flux at the boundary of anisotropic scattering on a homogeneous solid sphere. The calculations are carried out for spherical media of radii 0.1, 1.0 and 10 mfp and for scattering albedos between 0.1 and 1.0. In addition, the calculations are given for media with transparent, diffuse reflecting and diffuse and specular reflecting boundaries. Two different weight functions are used to verify the boundary conditions. Our results are compared with those given by the Galerkin technique and show greater accuracy for thick and highly scattering media.     

Pomraning-Eddington approximation for radiative transfer in a spherical turbid medium

The Pomraning-Eddington approximation is used to solve the radiative transfer problem for anisotropic scattering in a spherical homogeneous turbid medium with diffuse and specular reflecting boundaries. This approximation replaces the radiative transfer integro-differential equation by a second-order differential equation which has an analytical solution in terms of the modified Bessel function. Here, we calculate the partial heat flux at the boundary of anisotropic scattering on a homogeneous solid sphere. The calculations are carried out for spherical media of radii 0.1, 1.0 and 10 mfp and for scattering albedos between 0.1 and 1.0. In addition, the calculations are given for media with transparent, diffuse reflecting and diffuse and specular reflecting boundaries. Two different weight functions are used to verify the boundary conditions. Our results are compared with those given by the Galerkin technique and show greater accuracy for thick and highly scattering media.     

Triple-decker: Interfacing atomistic–mesoscopic–continuum flow regimes

Multiscale flow phenomena in microfluidic and biomedical applications require the use of heterogeneous modeling approaches. In this paper we present a hybrid method based on coupling the Molecular Dynamics (MD) method, the Dissipative Particle Dynamics (DPD) method, and the incompressible Navier–Stokes (NS) equations. MD, DPD, and NS are formulated in separate subdomains and are coupled via an overlapping region by communicating state information at the subdomain boundaries. Imposition of boundary conditions in the MD and DPD systems involves particle insertion and deletion, specular wall reflection and body force terms. The latter includes a boundary pressure force in order to minimize near-boundary density fluctuations, and an adaptive shear force which enforces the tangential velocity component of boundary conditions. The triple-decker algorithm is verified for prototype flows, including simple and multi-layer fluids (Couette, Poiseuille, and lid-driven cavity), using highly accurate reference solutions. A zero-thickness interface is also possible if it is aligned with the flow streamlines.