激光烧蚀瑞利－泰勒不稳定性模拟

 给出了激光烧蚀流体不稳定性计算程序EUL2D的物理方程,介绍了计算中使用的活动网格和一些技术问题处理。EUL2D程序的计算结果与Takabe公式、FAST2D程序和LASNEX程序的结果较好符合。数值计算日本大阪大学激光烧蚀瑞利－泰勒不稳定性实验,再现了实验结果。发现了横向电子热传导烧蚀在长波长扰动的非线性瑞利－泰勒不稳定性演变中起重要作用。     

A deterministic scheme for Smoluchowski's coagulation equation based on binary grid refinement

We present a deterministic scheme for the discrete Smoluchowski's coagulation equation based on a binary grid refinement. Starting from the binary grid Ω₀={1,2,4,8,16,. . .}, we first introduce an appropriate grid refinement by adding at each level 2^l grid points in every binary subsection of the grid Ω_l. In a next step we derive an approximate equation for the dynamic behavior on each level Ω_l based on a piecewise constant approximation of the right hand side of Smoluchowski's equation. Numerical results show that the computational effort can be drastically decreased compared to the corresponding complete integer grid. When considering unbounded kernels in Smoluchowski's equation we use an adaptive time step method to overcome numerical instabilities which may occur at the tails of the density function.     

Fast evaluation of trigonometric polynomials from hyperbolic crosses

The discrete Fourier transform in d dimensions with equispaced knots in space and frequency domain can be computed by the fast Fourier transform (FFT) in arithmetic operations. In order to circumvent the ‘curse of dimensionality’ in multivariate approximation, interpolations on sparse grids were introduced. In particular, for frequencies chosen from an hyperbolic cross and spatial knots on a sparse grid fast Fourier transforms that need only arithmetic operations were developed. Recently, the FFT was generalised to nonequispaced spatial knots by the so-called NFFT. In this paper, we propose an algorithm for the fast Fourier transform on hyperbolic cross points for nonequispaced spatial knots in two and three dimensions. We call this algorithm sparse NFFT (SNFFT). Our new algorithm is based on the NFFT and an appropriate partitioning of the hyperbolic cross. Numerical examples confirm our theoretical results.     

基于二重网格的动网格松弛法改进

相比传统的弹簧法等方法,基于球松弛算法的动网格松弛法在复杂边界大变形条件下可以得到质量更高的边界网格以及更大的极限变形量,但该方法在时间效率上还有提升的空间.引入二重网格,采用动网格松弛法进行稀疏网格的网格变形,将边界位移传递到整个网格计算域;再利用二重网格映射,将稀疏网格位移映射到原有计算网格的节点上.算例表明,改进...     

A first-order system approach for diffusion equation. II: Unification of advection and diffusion

In this paper, we unify advection and diffusion into a single hyperbolic system by extending the first-order system approach introduced for the diffusion equation [J. Comput. Phys., 227 (2007) 315–352] to the advection–diffusion equation. Specifically, we construct a unified hyperbolic advection–diffusion system by expressing the diffusion term as a first-order hyperbolic system and simply adding the advection term to it. Naturally then, we develop upwind schemes for this entire   system; there is thus no need to develop two different schemes, i.e., advection and diffusion schemes. We show that numerical schemes constructed in this way can be automatically uniformly accurate, allow O(h)$O(h)$ time step, and compute the solution gradients (viscous stresses/heat fluxes for the Navier–Stokes equations) simultaneously to the same order of accuracy as the main variable, for all Reynolds numbers. We present numerical results for boundary-layer type problems on non-uniform grids in one dimension and irregular triangular grids in two dimensions to demonstrate various remarkable advantages of the proposed approach. In particular, we show that the schemes solving the first-order advection–diffusion system give a tremendous speed-up in CPU time over traditional scalar schemes despite the additional cost of carrying extra variables and solving equations for them. We conclude the paper with discussions on further developments to come.     

A study of properties of adaptive quadratic grids for three-dimensional near-surface field computations

Curved geometries and the corresponding near-surface fields typically require a large number of linear computational elements. High-order numerical solvers have been primarily used with low-order meshes. There is a need for curved, high-order computational elements. Typical near-surface meshes consist of hexahedral and/or prismatic elements. The present work studies the employment of quadratic meshes that are relatively coarse for field simulations. Directionally quadratic high-order elements are proposed for the near-surface field regions. The quadratic meshes are compared with the conventional low-order ones in terms of accuracy and efficiency. The cases considered include closed surface volume calculations, as well as computation of gradients of several analytic fields. A special method of adaptive local quadratic meshes is proposed and evaluated. Truncation error analysis for quadratic grids yields comparison with the conventional linear hexahedral/prismatic meshes, which are subject to typical distortions such as stretching, skewness, and torsion.     

Numerical convergence on adaptive grids for control volume methods

An adaptive technique for control‐volume methods applied to second order elliptic equations in two dimensions is presented. The discretization method applies to initially Cartesian grids aligned with the principal directions of the conductivity tensor. The convergence behavior of this method is investigated numerically. For solutions with low Sobolev regularity, the found L² convergence order is two for the potential and one for the flow density. The system of linear equations is better conditioned for the adaptive grids than for uniform grids. The test runs indicate that a pure flux‐based refinement criterion is preferable.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008