Implementation of ADER scheme for a bore on an unsaturated permeable slope

The paper details the implementation of the Godunov‐type finite volume Arbitrary high order schemes using Derivatives (ADER) scheme for the case of a large source term in the continuity equation of the nonlinear shallow water equations. The particular application is the movement of a bore on a highly permeable slope. The large source term is caused by the infiltration into the initially unsaturated slope material. Infiltration is modelled as vertical downwards piston‐like flow with Forchheimer quadratic parameterisation of the resistance law. The corresponding ODE is solved using the fourth‐order Runge–Kutta method. The surface and subsurface flow models have been tested by comparison with analytical solutions. Example predictions of surface bore propagation and wetting front propagation are presented for a range of slope permeabilities. The effects of permeability on bore run‐up, water depths and velocities are illustrated. The ADER scheme is capable of handling the source term, including the extreme case when this term dominates the volume balance. Copyright © 2011 John Wiley & Sons, Ltd.     

Numerical modeling of transient two-dimensional viscoelastic waves

This paper deals with the numerical modeling of transient mechanical waves in linear viscoelastic solids. Dissipation mechanisms are described using the generalized Zener model. No time convolutions are required thanks to the introduction of memory variables that satisfy local-in-time differential equations. By appropriately choosing the relaxation parameters, it is possible to accurately describe a large range of materials, such as solids with constant quality factors. The evolution equations satisfied by the velocity, the stress, and the memory variables are written in the form of a first-order system of PDEs with a source term. This system is solved by splitting it into two parts: the propagative part is discretized explicitly, using a fourth-order ADER scheme on a Cartesian grid, and the diffusive part is then solved exactly. Jump conditions along the interfaces are discretized by applying an immersed interface method. Numerical experiments of wave propagation in viscoelastic and fluid media show the efficiency of this numerical modeling for dealing with challenging problems, such as multiple scattering configurations.     

High‐order ADER‐WENO ALE schemes on unstructured triangular meshes—application of several node solvers to hydrodynamics and magnetohydrodynamics

In this paper, we present a class of high‐order accurate cell‐centered arbitrary Lagrangian–Eulerian (ALE) one‐step ADER weighted essentially non‐oscillatory (WENO) finite volume schemes for the solution of nonlinear hyperbolic conservation laws on two‐dimensional unstructured triangular meshes. High order of accuracy in space is achieved by a WENO reconstruction algorithm, while a local space–time Galerkin predictor allows the schemes to be high order accurate also in time by using an element‐local weak formulation of the governing PDE on moving meshes. The mesh motion can be computed by choosing among three different node solvers, which are for the first time compared with each other in this article: the node velocity may be obtained either (i) as an arithmetic average among the states surrounding the node, as suggested by Cheng and Shu, or (ii) as a solution of multiple one‐dimensional half‐Riemann problems around a vertex, as suggested by Maire, or (iii) by solving approximately a multidimensional Riemann problem around each vertex of the mesh using the genuinely multidimensional Harten–Lax–van Leer Riemann solver recently proposed by Balsara et al. Once the vertex velocity and thus the new node location have been determined by the node solver, the local mesh motion is then constructed by straight edges connecting the vertex positions at the old time level tⁿ with the new ones at the next time level t^{n + 1}. If necessary, a rezoning step can be introduced here to overcome mesh tangling or highly deformed elements. The final ALE finite volume scheme is based directly on a space–time conservation formulation of the governing PDE system, which therefore makes an additional remapping stage unnecessary, as the ALE fluxes already properly take into account the rezoned geometry. In this sense, our scheme falls into the category of direct ALE methods. Furthermore, the geometric conservation law is satisfied by the scheme by construction. We apply the high‐order algorithm presented in this paper to the Euler equations of compressible gas dynamics as well as to the ideal classical and relativistic magnetohydrodynamic equations. We show numerical convergence results up to fifth order of accuracy in space and time together with some classical numerical test problems for each hyperbolic system under consideration. Copyright © 2014 John Wiley & Sons, Ltd.     

Numerical studies of the cold flow field in model combustion chambers

Numerical analyses of the cold turbulent flow in model combustion chambers weremade by usingκ.εturbulent model.The hybrid difference scheme and SNIP methodwere employed.Numerical solutions for retouchment length and velocity distributions wereobtained in the recirculating zone of the combustion chambers.The calculation results werein fairly good agreement with the reported experimental data.The work presented in thispaper was a basic part of the calculation model of sudden-enlarged combustion chambers.     

一维守恒的Lagrangian ADER格式

基于欧拉框架下ADER格式,构造一维守恒只有一个时间步的、高精度中心型拉格朗日ADER(LADER)格式.构造r阶LADER格式包括:从欧拉方程出发推导拉格朗日框架下积分形式的方程、采用WENO方法高精度重构节点处守恒量和从1阶到r-1阶的空间导数、求拉氏框架下这些变量的Godunov值,并计算1阶到r-1阶的时间全导数,最后高精度离散积分形式的流通量函数.对光滑流场的模拟表明,LADER格式达到设计的精度;对含强间断的流场模拟表明,数值解在间断附近基本无振荡.     

Fast Stimulation of Millimeter Wave Waveguide Filters by Boundary Marching Method

The boundary marching method is applied for the analysis of the waveguide bandpass filers. The vector finite element method with the perfectly matched layers (PML) as the matching load is given for parameter extraction of millimeter wave filters. The implementation of the fast boundary marching method is described in detail. The reflection and insertion losses of millimeter wave filters are obtained and compared with those obtained from literature.     

共轭多烯分子极化率的量子化学研究

用引入外电场微扰的cNDO/2法计算了共轭多烯分子各种异构体的全价电子及π体系的极化率;讨论了影响共轭多烯电子极化率的诸因素及其变化规律,并对比了己三烯2种异构体的电子极化率,解释了它们有关物理化学性质间的差异。     

Numerical modeling of 1D transient poroelastic waves in the low-frequency range

Propagation of transient mechanical waves in porous media is numerically investigated in 1D. The framework is the linear Biot model with frequency-independent coefficients. The coexistence of a propagating fast wave and a diffusive slow wave makes numerical modeling tricky. A method combining three numerical tools is proposed: a fourth-order ADER scheme with time-splitting to deal with the time-marching, a space-time mesh refinement to account for the small-scale evolution of the slow wave, and an interface method to enforce the jump conditions at interfaces. Comparisons with analytical solutions confirm the validity of this approach.     

Analysis of ADER and ADER-WAF schemes

^{We study stability properties and truncation errors of the finite-volumeADER schemes on structured meshes as applied to the linear advectionequation with constant coefficients in one-, two- and three-spatialdimensions. Stability of linear ADER schemes is analysed bymeans of the von Neumann method. For nonlinear schemes, we deducethe stability region from numerical experiments. The truncationerror analysis is carried out for linear ADER schemes in one-,two- and three-space dimensions and for nonlinear ADER schemesin one-space dimension.}     

对积分恒等式的一点补充和有限元的局部校正结果

１．积分恒等式简介其中ｈ＝ｍａｘ｛ｈｅ,ｋｅ｝, 易见用 Ｑ１（ｅ）表示 ｅ上全体双线性函数,ｕＩ∈ Ｑ１（ｅ）为ｕ在 ｅ上的双线性插值．文［１, ２］曾给出了一系列的积分恒等式,列举如下： Ａ：二阶恒等式,用于超收敛估计：对任给ｖ∈Ｑ１（ｅ）,有以及由于Ｉｅ１２的展开式中含有因子б１б２ｖ,将破坏超收敛估计,故对此项关于ｙ分部积分,得展开式其中τ１,τ２分别为ｅ的上下边.（１．３）,（１．４）和（１．６）是作导数超收敛估计的基本展开式．当然我们更有０次项的展开式．在下一节将讨论林氏积分表． 为了进一步…