地震波动方程的局部间断有限元方法数值模拟

近年来,随着地震波数值模拟对计算精度和效率的要求越来越高,间断有限元方法开始受到越来越多的关注.本文中,针对具有吸收边界条件的二维地震声波波动方程,作者提出了一种基于局部间断有限元方法的数值模拟算法.该算法在空间上使用局部间断有限元方法进行离散,在时间上采用了显式蛙跳格式.在这种时空离散的组合方式下,每个时间步上,此算法在空间剖分的每个单元上的求解计算是相互独立的,因而具有极高的并行性.通过数值算例,我们将该算法与连续有限元方法进行了比较.结果表明,本算法不仅具有对起伏构造的良好适应性,而且在计算效率和计算精度等方面,都具有优越性.     

Reactive Rayleigh–Taylor turbulent mixing: a one-dimensional-turbulence study

We study the problem of reactive Rayleigh–Taylor turbulence in the Boussinesq framework using one-dimensional-turbulence (ODT) simulations. In this problem a reaction zone between overlying heavy/cold reactants and underlying light/hot products moves against gravity. First, we show that ODT results for global quantities in non-reactive Rayleigh–Taylor turbulence are within those from direct numerical simulations (DNS). This comparison give us confidence in using ODT to study unexplored flow regimes in the reactive case. Then, we show how ODT predicts an early stage of reactive Rayleigh–Taylor turbulence that behaves similarly to the non-reactive case, as observed in previous DNS. More importantly, ODT indicates a later stage where the growth of the reaction zone reduces considerably. The present work can be seen as a step towards the study of supernova flames with ODT.     

Book Review of Accretion Power in Astrophysics (3rd Edition) by Juhan Frank,Andrew King,Derek Raine Cambridge University Press, 2002, XIV+384 pp., £27.95, hardback (ISBN 0 521 62053 8), paperback (ISBN 0 521 62957 8).

The velocity, pressure, perturbation magnetic field, helicity and electromotive force driven by an isolated buoyant parcel in an unbounded, rapidly rotating, electrically conducting fluid in the limit of small Elsasser number and very small Ekman number are calculated, visualized and analyzed. On the scale of the parcel, the solution is identical to that obtained in the limit of small Ekman number and zero Elsasser number. On the scale of the Taylor-column, it is elongated in the direction of the applied magnetic field and compressed in the direction perpendicular to it. The α-effect calculated by averaging the electromotive force on planes normal to rotation is strongly anisotropic: near the parcel and in the inner part of the Taylor-column it is strongest when the applied magnetic field is perpendicular to rotation and gravity; in the outer part of the Taylor-column it is strongest when the applied magnetic field is in the same plane as rotation and gravity.     

Dynamic p-enrichment schemes for multicomponent reactive flows

We present a family of p-enrichment schemes. These schemes may be separated into two basic classes: the first, called fixed tolerance schemes, rely on setting global scalar tolerances on the local regularity of the solution, and the second, called dioristic schemes, rely on time-evolving bounds on the local variation in the solution. Each class of p-enrichment scheme is further divided into two basic types. The first type (the Type I schemes) enrich along lines of maximal variation, striving to enhance stable solutions in “areas of highest interest.” The second type (the Type II schemes) enrich along lines of maximal regularity in order to maximize the stability of the enrichment process. Each of these schemes are tested on three model systems. The first is an academic exact system where basic analysis is easily performed. Then we discuss a pair of application model problems arising in coastal hydrology. The first being a contaminant transport model, which addresses a declinature problem for a contaminant plume with respect to a bay inlet setting. And the second, a multicomponent chemically reactive flow model of estuary eutrophication arising in the Gulf of Mexico.     

Discontinuous Galerkin methods for modeling Hurricane storm surge

Storm surge due to hurricanes and tropical storms can result in significant loss of life, property damage, and long-term damage to coastal ecosystems and landscapes. Computer modeling of storm surge can be used for two primary purposes: forecasting of surge as storms approach land for emergency planning and evacuation of coastal populations, and hindcasting of storms for determining risk, development of mitigation strategies, coastal restoration and sustainability.Storm surge is modeled using the shallow water equations, coupled with wind forcing and in some events, models of wave energy. In this paper, we will describe a depth-averaged (2D) model of circulation in spherical coordinates. Tides, riverine forcing, atmospheric pressure, bottom friction, the Coriolis effect and wind stress are all important for characterizing the inundation due to surge. The problem is inherently multi-scale, both in space and time. To model these problems accurately requires significant investments in acquiring high-fidelity input (bathymetry, bottom friction characteristics, land cover data, river flow rates, levees, raised roads and railways, etc.), accurate discretization of the computational domain using unstructured finite element meshes, and numerical methods capable of capturing highly advective flows, wetting and drying, and multi-scale features of the solution.The discontinuous Galerkin (DG) method appears to allow for many of the features necessary to accurately capture storm surge physics. The DG method was developed for modeling shocks and advection-dominated flows on unstructured finite element meshes. It easily allows for adaptivity in both mesh (h) and polynomial order (p) for capturing multi-scale spatial events. Mass conservative wetting and drying algorithms can be formulated within the DG method.In this paper, we will describe the application of the DG method to hurricane storm surge. We discuss the general formulation, and new features which have been added to the model to better capture surge in complex coastal environments. These features include modifications to the method to handle spherical coordinates and maintain still flows, improvements in the stability post-processing (i.e. slope-limiting), and the modeling of internal barriers for capturing overtopping of levees and other structures. We will focus on applications of the model to recent events in the Gulf of Mexico, including Hurricane Ike.     

Accuracy of numerical simulations of contaminant transport in heterogeneous aquifers: A comparative study

This work deals with a comparison of different numerical schemes for the simulation of contaminant transport in heterogeneous porous media. The numerical methods under consideration are Galerkin finite element (GFE), finite volume (FV), and mixed hybrid finite element (MHFE). Concerning the GFE we use linear and quadratic finite elements with and without upwind stabilization. Besides the classical MHFE a new and an upwind scheme are tested. We consider higher order finite volume schemes as well as two time discretization methods: backward Euler (BE) and the second order backward differentiation formula BDF (2). It is well known that numerical (or artificial) diffusion may cause large errors. Moreover, when the Péclet number is large, a numerical code without some stabilising techniques produces oscillating solutions. Upwind schemes increase the stability but show more numerical diffusion. In this paper we quantify the numerical diffusion for the different discretization schemes and its dependency on the Péclet number. We consider an academic example and a realistic simulation of solute transport in heterogeneous aquifer. In the latter case, the stochastic estimates used as reference were obtained with global random walk (GRW) simulations, free of numerical diffusion. The results presented can be used by researchers to test their numerical schemes and stabilization techniques for simulation of contaminant transport in groundwater.     

Impact of mega-scale sand extraction on tidal dynamics in semi-enclosed basins: An idealized model study with application to the Southern North Sea

Long-term considerations of repeated and increasing sand extraction on the Netherlands Continental Shelf (North Sea) may lead to the creation of a mega-scale extraction trench in front of the Dutch coast (length hundreds of km, width over 10 km, depth several m). We investigate the impact of such a huge topographic intervention on tidal dynamics, which is a key aspect in hydrodynamics, and indirectly also affecting morphodynamics and ecology.     

Numerical modeling of two-phase flow in heterogeneous permeable media with different capillarity pressures

Contrast in capillary pressure of heterogeneous permeable media can have a significant effect on the flow path in two-phase immiscible flow. Very little work has appeared on the subject of capillary heterogeneity despite the fact that in certain cases it may be as important as permeability heterogeneity. The discontinuity in saturation as a result of capillary continuity, and in some cases capillary discontinuity may arise from contrast in capillary pressure functions in heterogeneous permeable media leading to complications in numerical modeling. There are also other challenges for accurate numerical modeling due to distorted unstructured grids because of the grid orientation and numerical dispersion effects. Limited attempts have been made in the literature to assess the accuracy of fluid flow modeling in heterogeneous permeable media with capillarity heterogeneity. The basic mixed finite element (MFE) framework is a superior method for accurate flux calculation in heterogeneous media in comparison to the conventional finite difference and finite volume approaches. However, a deficiency in the MFE from the direct use of fractional flow formulation has been recognized lately in application to flow in permeable media with capillary heterogeneity. In this work, we propose a new consistent formulation in 3D in which the total velocity is expressed in terms of the wetting-phase potential gradient and the capillary potential gradient. In our formulation, the coefficient of the wetting potential gradient is in terms of the total mobility which is smoother than the wetting mobility. We combine the MFE and discontinuous Galerkin (DG) methods to solve the pressure equation and the saturation equation, respectively. Our numerical model is verified with 1D analytical solutions in homogeneous and heterogeneous media. We also present 2D examples to demonstrate the significance of capillary heterogeneity in flow, and a 3D example to demonstrate the negligible effect of distorted meshes on the numerical solution in our proposed algorithm.     

结构动力方程的显式级数积分格式

将Newmark-β法中常平均加速度法的基本假定与精细指数算法结合,根据指数矩阵的Taylor级数展开式,提出了动力方程的显式级数解,并设计了相应的时程积分算法.该算法的精度可根据Taylor级数展开式的项数进行灵活控制.算例的结果表明:在满足稳定性条件的前提下,随着时间步长的增加,其精度优于传统的时程积分法.通过稳定性的分析,指出其稳定性条件是显然满足的.     

A positive definite continuous FEM model for advection

This work introduces a continuous and sign-preserving finite element model (FEM) for advection problems. The model is formulated by integrating flux corrected transport technique (FCT) with the characteristic based (CB) FEM. Low order solution for the FCT has the form of element contribution and derives from an upwind monotone scheme with the minimum necessary diffusion for positivity. Selected numerical experiments illustrate the efficacy of the method by comparing results with some successful models, by demonstrating an approximate conservation of the accuracy of original CB algorithm once the complete procedure is operating, and by testing the model for severe time dependent advective flows.