Efficient incorporation of channel cross-section geometry uncertainty into regional and global scale flood inundation models

This paper investigates the challenge of representing structural differences in river channel cross-section geometry for regional to global scale river hydraulic models and the effect this can have on simulations of wave dynamics. Classically, channel geometry is defined using data, yet at larger scales the necessary information and model structures do not exist to take this approach. We therefore propose a fundamentally different approach where the structural uncertainty in channel geometry is represented using a simple parameterization, which could then be estimated through calibration or data assimilation. This paper first outlines the development of a computationally efficient numerical scheme to represent generalised channel shapes using a single parameter, which is then validated using a simple straight channel test case and shown to predict wetted perimeter to within 2% for the channels tested. An application to the River Severn, UK is also presented, along with an analysis of model sensitivity to channel shape, depth and friction. The channel shape parameter was shown to improve model simulations of river level, particularly for more physically plausible channel roughness and depth parameter ranges. Calibrating channel Manning’s coefficient in a rectangular channel provided similar water level simulation accuracy in terms of Nash-Sutcliffe efficiency to a model where friction and shape or depth were calibrated. However, the calibrated Manning coefficient in the rectangular channel model was ~2/3 greater than the likely physically realistic value for this reach and this erroneously slowed wave propagation times through the reach by several hours. Therefore, for large scale models applied in data sparse areas, calibrating channel depth and/or shape may be preferable to assuming a rectangular geometry and calibrating friction alone.

Summertime moisture transport over Southeastern South America and extratropical cyclones behavior during inter-El Nio events

The impact of the inter-El Nio (EN) variability on the moisture availability over Southeastern South America (SESA) is investigated. Also, an automatic tracking scheme was used to analyze the extratropical cyclones properties (system density - SD and central pressure - CP) in this region. During the austral summer period from 1977-2000, the differences for the upper-level wave train anomaly composites seem to determine the rainfall composite differences. In fact, the positive rainfall anomalies over most of the SESA domain during the strong EN events are explained by an upper-level cyclonic center over the tropics and an anticyclonic center over the eastern subtropical area. This pattern seems to contribute to upward vertical motion at 500 hPa and reinforcement of the meridional moisture transport from the equatorial Atlantic Ocean and western Amazon basin to the SESA region. These features may contribute to the positive SD and negative CP anomalies explaining part of the positive rainfall anomalies found there. On the other hand, negative rainfall anomalies are located in the northern part of SESA for the weak EN years when compared to those for the strong events. Also, positive anomalies are found in the southern part, albeit less intense. It was associated with the weakening of the meridional moisture transport from the tropics to the SESA that seems have to contributed with smaller SD and CP anomalies over the most part of subtropics, when compared to the strong EN years.

A discontinuous-Galerkin-based immersed boundary method with non-homogeneous boundary conditions and its application to elasticity

We propose a discontinuous-Galerkin-based immersed boundary method for elasticity problems. The resulting numerical scheme does not require boundary fitting meshes and avoids boundary locking by switching the elements intersected by the boundary to a discontinuous Galerkin approximation. Special emphasis is placed on the construction of a method that retains an optimal convergence rate in the presence of non-homogeneous essential and natural boundary conditions. The role of each one of the approximations introduced is illustrated by analyzing an analog problem in one spatial dimension. Finally, extensive two- and three-dimensional numerical experiments on linear and nonlinear elasticity problems verify that the proposed method leads to optimal convergence rates under combinations of essential and natural boundary conditions. (C) 2009 Elsevier B.V. All rights reserved.

High-order upwinding and the hydraulic jump

This work is concerned with the computation of incompressible axisymmetric and fall three-dimensional free-surface flows. In particular, the circular-hydraulic jump is simulated and compared with approximate analytic solutions. However, the principal thrust of this paper is to provide a real problem as a test bed for comparing the many existing convective approximations. Their performance is compared; SMART, HLPA and VONOS emerge as acceptable upwinding methods for this problem. Copyright (C) 2002 John Wiley Sons, Ltd.

Escape and transport for an open bouncer: Stretched exponential decays

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The element-free Galerkin method applied to the study of fully developed magnetohydrodynamic duct flows

In this paper, the meshless method is introduced to magnetohydrodynamics. A numerical scheme based on the element-free Galerkin method is used to solve the laminar steady-state two-dimensional fully developed magnetohydrodynamic flow in a rectangular duct. Accurate and convergent solutions are achieved for low to moderately high Hartmann numbers.

Three-dimensional finite element analysis of MHD duct flow by the penalty function formulation

A numerical scheme based on the Finite Element Method (FEM) is presented to calculate the full solution of a three-dimensional steady magnetohydrodynamic (MHD) flow with moderately high Hartmann numbers and interaction parameters. An incompressible, viscous and electrically conducting liquid-metal is considered. Assuming a low magnetic Reynolds number, the solution method solves the coupled Navier-Stokes and Maxwell's equations through the use of a penalty function method. Results are presented for Hartmann numbers in the range 10(2)-10(3).

A Transmission Problem for Euler-Bernoulli beam with Kelvin-Voigt Damping

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Stability analysis of Crank-Nicolson and Euler schemes for time-dependent diffusion equations

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Parallel implementation of a robust optical flow technique

[EN] The accuracy and performance of current variational optical ow methods have considerably increased during the last years. The complexity of these techniques is high and enough care has to be taken for the implementation. The aim of this work is to present a comprehensible implementation of recent variational optical flow methods. We start with an energy model that relies on brightness and gradient constancy terms and a ow-based smoothness term. We minimize this energy model and derive an e cient implicit numerical scheme. In the experimental results, we evaluate the accuracy and performance of this implementation with the Middlebury benchmark database. We show that it is a competitive solution with respect to current methods in the literature. In order to increase the performance, we use a simple strategy to parallelize the execution on multi-core processors.

TV-L1 optical flow estimation

[EN] This article describes an implementation of the optical flow estimation method introduced by Zach, Pock and Bischof. This method is based on the minimization of a functional containing a data term using the L norm and a regularization term using the total variation of the flow. The main feature of this formulation is that it allows discontinuities in the flow field, while being more robust to noise than the classical approach. The algorithm is an efficient numerical scheme, which solves a relaxed version of the problem by alternate minimization.

Reliable estimation of dense optical flow fields with large displacements

[EN] In this paper we show that a classic optical flow technique by Nagel and Enkelmann can be regarded as an early anisotropic diffusion method with a diffusion tensor. We introduce three improvements into the model formulation that avoid inconsistencies caused by centering the brightness term and the smoothness term in different images use a linear scale-space focusing strategy from coarse to fine scales for avoiding convergence to physically irrelevant local minima, and create an energy functional that is invariant under linear brightness changes.  Applying a gradient descent method to the resulting energy functional leads to a system of diffusion-reaction equations. We prove that this system has a unique solution under realistic assumptions on the initial data, and we present an efficient linear implicit numerical scheme in detail. Our method creates flow fields with 100% density over the entire image domain, it is robust under a large range of parameter variations, and it can recover displacement fields that are far beyond the typical one-pixel limits which are characteristic for many differential methods for determining optical flow. We show that it performs better than the classic optical flow methods with 100%  density that are evaluated by Barron et al. (1994). Our software is available from the Internet.

A scale-space aproach to nonlocal optical flow calculations

[EN] This paper presents an interpretation of a classic optical flow method by Nagel and Enkelmann as a tensor-driven anisotropic diffusion approach in digital image analysis. We introduce an improvement into the model formulation, and we establish well-posedness results for the resulting system of parabolic partial differential equations. Our method avoids linearizations in the optical flow constraint, and it can recover displacement fields which are far beyond the typical one-pixel limits that are characteristic for many differential methods for optical flow recovery. A robust numerical scheme is presented in detail. We avoid convergence to irrelevant local minima by embedding our method into a linear scale-space framework and using a focusing strategy from coarse to fine scales. The high accuracy of the proposed method is demonstrated by means of a synthetic and a real-world image sequence.

Regularizing a set of unstructured 3D points from a sequence of stereo images

[EN] In this paper we present a method for the regularization of a set of unstructured 3D points obtained from a sequence of stereo images. This method takes into account the information supplied by the disparity maps computed between pairs of images to constraint the regularization of the set of 3D points. We propose a model based on an energy which is composed of two terms: an attachment term that minimizes the distance from 3D points to the projective lines of camera points, and a second term that allows for the regularization of the set of 3D points by preserving discontinuities presented on the disparity maps. We embed this energy in a 2D finite element method. After minimizing, this method results in a large system of equations that can be optimized for fast computations. We derive an efficient implicit numerical scheme which reduces the number of calculations and memory allocations.

Mixed finite-element methods for elliptic convection-dominated problems arising in semiconductor physics

In this work we develop and analyze an adaptive numerical scheme for simulating a class of macroscopic semiconductor models. At first the numerical modelling of semiconductors is reviewed in order to classify the Energy-Transport models for semiconductors that are later simulated in 2D. In this class of models the flow of charged particles, that are negatively charged electrons and so-called holes, which are quasi-particles of positive charge, as well as their energy distributions are described by a coupled system of nonlinear partial differential equations. A considerable difficulty in simulating these convection-dominated equations is posed by the nonlinear coupling as well as due to the fact that the local phenomena such as "hot electron effects" are only partially assessable through the given data. The primary variables that are used in the simulations are the particle density and the particle energy density. The user of these simulations is mostly interested in the current flow through parts of the domain boundary - the contacts. The numerical method considered here utilizes mixed finite-elements as trial functions for the discrete solution. The continuous discretization of the normal fluxes is the most important property of this discretization from the users perspective. It will be proven that under certain assumptions on the triangulation the particle density remains positive in the iterative solution algorithm. Connected to this result an a priori error estimate for the discrete solution of linear convection-diffusion equations is derived. The local charge transport phenomena will be resolved by an adaptive algorithm, which is based on a posteriori error estimators. At that stage a comparison of different estimations is performed. Additionally a method to effectively estimate the error in local quantities derived from the solution, so-called "functional outputs", is developed by transferring the dual weighted residual method to mixed finite elements. For a model problem we present how this method can deliver promising results even when standard error estimator fail completely to reduce the error in an iterative mesh refinement process.