检索结果-内蒙古大学图书馆

Using H-Convergence to Calculate the numerical errors for 1D Unsaturated Seepage Under Steady-State Conditions

INTERNATIONAL JOURNAL FOR numerical AND ANALYTICAL METHODS IN GEOMECHANICS 2025年第1期49卷 345-358页

作者： Chapuis, Robert P. Taveau, Coline Duhaime, Francois Weber, Simon Marefat, Vahid Zhang, Lu Blessent, Daniela Bouaanani, Najib Pelletier, Dominique Polytech Montreal Dept Civil Geol & Min Engn Montreal PQ Canada SNC Lavalin Montreal PQ Canada Ecole Technol Super Dept Construct Engn Montreal PQ Canada Geotech Engn Team Lead BBA Montreal PQ Canada Jilin Univ Coll Construction Engn Changchun Peoples R China Univ Medellin Environm Engn Program Medellin Colombia Polytech Montreal Dept Mech Engn Montreal PQ Canada

Unsaturated zones are important for geotechnical design, geochemical reactions, and microbial reactions. The numerical analysis of unsaturated seepage is complex because it involves highly nonlinear partial differential equations. The permeability can vary by orders of magnitude over short vertical distances. This article defines and uses H-convergence tests to quantify numerical errors made by uniform meshes with element size (ES) for 1D steady-state conditions. The quantitative H-convergence should not be confused with a qualitative mesh sensitivity study. The difference between numerical and mathematical convergences is stated. A detailed affordable method for an H-convergence test is presented. The true but unknown solution is defined as the asymptote of the numerical solutions for all solution components when ES decreases to zero. The numerical errors versus ES are then assessed with respect to the true solution, and using a log-log plot, which indicates whether a code is correct or incorrect. If a code is correct, its results follow the rules of mathematical convergence in a mathematical convergence domain (MCD) which is smaller than the numerical convergence domain (NCD). If a code is incorrect, it has an NCD but no MCD. Incorrect algorithms of incorrect codes need to be modified and repaired. Existing codes are shown to converge numerically within large NCDs but generate large errors, up to 500%, in the NCDs, a dangerous situation for designers.

关键词： groundwater mathematical convergence numerical analysis numerical convergence numerical errors unsaturated

来源：评论

学校读者我要写书评

暂无评论

numerical errors in Ice Microphysics Parameterizations and their Effects on Simulated Regional Climate

引用

ASIA-PACIFIC JOURNAL OF ATMOSPHERIC SCIENCES 2022年第5期58卷 679-695页

作者： Kim, Ki-Byung Lim, Kyo-Sun Sunny Lee, Jiwoo Kyungpook Natl Univ Ctr Atmospher REmote Sensing CARE Dept Atmospher Sci Daegu South Korea Lawrence Livermore Natl Lab Livermore CA 94550 USA

The major characteristics of ice microphysics in Weather Research and Forecasting (WRF) Double-Moment 6-class (WDM6) bulk-type cloud microphysics originate from the diagnosed ice number concentration, which is a function of the cloud-ice mixing ratio. In this study, we correct numerical errors in ice microphysics processes of the WDM6, in which the cloud-ice shape is assumed as single bullets and examine the impact on regional climate simulations. By rederiving the relationships between cloud microphysics characteristics, including the one linking the cloud-ice mixing ratio and number concentration, we remove numerical errors intrinsic to the description of cloud-ice characteristics in the original WDM6 microphysics scheme. The revised WDM6 is tested using a WRF framework for regional climate simulations over the East Asian region. We find that our correction to the WDM6 improves the model's performance in capturing the observed distribution of the monsoon rain band. A reduction in cloud ice is significant in the revised WDM6, which strengthens the Western North Pacific High. By conducting the additional sensitivity experiment in which the characteristics of cloud-ice shape are revised as the one for the column type, our study also finds out that the impacts of the existing numerical errors on the simulated monsoon is as large as the ones of the changes in cloud-ice shape.

关键词： numerical errors WDM6 Cloud ice Regional climate simulation WRF

来源：评论

学校读者我要写书评

暂无评论

Revisiting numerical errors in direct and large eddy simulations of turbulence:: Physical and spectral spaces analysis

引用

JOURNAL OF COMPUTATIONAL PHYSICS 2001年第2期174卷 816-851页

作者： Fedioun, I Lardjane, N Gökalp, I Univ Orleans LME EPEE ESEM F-45072 Orleans 2 France CNRS LCSR EPEE F-45071 Orleans France

Some recent studies on the effects of truncation and aliasing errors on the large eddy simulation (LES) of turbulent flows via the concept of modified wave number are revisited. It is shown that all the results obtained for nonlinear partial differential equations projected and advanced in time in spectral space are not straightforwardly applicable to physical space calculations due to the nonequivalence by Fourier transform of spectral aliasing errors and numerical errors on a set of grid points in physical space. The consequences of spectral static aliasing errors on a set of grid points are analyzed in one dimension of space for quadratic products and their derivatives. The dynamical process that results through time stepping is illustrated on the Burgers equation. A method based on midpoint interpolation is proposed to remove in physical space the static grid point errors involved in divergence forms. It is compared to the sharp filtering technique on finer grids suggested by previous authors. Global performances resulting from combination of static aliasing errors and truncation errors are then discussed for all classical forms of the convective terms in Navier-Stokes equations. Some analytical results previously obtained on the relative magnitude of subgrid scale terms and numerical errors are confirmed with 3D realistic random fields. The physical space dynamical behavior and the stability of typical associations of numerical schemes and forms of nonlinear terms are finally evaluated on the LES of self-decaying homogeneous isotropic turbulence. It is shown that the convective form (if conservative properties are not strictly required) associated with highly resolving compact finite difference schemes provides the best compromise, which is nearly equivalent to dealiased pseudo-spectral calculations. (C) 2001 Elsevier Science.

关键词： large eddy simulation numerical errors stability dealiasing techniques Navier-Stokes equations turbulence finite difference modified wave number pseudo-spectral discretization self-decaying homogeneous isotropic turbulence

来源：评论

学校读者我要写书评

暂无评论

Real-world hydro-power unit-commitment: Dealing with numerical errors and feasibility issues

引用

ENERGY 2019年第1期184卷 91-104页

作者： Sahraoui, Youcef Bendotti, Pascale D'Ambrosio, Claudia EDF R&D Dept OSIRIS F-92141 Clamart France Ecole Polytech LIX CNRS UMR7161 F-91128 Palaiseau France

This article deals with feasibility issues of the hydro-unit commitment relative to units along a valley in the price-taker revenue-maximizing setting. The problem is formulated as a mixed-integer linear programming model. Besides physical constraints, we consider two additional specifications that apply to a subset of units and reservoirs within a valley, namely the power-flow curves of each unit feature discrete operational points and each reservoir level should meet target volumes. These specifications, together with the standard issues affecting real-world data, make our problem harder to solve, often infeasible. We follow a step-by-step approach to identify and repair one source of infeasibility at a time, namely numerical errors and model infeasibilities. The former is analyzed and fixed through tools like an exact solver and a model and data preprocessing. The remaining infeasibilities are eliminated with a 2-stage method. In the first stage, a minimal deviation from target volumes, i.e., strategic, thus relaxable, constraints, is computed to make the problem feasible. In the second stage, the original problem is solved with a possible deviation from the target volumes as defined in the first stage. Computational results confirm the effectiveness of the proposed method to recover feasibility on a challenging real-world test set. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Integer linear programming Hydro unit-commitment numerical errors Feasibility

来源：评论

学校读者我要写书评

暂无评论

On the numerical errors in the 2-D FE/FDTD algorithm for different hybridization schemes

引用

IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS 2004年第4期14卷 168-170页

作者： Venkatarayalu, NV Beng, GY Li, LW Natl Univ Singapore Temasek Labs Singapore Singapore Natl Univ Singapore Dept Elect & Comp Engn Singapore 117548 Singapore

numerical experiments are carried out to study the accuracy of the two-dimensional Finite-Element/Finite-Difference Time-Domain (FE/FDTD) hybrid algorithm with three different hybridization schemes. The physical space is split into two domains viz., the finite difference (FD) and finite element (FE) domains. In the FD domain, a uniform Cartesian grid is used and in the FE domain, triangular elements with edge vector basis functions are used. Newmark-beta scheme is used for temporal discretization in the FE domain. The unphysical reflections introduced by the FE domain for the different schemes are compared by computing the 2-D radar cross section of the FE domain surrounded by the FD domain. Computed results of scattering by a PEC circular cylinder for TEz, incidence using the three schemes and the traditional FDTD algorithm are presented.

关键词： finite-difference time-domain (FE/FDTD) finite-element hybrid algorithm numerical errors time domain methods

来源：评论

学校读者我要写书评

暂无评论

Study of numerical errors in direct numerical simulation and large eddy simulation

引用

Applied Mathematics and Mechanics(English Edition) 2008年第7期29卷 871-880页

作者：杨小龙符松 Research Center for Advanced Power-Strain Technology Hunan University School of Aerospace Engineering Tsinghua University

By comparing the energy spectrum and total kinetic energy, the effects of numerical errors （which arise from aliasing and discretization errors）, subgrid-scale （SGS） models, and their interactions on direct numerical simulation （DNS） and large eddy simulation （LES） are investigated, The decaying isotropic turbulence is chosen as the test case. To simulate complex geometries, both the spectral method and Pade compact difference schemes are studied. The truncated Navier-Stokes （TNS） equation model with Pade discrete filter is adopted as the SGS model. It is found that the discretization error plays a key role in DNS. Low order difference schemes may be unsuitable. However, for LES, it is found that the SGS model can represent the effect of small scales to large scales and dump the numerical errors. Therefore, reasonable results can also be obtained with a low order discretization scheme.

关键词： numerical errors truncated Navier-Stokes (TNS) model Pade compact difference scheme discrete filter large eddy simulation (LES)

来源：评论

学校读者我要写书评

暂无评论

Estimating numerical errors due to operator splitting in global atmospheric chemistry models: Transport and chemistry

引用

JOURNAL OF COMPUTATIONAL PHYSICS 2016年 305卷 372-386页

作者： Santillana, Mauricio Zhang, Lin Yantosca, Robert Harvard Univ Sch Engn & Appl Sci Cambridge MA 02138 USA Boston Childrens Hosp Computat Hlth Informat Program Boston MA 02115 USA Peking Univ Sch Phys Dept Atmospher & Ocean Sci Lab Climate & Ocean Atmosphere Sci Beijing 100871 Peoples R China

We present upper bounds for the numerical errors introduced when using operator splitting methods to integrate transport and non-linear chemistry processes in global chemical transport models (CTM). We show that (a) operator splitting strategies that evaluate the stiff non-linear chemistry operator at the end of the time step are more accurate, and (b) the results of numerical simulations that use different operator splitting strategies differ by at most 10%, in a prototype one-dimensional non-linear chemistry-transport model. We find similar upper bounds in operator splitting numerical errors in global CTM simulations. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Atmospheric chemistry Operator splitting Model verification numerical errors

来源：评论

学校读者我要写书评

暂无评论

A new exact upscaling formula and investigations of numerical errors in simulation of single- and two-phase Darcy flow in barrier geometries

引用

TRANSPORT IN POROUS MEDIA 2002年第2-3期46卷 233-249页

作者： Wessel-Berg, D Bergmo, PES SINTEF Petr Res Trondheim Norway

The pressure solution to a class of boundary value problems relevant for 2D Darcy flow in barrier geometries is derived using theta functions and elliptic integrals. From this solution an exact upscaling formula is established giving the effective permeability for flow through a homogenous layer bounded by two infinitely thin barriers with a single gap in each barrier. Comparisons with the exact pressure solution shows that the standard first order finite difference scheme underpredicts the volumetric flux in such barrier geometries when a given pressure drop is applied. Actually, using a coarse grid just fine enough to catch the description of the barrier geometry, the numerical scheme (the 'pressure solver') may underpredict the flux by more than a factor four. This numerical error is also present for two phase flow in the same type of geometry, and can be estimated from the corresponding single phase simulation. The errors observed for increasingly refined grids are tabulated for a few single and two-phase cases. Also exact pressure solutions for two examples are tabulated for benchmarking purposes.

关键词： upscaling exact solution barrier geometry numerical errors

来源：评论

学校读者我要写书评

暂无评论

Zernike Moment-Based Approach for Detecting Duplicated Image Regions by a Modified Method to Reduce Geometrical and numerical errors 15th

Zernike Moment-Based Approach for Detecting Duplicated Image...

引用

15th International Conference on Computational Science and Its Applications (ICCSA)

作者： Le-Tien, Thuong Huynh-Ngoc, Tan Huynh-Kha, Tu Marie, Luong HCM City Univ Technol Dept Elect Elect Engn Ho Chi Minh City Vietnam Mannheim Univ Appl Sci Fac Informat Tech Mannheim Germany HCM City Int Univ Sch Comp Sci & Engn Ho Chi Minh City Vietnam Univ Paris 13 Inst Galilee Labo L2TI Paris France

ISBN: (纸本)9783319214108;9783319214092

In the paper, the approach is focused on the Zernike Moment-based model of ROI image (Region of Interest) and its parameters for an efficient image processing in the forensic issue. By considering the factors affecting the identification of an duplicated image, the change of ROI's size is determined through the proposed algorithm. The proposed technique has shown a good improvement in reducing significantly Geometrical errors (G.E) and numerical errors (N.E) performed better than that of the Zernike-based traditional technique. The duplicated detection program has been written by C++ and supporting OpenCV and Boost libraries that help to verify the images authentication.

关键词： Zernike moments Geometrical errors numerical errors Geometric moments Region of Interest (ROI) FLANN library-Fast library for approximation nearest neighbors

来源：评论

学校读者我要写书评

暂无评论

Debugging and Detecting numerical errors in Computation with Posits 2020

Debugging and Detecting Numerical Errors in Computation with...

引用

41st ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI)

作者： Chowdhary, Sangeeta Lim, Jay P. Nagarakatte, Santosh Rutgers State Univ Dept Comp Sci New Brunswick NJ 08901 USA

ISBN: (纸本)9781450376136

Posit is a recently proposed alternative to the floating point representation (FP). It provides tapered accuracy. Given a fixed number of bits, the posit representation can provide better precision for some numbers compared to FP, which has generated significant interest in numerous domains. Being a representation with tapered accuracy, it can introduce high rounding errors for numbers outside the above golden zone. Programmers currently lack tools to detect and debug errors while programming with posits. This paper presents PositDebug, a compile-time instrumentation that performs shadow execution with high precision values to detect various errors in computation using posits. To assist the programmer in debugging the reported error, PositDebug also provides directed acyclic graphs of instructions, which are likely responsible for the error. A contribution of this paper is the design of the metadata per memory location for shadow execution that enables productive debugging of errors with long-running programs. We have used PositDebug to detect and debug errors in various numerical applications written using posits. To demonstrate that these ideas are applicable even for FP programs, we have built a shadow execution framework for FP programs that is an order of magnitude faster than Herbgrind.

关键词： Posits dynamic analysis numerical errors

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：