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A simple method of depressing numerical dissipation effects during wave simulation within the Euler model

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Acta Oceanologica Sinica 2020年第1期39卷 141-156页

作者： Zhe Hu Xiaoying Zhang Weicheng Cui Fang Wang Xiaowen Li Yan Li Key Laboratory of Ships and Ocean Engineering of Fujian Province School of Marine EngineeringJimei UniversityXiamen 361021China Deep Sea Technology Research Center School of EngineeringWest Lake UniversityHangzhou 310024China Hadal Science and Technology Research Center College of Marine SciencesShanghai Ocean UniversityShanghai 201306China

numerical wave tanks are widely-acknowledged tools in studying waves and wave-structure interactions. They can generate waves under realistic scales and offers more information on the fluid field. However, most numerical wave tanks suffer from issues known as the numerical dissipation and numerical dispersion. The former causes wave energy to be slowly dissipated and the latter shifts wave frequencies during wave propagation. This paper proposes a simple method of depressing numerical dissipation effects on the basis of solving Euler equations using the finite difference method(FDM). The wave propagation solutions are solved analytically taking into account the influence of the damping terms. The main idea of the method is to append a source term to the momentum equation, whose strength is determined by how strong the numerical damping effect is. The method is verified by successfully depressing numerical effects during the simulation of regular linear waves, Stokes waves and irregular waves. By applying the method, wave energy is able to be close to its initial value after long distance of travel.

关键词： numerical dissipation numerical wave tank wave simulation numerical damping reduction finite difference method

Modifying and Reducing numerical dissipation in A Two-Dimensional Central-Upwind Scheme

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Advances in Applied Mathematics and Mechanics 2012年第3期4卷 340-353页

作者： Chi-Jer Yu Chii-Tung Liu Department of Applied Mathematics National Chiao Tung University1001 University RoadHsinchu 300Taiwan Department of Computer Science and Information Engineering Chaoyang University of Technology168 Jifong E.Rd.Wufong Township Taichung County 41349Taiwan

This study presents a modification of the central-upwind Kurganov scheme for approximating the solution of the 2D Euler *** prototype,extended from a 1D model,reduces substantially less dissipation than *** problem arises from over-restriction of some slope limiters,which keep slopes between interfaces of cells to be *** study reports the defect and presents a re-derived optimal *** experiments highlight the significance of this formula,especially in long-time,large-scale simulations.

关键词： Hyperbolic systems of conservation laws Godunov-type finite-volume methods central-upwind scheme Kurganov numerical dissipation anti-diffusion

A high-order SPH method by introducing inverse kernels

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Chinese Journal of Aeronautics 2017年第1期30卷 1-14页

作者： Fang Le Marongiu Jean Christophe Leduc Julien Amicarelli Andrea Caro Joёlleb LMP Ecole centrale de Pekin Beihang University Co-Innovation Center for Advanced Aero-Engine 100083 Beijing China LMFA Ecole centrale de Lyon 69130 Ecully BP 163 France Laboratoire International Associe Beihang University 100083 Beijing China ANDRITZ HYDRO AG Rue des Deux-Gares 6 1800 Vevey Switzerland

The smoothed particle hydrodynamics（SPH） method is usually expected to be an efficient numerical tool for calculating the fluid-structure interactions in compressors; however, an endogenetic restriction is the problem of low-order consistency. A high-order SPH method by introducing inverse kernels, which is quite easy to be implemented but efficient, is proposed for solving this restriction. The basic inverse method and the special treatment near boundary are introduced with also the discussion of the combination of the Least-Square（LS） and Moving-Least-Square（MLS） methods. Then detailed analysis in spectral space is presented for people to better understand this method. Finally we show three test examples to verify the method behavior.

关键词： Consistency High-order method Inverse method numerical dissipation numerical instability Smoothed particle hydrodynamics

Shedding vortex simulation method based on viscous compensation technology research

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Chinese Physics B 2022年第4期31卷 414-425页

作者： Hao Zhou Lei Wang Zhang-Feng Huang Jing-Zhi Ren Department of Mechanics Tianjin UniversityTianjin 300072China Science and Technology on Space Physics Laboratory China Academy of Launch Vehicle TechnologyBeijing 100076China

Owing to the influence of the viscosity of the flow field,the strength of the shedding vortex decreases gradually in the process of backward ***-scale vortexes constantly break up,forming smaller *** engineering,when numerical simulation of vortex evolution process is carried out,a large grid is needed to be arranged in the area of outflow field far from the boundary layer in order to ensure the calculation *** a result,small scale vortexes at the far end of the flow field cannot be captured by the sparse grid in this region,resulting in the dissipation or even disappearance of *** this paper,the effect of grid scale is quantified and compared with the viscous effect through theoretical *** theoretical relationship between the mesh viscosity and the original viscosity of the flow field is established,and the viscosity term in the turbulence model is *** method proves to be able to effectively improve the intensity of small-scale shedding vortexes at the far end of the flow field under the condition of sparse *** error between the simulation results and the results obtained by using fine mesh is greatly reduced,the calculation time is shortened,and the high-precision and efficient simulation of the flow field is realized.

关键词： shedding vortex viscosity analysis numerical dissipation turbulence models

Improved quadratic isogeometric element simulation of one-dimensional elastic wave propagation with central difference method

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Applied Mathematics and Mechanics(English Edition) 2018年第5期39卷 703-716页

作者： Weibin WEN Shibin LUO Shengyu DUAN Jun LIANG Daining FANG School of Civil Engineering Central South University State Key Laboratory of Explosion Science and Technology Beijing Institute of Technology College of Engineering Peking University

Two improved isogeometric quadratic elements and the central difference scheme are used to formulate the solution procedures of transient wave propagation prob- lems. In the proposed procedures, the lumped matrices corresponding to the isogeomet- ric elements are obtained. The stability conditions of the solution procedures are also acquired. The dispersion analysis is conducted to obtain the optimal Courant-Friedrichs- Lewy （CFL） number or time-step sizes corresponding to the spatial isogeometric elements. The dispersion analysis shows that the isogeometric quadratic element of the fourth-order dispersion error （called the isogeometric analysis （IGA）-f quadratic element） provides far more desirable numerical dissipation/dispersion than the element of the second-order dis- persion error （called the IGA-s quadratic element） when appropriate time-step sizes are selected. The numerical simulations of one-dimensional （1D） transient wave propagation problems demonstrate the effectiveness of the proposed solution procedures.

关键词： structural dynamics wave propagation isogeometric analysis (IGA) numerical dissipation time integration

An improved CESE method and its application to steady-state coronal structure simulation

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Science China Earth Sciences 2014年第1期57卷 153-166页

作者： ZHOU YuFen FENG XueShang SIGMA Weather Group State Key Laboratory for Space Weather Center for Space Science and Applied ResearchChinese Academy of Sciences

This paper presents an improved space-time conservation element and solution element(CESE)method by applying a non-staggered space-time mesh system and simply improving the calculation of flow variables and applies it to magnetohydrodynamics(MHD)*** improved CESE method can improve the solution quality even with a large disparity in the Courant number(CFL)when using a fixed global marching ***,for a small CFL(saynumerical dissipation and retain the solution quality,which are verified by two benchmark *** meanwhile,comparison with the original CESE scheme shows better resolution of the improved scheme ***,we demonstrate its validation through the application of this method in three-dimensional coronal dynamical structure with dipole magnetic fields and measured solar surface magnetic fields as the initial input.

关键词： improved CESE scheme numerical dissipation steady-state coronal structure

Energetics of lateral eddy diffusion/advection: Part II. numerical diffusion/diffusivity and gravitational potential energy change due to isopycnal diffusion

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Acta Oceanologica Sinica 2014年第3期33卷 19-39页

作者： HUANG Rui Xin Department of Physical Oceanography Woods Hole Oceanographic Institution

Study of oceanic circulation and climate requires models which can simulate tracer eddy diffusion and ad vection accurately. It is shown that the traditional Eulerian coordinates can introduce large artificial hori zontal diffusivity/viscosity due to the incorrect alignment of the axis. Therefore, such models can smear sharp fronts and introduce other numerical artifacts. For simulation with relatively low resolution, large lateral diffusion was explicitly used in models; therefore, such numerical diffusion may not be a problem. However, with the increase of horizontal resolution, the artificial diffusivity/viscosity associated with hori zontal advection in the commonly used Eulerian coordinates may become one of the most challenging ob stacles for modeling the ocean circulation accurately. Isopycnal eddy diffusion （mixing） has been widely used in numerical models. The common wisdom is that mixing along isopycnal is energy free. However, a careful examination reveals that this is not the case. In fact, eddy diffusion can be conceptually separated into two steps： stirring and subscale diffusion. Due to the thermobaric effect, stirring, or exchanging water masses, along isopycnal surface is associated with the change of GPE in the mean state. This is a new type of instability, called the thermobaric instability. In addition, due to cabbeling subscale diffusion of water parcels always leads to the release of GPE. The release of GPE due to isopycnal stirring and subscale diffusion may lead to the thermobaric instability.

关键词： Eulerian coordinates numerical diffusivity numerical dissipation energetics of isopycnal eddydiffusion

Analytical exploration of γ-function explicit method for pseudodynamic testing of nonlinear systems

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Earthquake Engineering and Engineering Vibration 2005年第1期4卷 117-127页

作者：张顺益宋裕祺 Department of Civil Engineering National Taipei University of Technology Chinese Taipei 106-08AssociateProfessor Department of Civil Engineering National Taipei University of Technology Chinese Taipei 106-08 Assistant Professor

It has been well studied that the γ-function explicit method can be effective in providing favorable numerical dissipation for linear elastic systems. However, its performance for nonlinear systems is unclear due to a lack of analytical evaluation techniques. Thus, a novel technique is proposed herein to evaluate its efficiency for application to nonlinear systems by introducing two parameters to describe the stiffness change. As a result, the numerical properties and error propagation characteristics of the γ-function explicit method for the pseudodynamic testing of a nonlinear system are analytically assessed. It is found that the upper stability limit decreases as the step degree of nonlinearity increases; and it increases as the current degree of nonlinearity increases. It is also shown that this integration method provides favorable numerical dissipation not only for linear elastic systems but also for nonlinear systems. Furthermore, error propagation analysis reveals that the numerical dissipation can effectively suppress the severe error propagation of high frequency modes while the low frequency responses are almost unaffected for both linear elastic and nonlinear systems.

关键词： pseudodynamic test nonlinear error propagation numerical dissipation

numerical ANALYSIS AND CONSTRUCTION OF LIMITER OF HIGH RESOLUTION DIFFERENCE SCHEME

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Applied Mathematics and Mechanics(English Edition) 1998年第7期19卷 677-686页

作者：张梦萍刘儒勋 Department of Mathematics University of Science and Technology of China Hefei P.R. China

In the paper, based on the theory of the remainder effects of difference schemes, some typical limiters are analysed and compared. For different limiters, the different strength of numerical dissipation and dispersion of schemes is the reason why the schemes show obvious different characteristics. After analysing and comparing the numerical dissipation and dispersion of various schemes, a new kind of limiter is proposed. The new scheme has high resolution in sharp discontinuities, and avoids the 'distortion' due to the stronger numerical dispersion in the relatively more smooth region. numerical experiments show that the scheme has good properties.

关键词： numerical dissipation numerical dispersion limiter