检索结果-南通市图书馆

helmholtz decomposition-based SPH

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Virtual Reality & Intelligent Hardware 2021年第2期3卷 118-128页

作者： Zhongyao YANG Maolin WU Shiguang LIU School of Computer Science and Technology Division of Intelligence and ComputingTianjin UniversityTianjin 300072China

Background SPH method has been widely used in the simulation of water scenes.As a numerical method of partial differential equations,SPH can easily deal with the distorted and complex boundary.In addition,the implementation of SPH is relatively simple,and the results are stable and not easy to diverge.However,SPH method also has its own limitations.In order to further improve the performance of SPH method and expand its application scope,a series of key and difficult problems restricting the development of SPH need to be improved.Methods In this paper,we introduce the idea of helmholtz decomposition into the framework of smoothed particle hydrodynamics(SPH)and propose a novel velocity projection scheme for three-dimensional water simulation.First,we apply helmholtz decomposition to a three-dimensional velocity field and decompose it into three orthogonal subspaces.Then,our method combines the idea of spatial derivatives in SPH to obtain a discrete Poisson velocity equation.Finally,the conjugate gradient(CG)is utilized to efficiently solve the Poisson equation.Results The experimental results show that the proposed scheme is suitable for various situations and has higher efficiency than the current SPH projection scheme.Conclusion Compared with the previous projection scheme,our solution does not need to modify the particle velocity indirectly by pressure projection,but directly by velocity field projection.The new scheme can be well integrated into the existing SPH framework,and can be applied to the interaction of water with static and dynamic obstacles,even for viscous fluid.

关键词： Water simulation SPH helmholtz decomposition Conjugate gradient

Extracting angle-domain common-image gathers in VTI media using ansiotropic-helmholtz P/S wave-mode decomposition

维普期刊数据库

同方期刊数据库评论

在线全文

学校读者我要写书评

暂无评论

Petroleum Science 2023年第3期20卷 1546-1561页

作者： Le-Le Zhang Yang Zhao Lu Liu Ke Chen Jia-Hui Zuo Yi-Xin Wang Ji-Dong Yang State Key Laboratory of Petroleum Resource and Prospecting Unconventional Petroleum Research InstituteChina University of PetroleumBeijing102249China Aramco Beijing Research Center Aramco AsiaBejing100102China Department of Geophysics China University of Petroleum(East China)QingdaoShandong266580China

Common-image gathers are extensively used in amplitude versus angle(AVA)and migration velocity analysis(MVA).The current state of methods for anisotropic angle gathers extraction use slant-stack,local Fourier transform or low-rank approximation,which requires much computation.Based on an anisotropic-helmholtz P/S wave-mode decomposition method,we propose a novel and efficient approach to produce angle-domain common-image gathers(ADCIGs)in the elastic reverse time migration(ERTM)of VTI media.To start with,we derive an anisotropic-helmholtz decomposition operator from the Christoffel equation in VTI media,and use this operator to derive the decomposed formulations for anisotropic P/S waves.Second,we employ the first-order Taylor expansion to calculate the normalized term of decomposed formulations and obtain the anisotropic-helmholtz decomposition method,which generates the separated P/S wavefields with correct amplitudes and phases.Third,we develop a novel way that uses the anisotropic-helmholtz decomposition operator to define the polari-zation angles for anisotropic P/S waves and substitute these angles to decomposing formulations.The polarization angles are then calculated directly from the separated vector P-and S-wavefields and converted to the phase angles.The ADCIGs are thusly produced by applying the phase angles to VTI ERTM.In addition,we develop a concise approximate expression of residual moveout(RMO)for PP-reflections of flat reflectors in VTI media,which avoids the complex transformations between the group angles and the phase angles.The approximate RMO curves show a good agreement with the exact solution and can be used as a tool to assess the migration velocity errors.As demonstrated by two selected examples,our ADCIGs not only produce the correct kinematic responses with regards to different velocity pertubatation,but also generate the reliable amplitude responses versus different angle.The final stacking images of ADCIGs data exhibit the identical imaging effect as that of VTI ERTM.

关键词： helmholtz decomposition Angle gathers Anisotropy Elastic-RTM

Stochastic Chaos of Exponential Oscillons and Pulsons

维普期刊数据库

同方期刊数据库评论

在线全文

学校读者我要写书评

暂无评论

American Journal of Computational Mathematics 2023年第4期13卷 533-577页

作者： Victor A. Miroshnikov Department of Mathematics and Data Analytics College of Mount Saint Vincent New York USA

An exact three-dimensional solution for stochastic chaos of I wave groups of M random internal waves governed by the Navier-Stokes equations is developed. The helmholtz decomposition is used to expand the Dirichlet problem for the Navier-Stokes equations into the Archimedean, Stokes, and Navier problems. The exact solution is obtained with the help of the method of decomposition in invariant structures. Differential algebra is constructed for six families of random invariant structures: random scalar kinematic structures, time-complementary random scalar kinematic structures, random vector kinematic structures, time-complementary random vector kinematic structures, random scalar dynamic structures, and random vector dynamic structures. Tedious computations are performed using the experimental and theoretical programming in Maple. The random scalar and vector kinematic structures and the time-complementary random scalar and vector kinematic structures are applied to solve the Stokes problem. The random scalar and vector dynamic structures are employed to expand scalar and vector variables of the Navier problem. Potentialization of the Navier field becomes available since vortex forces, which are expressed via the vector potentials of the helmholtz decomposition, counterbalance each other. On the contrary, potential forces, which are described by the scalar potentials of the helmholtz decomposition, superimpose to generate the gradient of a dynamic random pressure. Various constituents of the kinetic energy are ascribed to diverse interactions of random, three-dimensional, nonlinear, internal waves with a two-fold topology, which are termed random exponential oscillons and pulsons. Quantization of the kinetic energy of stochastic chaos is developed in terms of wave structures of random elementary oscillons, random elementary pulsons, random internal, diagonal, and external elementary oscillons, random wave pulsons, random internal, diagonal, and external wave oscillons, random group pulsons, random internal, diagon

关键词： The Navier-Stokes Equations Stochastic Chaos helmholtz decomposition Exact Solution decomposition into Invariant Structures Experimental and Theoretical Programming Quantization of Kinetic Energy Random Elementary Oscillon Random Elementary Pulson Random Internal Elementary Oscillon Random Diagonal Elementary Oscillon Random External Elementary Oscillon Random Wave Pulson Random Internal Wave Oscillon Random Diagonal Wave Oscillon Random External Wave Oscillon Random Group Pulson Random Internal Group Oscillon Random Diagonal Group Oscillon Random External Group Oscillon Random Energy Pulson Random Internal Energy Oscillon Random Diagonal Energy Oscillon Random External Energy Oscillon Random Cumulative Energy Pulson

Anisotropic Curl-free Wavelet Bases on the Unit Cube

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2013年第4期29卷 801-814页

作者： Ying Chun JIANG School of Mathematics and Computational Science Guilin University of Electronic Technology

This paper deals with the construction of anisotropic curl-free wavelets on the cube [0,1]3, which satisfies the specific boundary conditions. First, one constructs curl-free wavelets on the unit cube based on one dimensional wavelets on the interval [0,1] with some boundary conditions. Then, the stability of the corresponding wavelets in curl-free space and the characterization of Sobolev spaces are studied. Finally, one gives a helmholtz decomposition and the representation of curl and div operators in wavelet coordinates.

关键词： Wavelets anisotropic curl-free cube helmholtz decomposition

New Formulas and Results for 3-Dimensional Vector Fields

维普期刊数据库

同方期刊数据库评论

在线全文

学校读者我要写书评

暂无评论

Applied Mathematics 2021年第11期12卷 1058-1096页

作者： Sadanand D. Agashe 2-B Anjaneya Society Mumbai India

New formulas are derived for once-differentiable 3-dimensional fields, using the operator . This new operator has a property similar to that of the Laplacian operator;however, unlike the Laplacian operator, the new operator requires only once-differentiability. A simpler formula is derived for the classical helmholtz decomposition. Orthogonality of the solenoidal and irrotational parts of a vector field, the uniqueness of the familiar inverse-square laws, and the existence of solution of a system of first-order PDEs in 3 dimensions are proved. New proofs are given for the helmholtz decomposition Theorem and the Divergence theorem. The proofs use the relations between the rectangular-Cartesian and spherical-polar coordinate systems. Finally, an application is made to the study of Maxwell’s equations.

关键词： Spherical-Polar Coordinates helmholtz decomposition Divergence Theorem Orthogonality Maxwell’s Equations

Relativity and the Solar Wind: The Maxwell-Equation Origins of the Solar-Wind Motional Electric Field

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Journal of Electromagnetic Analysis and Applications 2016年第8期8卷 133-151页

作者： Joseph E. Borovsky Space Science Institute Boulder CO USA CSSE University of Michigan Ann Arbor MI USA

The motional electric field of the solar wind as seen by the Earth is examined theoretically and with spacecraft measurements. As it flows outward from the sun, the solar-wind plasma carries a spatially structured magnetic field with it. To calculate the motional electric field of the solar wind the spatially structured magnetic field is Lorentz transformed;for a full physical understanding, it is also necessary to Lorentz transform the current densities and charge densities in the solar wind. Referring to Maxwell’s equations, two related questions are asked: 1) Is the source of the solar-wind motional electric field charge density in the solar wind, time derivatives of current densities in the solar wind, or both? 2) Is the solar-wind motional electric field at Earth an electrostatic field, an induction field, or a superposition of the two? A helmholtz decomposition of the motional electric field of the solar wind is made into a divergence-origin (electrostatic) and a curl-origin (induction) electric field. The global electric field associated with the outward advection of the global Parker-spiral magnetic field is found to be electrostatic with its origin being a distributed charge density in the solar-wind plasma. The electrostatic versus induction nature of the time-varying electric field associated with the advection of mesoscale magnetic structure varies with time as differently shaped magnetic structures in the solar-wind plasma pass the Earth;the mesoscale structure of the solar-wind plasma contains sheets of space charge and sheets wherein the current density has nonzero time derivatives.

关键词： Lorentz Transformation Electric Field Induction helmholtz decomposition Solar Wind Magnetic Structure Heliosphere Plasma