A numerical method for solving Vlasov's system of equations, based on a combination of the particles in a cell and the “water bag” methods

1979 ◽  
Vol 19 (1) ◽  
pp. 170-178
Author(s):  
N.E. Andreev ◽  
V.P. Silin ◽  
G.L. Stenchikov
Keyword(s):  
Numerical Method ◽  
System Of Equations ◽  
A Cell

DEFINITION OF HYDRAULIC RESISTANCE OF UNDERGROUND OIL PIPELINE

2020 ◽  
Vol 69 (1) ◽  
pp. 56-61
Author(s):  
L. Yermekkyzy ◽  
Keyword(s):  
Heat Transfer ◽  
Inverse Problem ◽  
Numerical Method ◽  
Hydraulic Resistance ◽  
High Viscosity ◽  
System Of Equations ◽  
Oil Viscosity ◽  
Oil Pipeline ◽  
Conservation Of Momentum ◽  
Definition Of

The results of solving the inverse problem of determining the hydraulic resistance of a main oil pipeline are presented. The formulation of the inverse problem is formulated, a numerical method for solving the system of equations is described. The hydraulic resistance of the pipeline during the "hot" pumping of high-curing and high-viscosity oil changes during operation. Oil temperature decreases along the length of the pipeline due to heat transfer from the soil, leading to an increase in oil viscosity and an increase in hydraulic resistance.The dependence of the hydraulic resistance of the pipeline on the parameters of oil pumping is determined by solving the inverse problem. The inverse problem statement consists of a system of equations of laws of conservation of momentum, mass, energy and hydraulic resistance in the form of Altshul with unknown coefficients. The system of partial differential equations of hyperbolic type for speed and pressure is solved by the numerical method of characteristics, and the heat transfer equations by the iterative method of running counting.

scholarly journals Calculation features of compressed-bent build-up timber columns with nonlinear-deformable shear bracings

2022 ◽  
Vol 1211 (1) ◽  
pp. 012007
Author(s):  
E V Popov ◽  
A V Karelsky ◽  
V V Sopilov ◽  
B V Labudin ◽  
V V Cherednichenko
Keyword(s):  
Problem Solving ◽  
Numerical Method ◽  
Compressive Force ◽  
Bending Moment ◽  
Longitudinal Axis ◽  
Nonlinear Dependence ◽  
System Of Equations ◽  
Loading Process ◽  
Is Development

Abstract Object of research is build-up compressed–bent and eccentrically compressed columns on yielding nonlinear – deformable shear bracings. Purpose of the research is development of a numerical method for calculation of columns, allowing to take in account the influence of deflection of elastic axis of bar on the increment of the bending moment from the action of longitudinal compressive force and the nonlinear dependence between the forces and deformations in the shear bracings. Problem-solving method consists in dividing the column into separate sections, a system of equations is compiled from the condition of equality of the increment of concentrated shears. The loading process is divided into a set number of stages, at each forces in the shear bracings, the stresses in the branches, and the buckling function of the elastic axis of the element are determined. The obtained values of forces in the shear bracings and buckling are used to specify stiffness of the bracings and component of the bending moment arising due to eccentric application of the longitudinal compressive force when longitudinal axis of the element is deflecting. To obtain the resulting values, the obtained forces, deflections and stresses in the branches at each calculation stage are summed up.

Application of AUSM Schemes to Multi-Dimensional Two-Phase Flow Problems

2003 ◽  
Author(s):  
Jose´ R. Garci´a-Cascales ◽  
Henri Paille`re
Keyword(s):  
Experimental Data ◽  
Phase Change ◽  
Numerical Method ◽  
Two Phase Flow ◽  
Equations Of State ◽  
System Of Equations ◽  
Phase Flow ◽  
Two Phase ◽  
Flow Problems ◽  
Future Work

In this paper we study the extension of AUSM schemes to multi-dimensional two-phase flow problems with phase change. We present the system of equations characterizing these problems, the closure relationships and the equations of state to close the system. We present some of the most important characteristics of the numerical method used in this work, discribing how primitive variables are determined from conserved variables. Numerical results, corresponding to a fast depressurization benchmark, are included and compared with some experimental data. Conclusions are then drawn and future work briefly described.

Counterexamples to a conjecture about spherical diagrams

1986 ◽  
Vol 100 (3) ◽  
pp. 539-543
Author(s):  
S. M. Gersten ◽  
James Howie
Keyword(s):  
Singular System ◽  
System Of Equations ◽  
A Cell

A spherical diagram over a 2-complex X consists of a tessellation T of the 2-sphere, together with a combinatorial map (that is, one which maps each cell homeomorphically on to a cell). In [2] and [6] a number of conjectures were made concerning spherical diagrams over a 2-complex X with H2(X) = 0. There are also related conjectures in [7]. The motivation for all of these conjectures is that they imply the Kervaire Conjecture: every non-singular system of equations over a group can be solved in some overgroup (see [1, 2, 4, 6, 7] for details and discussion).

Free element method and its application in CFD

2019 ◽  
Vol 36 (8) ◽  
pp. 2747-2765 ◽  
Author(s):  
X.W. Gao ◽  
Huayu Liu ◽  
Miao Cui ◽  
Kai Yang ◽  
Haifeng Peng
Keyword(s):  
Fluid Mechanics ◽  
Numerical Method ◽  
Compressible Fluid ◽  
System Of Equations ◽  
Individual Element ◽  
Governing Equations ◽  
Content Type ◽  
Set Up ◽  
Free Element ◽  
Element Method

Purpose The purpose of this paper is to propose a new strong-form numerical method, called the free element method, for solving general boundary value problems governed by partial differential equations. The main idea of the method is to use a locally formed element for each point to set up the system of equations. The proposed method is used to solve the fluid mechanics problems. Design/methodology/approach The proposed free element method adopts the isoparametric elements as used in the finite element method (FEM) to represent the variation of coordinates and physical variables and collocates equations node-by-node based on the newly derived element differential formulations by the authors. The distinct feature of the method is that only one independently formed individual element is used at each point. The final system of equations is directly formed by collocating the governing equations at internal points and the boundary conditions at boundary points. The method can effectively capture phenomena of sharply jumped variables and discontinuities (e.g. the shock waves). Findings a) A new numerical method called the FEM is proposed; b) the proposed method is used to solve the compressible fluid mechanics problems for the first time, in which the shock wave can be naturally captured; and c) the method can directly set up the system of equations from the governing equations. Originality/value This paper presents a completely new numerical method for solving compressible fluid mechanics problems, which has not been submitted anywhere else for publication.

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