Numerical Method Based on DGM for Solving the System of Equations Describing Motion of Viscoelastic Fluid with Memory

Author(s):  
Ivan Soukup
2020 ◽  
Vol 69 (1) ◽  
pp. 56-61
Author(s):  
L. Yermekkyzy ◽  

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.


2022 ◽  
Vol 1211 (1) ◽  
pp. 012007
Author(s):  
E V Popov ◽  
A V Karelsky ◽  
V V Sopilov ◽  
B V Labudin ◽  
V V Cherednichenko

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.


Author(s):  
Jose´ R. Garci´a-Cascales ◽  
Henri Paille`re

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.


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