Wyniki wyszukiwania - BazTech

1

Simulation of seismic wave propagation in poroelastic media using vectorized Biot’s equations: an application to a CO2 sequestration monitoring case

Anthony Emmanuel, Vedanti Nimisha

Acta Geophysica

|

2020

|

Vol. 68, no. 2

435--444

EN

Wave propagation through porous media allows us to understand the response and interaction that occur between the elastic rock matrix and the fuid. This interaction has been described by Biot in his theory of poroelasticity. Seismic wave simulation using Biot’s formulations is computationally expensive when compared with the acoustic and elastic cases. This computational burden can be reduced by reformulating the numerical derivative operators to improve the efciency. To achieve this, we used a staggered-grid fnite diference operator to discretize 2D velocity stress equations as given by Biot’s theory. A vectorized derivative is applied on the staggered grid by shifting the coordinates. The reformulated equations were applied to compute the seismic response of a reservoir, where CO2 is being injected and the efect of injected CO2 in the formation is clearly seen in the synthetic data generated. The algorithm was coded in Python and to test its efciency, the simulation run-time was compared for both serial and vectorized equations, and the speed-up ratio was calculated. Our results show a decrease in the simulation run-time for the vectorized execution with over a factor of a hundred percent (100%). We further observed that the amplitudes of the events increase with an increase in CO2 saturation in the formation. This matches well with the real data.

2

Analiza stanów krytycznych mostu w czasoprzestrzeni

Obrębski J.

Mechanik

|

2018

|

R. 91, nr 7

591--593

PL

W pracy zbadano możliwość oceny stanu krytycznego mostu pod wpływem obciążeń ruchomych, z zastosowaniem jednolitego kryterium oceny geometrycznej zmienności i utraty stateczności konstrukcji oraz czasoprzestrzeni modelowanej różnicami skończonymi. Oba ujęcia numeryczne zostały zaproponowane przez autora. Wspomnianym kryterium jest zerowa wartość głównego wyznacznika dynamicznej macierzy sztywności dla mostu, a nawet zadania – gdy obciążenie porusza się dalej poza przęsłem. Wyniki przykładów liczbowych pokazują skuteczność metody i wpływ różnych parametrów na stanykrytyczne.

EN

In the paper was pointed possibility to evaluate critical state of bridge under travelling loading, applying uniform criterion for geometrical changeability and instability of structure and 3D-time space method modelled by finite differences. The both numerical methods are formulated by present author. In the above criterion is used value of main determinant of dynamical stiffness matrix for bridge or even for task, when loading is travelling beyond span. Results shows efficacy of the method and influence of some parameters.

3

The effect of multigrid parameters in a 3D heat diffusion equation

de Oliveira F., Franco S. R., Villela Pinto M. A.

International Journal of Applied Mechanics and Engineering

|

2018

|

Vol. 23, no. 1

213--221

EN

The aim of this paper is to reduce the necessary CPU time to solve the three-dimensional heat diffusion equation using Dirichlet boundary conditions. The finite difference method (FDM) is used to discretize the differential equations with a second-order accuracy central difference scheme (CDS). The algebraic equations systems are solved using the lexicographical and red-black Gauss-Seidel methods, associated with the geometric multigrid method with a correction scheme (CS) and V-cycle. Comparisons are made between two types of restriction: injection and full weighting. The used prolongation process is the trilinear interpolation. This work is concerned with the study of the influence of the smoothing value (v), number of mesh levels (L) and number of unknowns (N) on the CPU time, as well as the analysis of algorithm complexity.

4

Czasoprzestrzeń w analizie dynamicznej mostów

Obrębski J. B.

Problemy Mechatroniki : uzbrojenie, lotnictwo, inżynieria bezpieczeństwa

|

2017

|

Vol. 8, Nr 3 (29)

109--126

PL

W pracy zaprezentowano kolejne zastosowania i możliwości analizy dynamicznej obiektów inżynierskich za pomocą czasoprzestrzeni z wykorzystaniem różnic skończonych, w ujęciu numerycznym zaproponowanym przez autora. Obiekty te mogą być poddane różnego rodzaju obciążeniom. Tym razem jest to dźwigar mostowy z pojazdami poruszającymi się po nim z określoną prędkością. Może to być jeden pojazd lub cała ich grupa. Rozważania przeprowadzono od ogólnych różniczkowych równań ruchu przez ich uproszczenia wynikające z przyjętych założeń dla mostu, do układu dwóch równań opisujących jego giętno-skrętne zachowanie się. Pokazano przykłady konkretnych zastosowań tej metody.

EN

The paper presents next application and possibilities of dynamical analysis for engineering structures by means of 3D-Time Space Method in numerical edition proposed by the author with application of finite differences. These structures can be charged by different kinds of loadings. This time, it is a bridge girder with a car or the whole group of different carriages moving with certain velocity. The considerations were taken, starting from general differential equations of motion, through their simplified versions - resulting from taken assumptions for a bridge, until a set of two equations describing its bending-torsion behaviour. There are given examples of particular applications of the method.

5

Effect of relative velocity between rough surfaces: hydrodynamic lubrication of rotary lip seal

Lahjouji I., El Gadari M., El Fahime B., Radouani M.

International Journal of Applied Mechanics and Engineering

|

2017

|

Vol. 22, no. 2

321--332

EN

Since the sixties, most of numerical studies that model the rotary lip seal lubrication have been restricted by assuming that one of the two opposing surfaces is smooth: either the lip or the shaft. This hypothesis, although it is verified only for a shaft roughness ten times smaller than that of the seal, is the best solution to avoid the transient term “∂h/∂t” in the deterministic approach. Thus, the subject of the present study is twofold. The first part validates the current hydrodynamic model with the international literature by assuming the asperities on the lip and shaft as a two-dimensional cosine function. In the second part the Reynolds equation for rough surfaces with relative motion is solved. The numerical results show that the relative motion between rough surfaces impacts significantly the load support and the leakage rate, but affects slightly the friction torque.

6

Thermo-Mechanical Responses of an Annular Cylinder with Temperature Dependent Material Properties under Thermoelasticity without Energy Dissipation

Kumar A., Kumari B., Mukhopadhyay S.

Computational Methods in Science and Technology

|

2017

|

Vol. 23, No. 4

317--329

EN

The present work is concerned with thermoelasticity without the energy dissipation theory for a problem of an infinitely long and isotropic annular cylinder of temperature dependent physical properties.We employ the thermoelasticity theory of GN-II and derive the basic governing equations with variable material properties. The formulation is then applied to solve a boundary value problem of an annular cylinder with its inner boundary assuming to be stress free and subjected to exponential decay in temperature and sinusoidal temperature distribution. The outer boundary is also assumed to be stress free and is maintained at reference temperature in both cases. We solve the non-linear coupled differential equations by applying the finite difference approach efficiently. We analyze the numerical results in a detailed way with the help of different graphs. The effects of temperature dependency of material properties on the thermo-mechanical responses for two different time dependent temperature distributions applied at the inner boundary are highlighted.

7

A high-accuracy method of computation of X-ray waves propagation through an optical system consisting many lenses

Kshevetskii S., Wojda P.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

|

2016

|

Vol. 20, No 2

171--186

EN

The propagation of X-ray waves through an optical system consisting of many X-ray refractive lenses is considered. Two differential equations are contemplated for solving the problem for electromagnetic wave propagation: first – an equation for the electric field, second – an equation derived for a complex phase of an electric field. Both equations are solved by the use of a finite-difference method. The simulation error is estimated mathematically and investigated. The presented results for equations show that in order to establish a high accuracy computation a much smaller number of points is needed to solve the problem of X-ray waves propagation through a multi-lens system when the method for the second equation is used. The reason for such a result is that the electric field of a wave after passing through many lenses is a quickly oscillating function of coordinates, while the electric field phase is a quickly increasing, but not oscillating function. Therefore, a very detailed difference grid, which is necessary to approximate the considered electric field can be replaced by not such a detailed grid, when computations are made for the complex wave of the electric field. The simulation error of both suggested methods is estimated. It is shown that the derived equation for a phase function allows efficient simulation of propagation of X-rays for the multi-lens optical system.

8

Load distribution in the worm meshing

Sabiniak H. G.

Journal of Theoretical and Applied Mechanics

|

2016

|

Vol. 54 nr 4

1169--1181

EN

The paper presents a theoretical analysis of deflections of circular and rectangular cantilever plates of an elastically built-in edge. The problem has been solved using the finite difference method. A method of determination of load distribution between two plates being in contact along an arbitrary line has been presented. Different shapes of these plates constitute models of mating of cylindrical and globoidal worm meshings. To verify the presented theory of searching for load distributions along the contact lines in these meshings, experimental investigations with the freezing of stresses in the cylindrical worm meshing have been carried out. Directions of investigations that would specify further theoretical considerations over load distribution in globoidal gear meshings have been indicated.

9

The discontinuous Galerkin method with higher degree finite difference compatibility conditions and arbitrary local and global basis functions

Jaśkowiec J.

Computer Assisted Methods in Engineering and Science

|

2016

|

Vol. 23, no. 2/3

109--132

EN

This paper focuses on the discontinuous Galerkin (DG) method in which the compatibility condition on the mesh skeleton and Dirichlet boundary condition on the outer boundary are enforced with the help of one-dimensional finite difference (FD) rules, while in the standard approach those conditions are satisfied by the penalty constraints. The FD rules can be of arbitrary degree and in this paper the rules are applied up to fourth degree. It is shown that the method presented in this paper gives better results in comparison to the standard version of the DG method. The method is based on discontinuous approximation, which means that it can be constructed using arbitrary local basis functions in each finite element. It is quite easy to incorporate some global basis functions in the approximation field and this is also shown in the paper. The paper is illustrated with a couple of two-dimensional examples.

10

Some quantitative evaluations on finite difference local and global results

Costamagna E.

Archives of Electrical Engineering

|

2016

|

Vol. 65, nr 2

263--272

EN

Refined Schwarz-Christoffel (SC) conformal transformations allow us to perform reliable quantitative evaluation of the accuracy of local computation of electric and magnetic fields with limited effort, which can be useful to complement well known comparisons of global results. In this paper some examples are presented for mesh point potentials obtained by means of finite difference (FD) methods, but it is possible that similar considerations will be useful in the case of finite element methods (FEM) or meshless computations too.

11

Implementation of Elastic Prestack Reverse-Time Migration Using an Efficient Finite-Difference Scheme

Yan H., Yang L., Dai H., Li X. Y.

Acta Geophysica

|

2016

|

Vol. 64, no. 5

1605--1625

EN

Elastic reverse-time migration (RTM) can reflect the underground elastic information more comprehensively than single-component Pwave migration. One of the most important requirements of elastic RTM is to solve wave equations. The imaging accuracy and efficiency of RTM depends heavily on the algorithms used for solving wave equations. In this paper, we propose an efficient staggered-grid finite-difference (SFD) scheme based on a sampling approximation method with adaptive variable difference operator lengths to implement elastic prestack RTM. Numerical dispersion analysis and wavefield extrapolation results show that the sampling approximation SFD scheme has greater accuracy than the conventional Taylor-series expansion SFD scheme. We also test the elastic RTM algorithm on theoretical models and a field data set, respectively. Experiments presented demonstrate that elastic RTM using the proposed SFD scheme can generate better images than that using the Taylor-series expansion SFD scheme, particularly for PS images. Furthermore, the application of adaptive variable difference operator lengths can effectively improve the computational efficiency of elastic RTM.

12

Stability of finite difference schemes for generalized von Foerster equations with renewal

Leszczyński H., Zwierkowski P.

Opuscula Mathematica

|

2014

|

Vol. 34, no. 2

375--386

EN

We consider a von Foerster-type equation describing the dynamics of a population with the production of offsprings given by the renewal condition. We construct a finite difference scheme for this problem and give sufficient conditions for its stability with respect to l1 and l∞ norms.

13

Radiation effects on MHD flow past an impulsively started infinite vertical plate with mass diffusion

Chandrakala P., Narayana Bhaskar P.

International Journal of Applied Mechanics and Engineering

|

2014

|

Vol. 19, no. 1

17--26

EN

The effects of thermal radiation on a flow past an impulsively started infinite vertical plate in the presence of a magnetic field have been studied. The fluid considered is a gray, absorbing-emitting radiation but non-scattering medium. The dimensionless governing equations are solved by an efficient, more accurate, unconditionally stable and fast converging implicit scheme. The effects of velocity and temperature for different parameters such as the thermal radiation, magnetic field, Schmidt number, thermal Grashof number and mass Grashof number are studied. It is observed that the velocity decreases in the presence of thermal radiation or a magnetic field.

14

Finite difference solution of unsteady flow past an oscillating semi-infinite vertical plate with variable surface temperature and uniform mass flux

Muthucumaraswamy R., Saravanan B.

International Journal of Applied Mechanics and Engineering

|

2014

|

Vol. 19, no. 4

709--724

EN

A finite difference solution of an unsteady flow past an oscillating semi-infinite vertical place with variable temperature and uniform mass flux is presented here. The fluid considered here is a gray, absorbing-emitting radiation but a non-scattering medium. The dimensionless governing equations are solved by an efficient, more accurate, and unconditionally stable and fast converging implicit scheme. The steady state velocity, temperature and concentration profiles are shown graphically. The effect of velocity and temperature for different physical parameters such as the thermal radiation, Schmidt number, thermal Grashof number and mass Grashof number is studied. It is observed that the velocity decreases in the presence of thermal radiation. It is also observed that the time taken to reach a steady-state is more in the case of vertical plate than horizontal plate.

15

Chemical reaction effects on MHD flow past an impulsively started isothermal vertical plate with uniform mass diffusion

Chandrakala P., Narayana Bhaskar P.

International Journal of Applied Mechanics and Engineering

|

2014

|

Vol. 19, no. 2

419--426

EN

A numerical technique is employed to derive a solution to the transient natural convection flow of an incompressible viscous fluid past an impulsively started infinite isothermal vertical plate with uniform mass diffusion in the presence of a magnetic field and homogeneous chemical reaction of first order. The governing equations are solved using implicit finite-difference method. The effects of velocity, temperature and concentration for different parameters such as the magnetic field parameter, chemical reaction parameter, Prandtl number, Schmidt number, thermal Grashof number and mass Grashof number are studied. It is observed that the fluid velocity decreases with increasing the chemical reaction parameter and the magnetic field parameter.

16

Numerical Solution of Unsteady Radiative Flow Past an Oscillating Semi - Infinite Vertical Plate with Uniform Mass Flux

Muthucumaraswamy R., Saravanan B.

Computational Methods in Science and Technology

|

2013

|

Vol. 19, No. 1

23--31

EN

Thermal radiation effects on unsteady flow past an oscillating semi-infinite isothermal vertical plate with uniform mass flux have been studied. The fluid considered here is a gray, absorbing-emitting radiation but non-scattering medium. The dimensionless governing equations are solved by an efficient, more accurate, and unconditionally stable and fast converging implicit scheme. The effect of velocity and temperature for different parameters like thermal radiation, Schmidt number, thermal Grashof number and mass Grashof number are studied. It is observed that the velocity decreases in the presence of thermal radiation.

17

Effects of heat transfer on dusty gas flow past a semi-infinite vertical plate

Kulandaivel T.

International Journal of Applied Mechanics and Engineering

|

2012

|

Vol. 17, no. 4

1339-1346

EN

Effects of heat transfer on dusty gas flow past a semi-infinite vertical plate with variable temperature is considered. The governing boundary layer equations for this problem are set up and non-dimensional governing equations are solved by an implicit finite difference scheme of Crank-Nicolson method, which is fast convergent and unconditionally stable. Gas velocity, dust particle velocity, temperature, skin-friction and Nusselt numbers are calculated numerically for various parameters and are shown graphically. It is observed that an increase in the mass concentration of dust causes a fall in the dusty gas velocity but an increase in the skin-friction.

18

Crank-Nicolson semi-implicit approach for numerical solutions of two- dimensional coupled nonlinear Burgers' equations

Srivastava V. K., Tamsir M.

International Journal of Applied Mechanics and Engineering

|

2012

|

Vol. 17, no. 2

571-581

EN

The two-dimensional Burgers' equation is a mathematical model which is used to describe various kinds of phenomena such as turbulence and viscous fluid. In this paper, Crank-Nicolson semi-implicit scheme is used to handle such problem. The proposed scheme forms a system of linear algebraic difference equations to be solved at each time-step. The linear system is solved by direct method. Numerical results are compared with those of exact solutions and other available results. The present method performs well. To our best knowledge no one has solved Burgers' equations using this scheme. The proposed scheme can be extended for solving non-linear problems arising in various branches of engineering and science.

19

Convergence of a finite difference scheme for von Foerster equation with functional dependence

Zwierkowski P.

Demonstratio Mathematica

|

2012

|

Vol. 45, nr 3

725-737

EN

We analyse a finite difference scheme for von Foerster-McKendrick type equations with functional dependence forward in time and backward with respect to one dimensional spatial variable. Some properties of solutions of a scheme are given. Convergence of a finite difference scheme is proved. The presented theory is illustrated by a numerical example.

20

Mathematical modeling of air duct heater using the finite difference method

Sarafraz M. M. M. M., Peyghambarzadeh S. M. S. M., Marahel A. A.

Polish Journal of Chemical Technology

|

2011

|

Vol. 13, nr 4

47-52

EN

In this research, mathematical modeling of a duct heater has been performed using energy conservation law, Stefan-Boltzman law in thermal radiation, Fourier’s law in conduction heat transfer, and Newton’s law of cooling in convection heat transfer. The duct was divided to some elements with equal length. Each element has been studied separately and air physical properties in each element have been used based on its temperature. The derived equations have been solved using the finite difference method and consequently air temperature, internal and external temperatures of the wall, internal and external convection heat transfer coeffi cients, and the quantity of heat transferred have been calculated in each element and effects of the variation of heat transfer parameters have been surveyed. The results of modelling presented in this paper can be used for the design and optimization of heat exchangers.