umurdin dalabaev | University of world economy and diplomacy (original) (raw)
Papers by umurdin dalabaev
EJAS-17966 Camera Ready European Journal of Applied Sciences – Vol. 12, No. 6, 2024
The article considers an approximate analytical solution of a linear parabolic equation with init... more The article considers an approximate analytical solution of a linear parabolic equation with initial and boundary conditions. Many problems in engineering applications are reduced to solving an initial-boundary value problem of parabolic type. There are various analytical, approximate-analytical and numerical methods for solving such problems. The most popular difference methods for solving an initial-boundary value problem of a parabolic equation are explicit, implicit and Crank-Nicolson schemes. Here, we consider methods for obtaining an approximate-analytical solution based on the movable node method and their comparative analysis of these schemes for specific test problems. A comparison of the exact and approximate solutions is made using specific examples.
www.ijres.org Volume 12 Issue 11 ǁ November 2024 ǁ PP. 134-138
The paper investigates the nature of the lifting force acting on a porous cylindrical particle. T... more The paper investigates the nature of the lifting force acting on a porous cylindrical particle. The porous cylinder
is located perpendicular to the flow and is flown by a viscous liquid in a flat channel. The calculation of the lifting
force acting on the cylinder is made for different values of the Reynolds number, porosity and their location in
the flow.
E3S web of conferences, 2024
AIP conference proceedings, 2024
This article discusses the issue of the possibility of calculating the approximation error. When ... more This article discusses the issue of the possibility of calculating the approximation error. When replacing differential equations with discrete ones, one of the key issues is the closeness of the discrete solution to the exact solution. For the difference solution of the problem, a grid area is formed. The discrete solution is determined at the nodal points. Traditionally, in questions of replacing a differential equation with a descriptive one, one usually indicates the degree of approximation of the O(h p) type. Here h is the grid step. However, it is possible to calculate the approximation error at nodal points based on the method of moving nodes. The method of moving nodes allows obtaining an approximate analytical expression. On the basis of the approximate form, it is possible to calculate the approximation error. On the other hand, at each node one can construct a differential analog of the difference equation. Using simple examples, the calculation of approximation errors is demonstrated and schemes of the collocation type are constructed .
E3S Web of Conferences
The paper considers the method of averaging over a movable liquid control volume for some problem... more The paper considers the method of averaging over a movable liquid control volume for some problems of fluid mechanics. The authors study the process of obtaining a solution for the problem of fluid flow with different configurations along the cross section of a pipe with a filled porous medium, as well as flow in an open-flow channel. Obtaining an approximate analytical solution based on a movable control volume is described. The well-known control volume method used in numerical analysis is used considering its displacement. The method of displacement makes it possible to obtain an analytical representation of the solution of the problem under consideration. At the same time, obtaining an analytical solution method is achieved by averaging the equation describing the flows over the control volume. Based on the obtained solution in the limit, we obtain solutions to the problem without considering porous media, and with different pipe cross-sections (flat, round, ellipsoidal and rect...
E3S web of conferences, Dec 31, 2022
The paper investigates the flow of an incompressible fluid in an open stream with an unequal bott... more The paper investigates the flow of an incompressible fluid in an open stream with an unequal bottom and slope. The uneven bottom is due to vegetation. The flow is modeled on the basis of the two-velocity Rakhmatulin model, in a laminar regime from zero velocity of the discrete phase. The flow of a viscous fluid in a channel with an open stream with vegetation at the bottom of the stream is considered. The results of numerical simulation of the hydrodynamic features of a two-dimensional viscous flow are presented. The Kozeny-Karman ratio is used as the force of interaction with vegetation. The methods of computational experiment are used to study the effects of non-uniformity of the fluid velocity field, which arise due to vegetation. A qualitative comparison of velocity inhomogeneities is carried out. For the numerical implementation of the resulting equation, which is a generalization of the Navier-Stokes equation, a SIMPLE-like algorithm with appropriate generalizations was used. A single algorithm is applied for the entire area, without highlighting the free and porous zone.
Rakhmatulin's Filtration Equation for Describing Blood Flow with Stenosis
The paper deals with the numerical simulation of the flow of Newtonian fluid by the control volum... more The paper deals with the numerical simulation of the flow of Newtonian fluid by the control volume method, which simulates the flow of blood in a blood vessel with stenosis. An interpenetrating model of two-phase media is used to describe the process. Based on this model, under appropriate simplifying assumptions, we obtain the Navier-Stokes equations in the free (outside the stenosis region) zone, and in the stenotic region, we obtain a system of equations generalizing the filtration equation. Stenosis is viewed as a porous medium. The influence of the Reynolds number and the degree of stenosis on the nature of the flow on the behavior of blood is investigated.
An explicit expression of ordinary difference schemes for differential equations by the moved node method
This article discusses the issue of the possibility of calculating the approximation error. When ... more This article discusses the issue of the possibility of calculating the approximation error. When replacing differential equations with discrete ones, one of the key issues is the closeness of the discrete solution to the exact solution. For the difference solution of the problem, a grid area is formed. The discrete solution is determined at the nodal points. Traditionally, in questions of replacing a differential equation with a descriptive one, one usually indicates the degree of approximation of the O(h p) type. Here h is the grid step. However, it is possible to calculate the approximation error at nodal points based on the method of moving nodes. The method of moving nodes allows obtaining an approximate analytical expression. On the basis of the approximate form, it is possible to calculate the approximation error. On the other hand, at each node one can construct a differential analog of the difference equation. Using simple examples, the calculation of approximation errors is demonstrated and schemes of the collocation type are constructed .
Book Publisher International (a part of SCIENCEDOMAIN International), May 4, 2021
In many environmental, industrial and biological processes, flows occur in a saturated porous flu... more In many environmental, industrial and biological processes, flows occur in a saturated porous fluid medium. The transport of substances between surface water and groundwater is a very serious problem. The basis of the mathematical model is based on the interpenetrating model (Rahmatullin model) of two-phase media. The proposed equations make it possible to study the flow of a liquid in and outside the porous region in a uniform manner. In this case, the Navier-Stokes equation is obtained in the liquid region. In the porous region, the equations are close to the Brinkman model. In connection with the description of the flow from the standpoint of a single equation for the entire region, there is no need to set boundary conditions in the separation region (such as Beavers – Joseph – Saffman). Cross-border conditions arise if the energy estimation is used for the porous region. In this case, the order of the systems of equations in each area is different. On the basis of the proposed model, the energy estimation for the equation of Rahmatullin is derived using energy inequalities. The difference scheme of the equation of Rahmatullin is constructed and the stability of the constructed scheme is obtained.
Journal of engineering physics and thermophysics, Nov 1, 2011
The character of the lift on a cylindrical (porous and solid) particle in Poiseuille flow of a pl... more The character of the lift on a cylindrical (porous and solid) particle in Poiseuille flow of a plane channel has been investigated. The lift at various values of the Reynolds number, the particle size, and its position in the flow have been calculated.
Journal of engineering physics and thermophysics, May 1, 1997
A solution of the problem of flow through an immovable granular layer is presented.
IOP conference series, Feb 1, 2022
Filtration of an incompressible liquid (gas) in a non-deformable porou s medium is investigated. ... more Filtration of an incompressible liquid (gas) in a non-deformable porou s medium is investigated. The results of numerical simulation of the hydrodynamic features of the flow arising after the passage of the liquid through a layer of an immobile porous medium are presented. An interpenetrating model of multiphase media is used to describe such flows. The porosity and permeability of the porous medium, as well as the force of interfacial interaction, are considered in the framework of compliance with the Kozeny-Karman ratio. The influence of the geometrical shape of the bulk layer on the nature and magnitude of the inhomogeneity of the flow velocity behind the obstacle is shown. Considering the shape of the porous medium significantly affects the flow parameters. Numerical simulation results are compared with experimental data. The effects of the non-uniformity of the fluid velocity field arising from the curvature of the layer surface and the influence of the arising inhomogeneity on the velocity are investigated by the methods of a computational experiment. A qualitative comparison is made of velocity inhomogeneities when a fluid flows through a porous obstacle. For the numerical implementation of the filtration equation of the interpenetrating model, a SIMPLElike algorithm was used.
It is known that the control volume method is widely used in numerical analysis for solving bound... more It is known that the control volume method is widely used in numerical analysis for solving boundary value problems. Using this approach allows obtaining an approximate-analytical method for obtaining a solution to boundary value problems. A method for averaging boundary value problems over the volume being moved is proposed. The control volume is unique and movable in the area under consideration. The solution of the problem is obtained by averaging the differential equation over the volume being moved. For two-dimensional boundary value problems, it is also recommended to average over one variable. On the basis of which an ordinary differential is obtained and the solution of which gives a better solution to the problem. Examples are given.
E3S Web of Conferences
The paper proposes a simple approximate method for solving differential equations for boundary va... more The paper proposes a simple approximate method for solving differential equations for boundary value problems. A method is proposed for averaging differential equations over a moving volume, which allows obtaining approximate analytical solutions of differential equations. The control volume is the only one in the considered area of the boundary value problem. In this case, the control volume is considered to be moved in the area under consideration. Based on the averaging of boundary value problems over the volume being moved, an algebraic equation is obtained. When averaging over one of the variables (in the case of a two-dimensional problem), ordinary differential equations are obtained. Examples are given.
E3S Web of Conferences
The flow of liquid through pipes with various configurations is found in many energy and technolo... more The flow of liquid through pipes with various configurations is found in many energy and technological processes. Knowledge of the distribution of velocity and flow through these pipes allows hydrological engineers to find resistance through the pipes and optimize the fluid pumping process. The article suggests a simple engineering method for finding the velocity over pipe sections
Book Publisher International (a part of SCIENCEDOMAIN International), May 16, 2022
Filtration of an incompressible liquid (gas) in a non-deformable porous medium is investigated. T... more Filtration of an incompressible liquid (gas) in a non-deformable porous medium is investigated. The results of numerical simulation of the hydrodynamic features of the flow arising after the passage of the liquid through a layer of an immobile porous medium are presented. An interpenetrating model of multiphase media is used to describe such flows. Kozeny-Karman relations are used as the interaction force. The influence of the geometrical shape of the bulk layer on the nature and magnitude of the inhomogeneity of the flow velocity around the obstacle is shown. The shape of the porous medium significantly affects the flow parameters. Numerical simulation results are compared with experimental data. The shape of the porous medium significantly affects the flow parameters. Numerical simulation results are compared with experimental data. The effects of non-uniformity of the fluid velocity field arising due to the shape of the layer surface are investigated by the methods of a computational experiment. A qualitative comparison is made of velocity inhomogeneities when a fluid flows through a porous obstacle. For the numerical implementation of the filtration equation of the interpenetrating model, a SIMPLE-like algorithm was used.
EJAS-17966 Camera Ready European Journal of Applied Sciences – Vol. 12, No. 6, 2024
The article considers an approximate analytical solution of a linear parabolic equation with init... more The article considers an approximate analytical solution of a linear parabolic equation with initial and boundary conditions. Many problems in engineering applications are reduced to solving an initial-boundary value problem of parabolic type. There are various analytical, approximate-analytical and numerical methods for solving such problems. The most popular difference methods for solving an initial-boundary value problem of a parabolic equation are explicit, implicit and Crank-Nicolson schemes. Here, we consider methods for obtaining an approximate-analytical solution based on the movable node method and their comparative analysis of these schemes for specific test problems. A comparison of the exact and approximate solutions is made using specific examples.
www.ijres.org Volume 12 Issue 11 ǁ November 2024 ǁ PP. 134-138
The paper investigates the nature of the lifting force acting on a porous cylindrical particle. T... more The paper investigates the nature of the lifting force acting on a porous cylindrical particle. The porous cylinder
is located perpendicular to the flow and is flown by a viscous liquid in a flat channel. The calculation of the lifting
force acting on the cylinder is made for different values of the Reynolds number, porosity and their location in
the flow.
E3S web of conferences, 2024
AIP conference proceedings, 2024
This article discusses the issue of the possibility of calculating the approximation error. When ... more This article discusses the issue of the possibility of calculating the approximation error. When replacing differential equations with discrete ones, one of the key issues is the closeness of the discrete solution to the exact solution. For the difference solution of the problem, a grid area is formed. The discrete solution is determined at the nodal points. Traditionally, in questions of replacing a differential equation with a descriptive one, one usually indicates the degree of approximation of the O(h p) type. Here h is the grid step. However, it is possible to calculate the approximation error at nodal points based on the method of moving nodes. The method of moving nodes allows obtaining an approximate analytical expression. On the basis of the approximate form, it is possible to calculate the approximation error. On the other hand, at each node one can construct a differential analog of the difference equation. Using simple examples, the calculation of approximation errors is demonstrated and schemes of the collocation type are constructed .
E3S Web of Conferences
The paper considers the method of averaging over a movable liquid control volume for some problem... more The paper considers the method of averaging over a movable liquid control volume for some problems of fluid mechanics. The authors study the process of obtaining a solution for the problem of fluid flow with different configurations along the cross section of a pipe with a filled porous medium, as well as flow in an open-flow channel. Obtaining an approximate analytical solution based on a movable control volume is described. The well-known control volume method used in numerical analysis is used considering its displacement. The method of displacement makes it possible to obtain an analytical representation of the solution of the problem under consideration. At the same time, obtaining an analytical solution method is achieved by averaging the equation describing the flows over the control volume. Based on the obtained solution in the limit, we obtain solutions to the problem without considering porous media, and with different pipe cross-sections (flat, round, ellipsoidal and rect...
E3S web of conferences, Dec 31, 2022
The paper investigates the flow of an incompressible fluid in an open stream with an unequal bott... more The paper investigates the flow of an incompressible fluid in an open stream with an unequal bottom and slope. The uneven bottom is due to vegetation. The flow is modeled on the basis of the two-velocity Rakhmatulin model, in a laminar regime from zero velocity of the discrete phase. The flow of a viscous fluid in a channel with an open stream with vegetation at the bottom of the stream is considered. The results of numerical simulation of the hydrodynamic features of a two-dimensional viscous flow are presented. The Kozeny-Karman ratio is used as the force of interaction with vegetation. The methods of computational experiment are used to study the effects of non-uniformity of the fluid velocity field, which arise due to vegetation. A qualitative comparison of velocity inhomogeneities is carried out. For the numerical implementation of the resulting equation, which is a generalization of the Navier-Stokes equation, a SIMPLE-like algorithm with appropriate generalizations was used. A single algorithm is applied for the entire area, without highlighting the free and porous zone.
Rakhmatulin's Filtration Equation for Describing Blood Flow with Stenosis
The paper deals with the numerical simulation of the flow of Newtonian fluid by the control volum... more The paper deals with the numerical simulation of the flow of Newtonian fluid by the control volume method, which simulates the flow of blood in a blood vessel with stenosis. An interpenetrating model of two-phase media is used to describe the process. Based on this model, under appropriate simplifying assumptions, we obtain the Navier-Stokes equations in the free (outside the stenosis region) zone, and in the stenotic region, we obtain a system of equations generalizing the filtration equation. Stenosis is viewed as a porous medium. The influence of the Reynolds number and the degree of stenosis on the nature of the flow on the behavior of blood is investigated.
An explicit expression of ordinary difference schemes for differential equations by the moved node method
This article discusses the issue of the possibility of calculating the approximation error. When ... more This article discusses the issue of the possibility of calculating the approximation error. When replacing differential equations with discrete ones, one of the key issues is the closeness of the discrete solution to the exact solution. For the difference solution of the problem, a grid area is formed. The discrete solution is determined at the nodal points. Traditionally, in questions of replacing a differential equation with a descriptive one, one usually indicates the degree of approximation of the O(h p) type. Here h is the grid step. However, it is possible to calculate the approximation error at nodal points based on the method of moving nodes. The method of moving nodes allows obtaining an approximate analytical expression. On the basis of the approximate form, it is possible to calculate the approximation error. On the other hand, at each node one can construct a differential analog of the difference equation. Using simple examples, the calculation of approximation errors is demonstrated and schemes of the collocation type are constructed .
Book Publisher International (a part of SCIENCEDOMAIN International), May 4, 2021
In many environmental, industrial and biological processes, flows occur in a saturated porous flu... more In many environmental, industrial and biological processes, flows occur in a saturated porous fluid medium. The transport of substances between surface water and groundwater is a very serious problem. The basis of the mathematical model is based on the interpenetrating model (Rahmatullin model) of two-phase media. The proposed equations make it possible to study the flow of a liquid in and outside the porous region in a uniform manner. In this case, the Navier-Stokes equation is obtained in the liquid region. In the porous region, the equations are close to the Brinkman model. In connection with the description of the flow from the standpoint of a single equation for the entire region, there is no need to set boundary conditions in the separation region (such as Beavers – Joseph – Saffman). Cross-border conditions arise if the energy estimation is used for the porous region. In this case, the order of the systems of equations in each area is different. On the basis of the proposed model, the energy estimation for the equation of Rahmatullin is derived using energy inequalities. The difference scheme of the equation of Rahmatullin is constructed and the stability of the constructed scheme is obtained.
Journal of engineering physics and thermophysics, Nov 1, 2011
The character of the lift on a cylindrical (porous and solid) particle in Poiseuille flow of a pl... more The character of the lift on a cylindrical (porous and solid) particle in Poiseuille flow of a plane channel has been investigated. The lift at various values of the Reynolds number, the particle size, and its position in the flow have been calculated.
Journal of engineering physics and thermophysics, May 1, 1997
A solution of the problem of flow through an immovable granular layer is presented.
IOP conference series, Feb 1, 2022
Filtration of an incompressible liquid (gas) in a non-deformable porou s medium is investigated. ... more Filtration of an incompressible liquid (gas) in a non-deformable porou s medium is investigated. The results of numerical simulation of the hydrodynamic features of the flow arising after the passage of the liquid through a layer of an immobile porous medium are presented. An interpenetrating model of multiphase media is used to describe such flows. The porosity and permeability of the porous medium, as well as the force of interfacial interaction, are considered in the framework of compliance with the Kozeny-Karman ratio. The influence of the geometrical shape of the bulk layer on the nature and magnitude of the inhomogeneity of the flow velocity behind the obstacle is shown. Considering the shape of the porous medium significantly affects the flow parameters. Numerical simulation results are compared with experimental data. The effects of the non-uniformity of the fluid velocity field arising from the curvature of the layer surface and the influence of the arising inhomogeneity on the velocity are investigated by the methods of a computational experiment. A qualitative comparison is made of velocity inhomogeneities when a fluid flows through a porous obstacle. For the numerical implementation of the filtration equation of the interpenetrating model, a SIMPLElike algorithm was used.
It is known that the control volume method is widely used in numerical analysis for solving bound... more It is known that the control volume method is widely used in numerical analysis for solving boundary value problems. Using this approach allows obtaining an approximate-analytical method for obtaining a solution to boundary value problems. A method for averaging boundary value problems over the volume being moved is proposed. The control volume is unique and movable in the area under consideration. The solution of the problem is obtained by averaging the differential equation over the volume being moved. For two-dimensional boundary value problems, it is also recommended to average over one variable. On the basis of which an ordinary differential is obtained and the solution of which gives a better solution to the problem. Examples are given.
E3S Web of Conferences
The paper proposes a simple approximate method for solving differential equations for boundary va... more The paper proposes a simple approximate method for solving differential equations for boundary value problems. A method is proposed for averaging differential equations over a moving volume, which allows obtaining approximate analytical solutions of differential equations. The control volume is the only one in the considered area of the boundary value problem. In this case, the control volume is considered to be moved in the area under consideration. Based on the averaging of boundary value problems over the volume being moved, an algebraic equation is obtained. When averaging over one of the variables (in the case of a two-dimensional problem), ordinary differential equations are obtained. Examples are given.
E3S Web of Conferences
The flow of liquid through pipes with various configurations is found in many energy and technolo... more The flow of liquid through pipes with various configurations is found in many energy and technological processes. Knowledge of the distribution of velocity and flow through these pipes allows hydrological engineers to find resistance through the pipes and optimize the fluid pumping process. The article suggests a simple engineering method for finding the velocity over pipe sections
Book Publisher International (a part of SCIENCEDOMAIN International), May 16, 2022
Filtration of an incompressible liquid (gas) in a non-deformable porous medium is investigated. T... more Filtration of an incompressible liquid (gas) in a non-deformable porous medium is investigated. The results of numerical simulation of the hydrodynamic features of the flow arising after the passage of the liquid through a layer of an immobile porous medium are presented. An interpenetrating model of multiphase media is used to describe such flows. Kozeny-Karman relations are used as the interaction force. The influence of the geometrical shape of the bulk layer on the nature and magnitude of the inhomogeneity of the flow velocity around the obstacle is shown. The shape of the porous medium significantly affects the flow parameters. Numerical simulation results are compared with experimental data. The shape of the porous medium significantly affects the flow parameters. Numerical simulation results are compared with experimental data. The effects of non-uniformity of the fluid velocity field arising due to the shape of the layer surface are investigated by the methods of a computational experiment. A qualitative comparison is made of velocity inhomogeneities when a fluid flows through a porous obstacle. For the numerical implementation of the filtration equation of the interpenetrating model, a SIMPLE-like algorithm was used.