scholarly journals STUDY OF SELF-SUPERPOSABLE FLUID MOTIONS IN CONFOCAL PARABOLOIDAL DUCTS

2021 ◽  
Vol 9 (12) ◽  
pp. 725-732
Author(s):  
Rajeev Mishra
Keyword(s):  
Fluid Dynamics ◽  
Fluid Flow ◽  
Boundary Conditions ◽  
Incompressible Fluid ◽  
Pressure Distribution ◽  
Basic Equations

In this paper, studies have been made on some self-superposable motion of incompressible fluid is confocal Paraboloidal ducts. The boundary conditions have been neglected therefore the solutions contain a set of constants. Pressure distribution and the nature of vorticity are discussed. Tendency of irrotationality of the fluid flow is also determined. The aim of the paper is to introduce a method for solving the basic equations of fluid dynamics in confocal paraboloidal coordinates by using the property of self superposability.

scholarly journals STUDY OF SELF-SUPERPOSABLE LIQUID IN OBLATE SPHEROIDAL SHAPE

2021 ◽  
Vol 9 (11) ◽  
pp. 683-690
Author(s):  
Rajeev Mishra ◽  
◽  
Sanjai Misra ◽  
Keyword(s):  
Fluid Dynamics ◽  
Boundary Conditions ◽  
Incompressible Fluid ◽  
Pressure Distribution ◽  
Oblate Spheroidal ◽  
Spheroidal Shape ◽  
Basic Equations ◽  
Spheroidal Coordinates

The paper studiesthe self-superposable motion of a liquid of a fluid which is incompressible in nature in oblate spheroidal shape. An incompressible fluid is defined as the fluid whose volume or density does not change with pressure. Thus, the main aim of this paper is to solve the basic equations of fluid dynamics in oblate spheroidal coordinates considering self-superposable nature of the fluid. The paper includes the study of nature of vorticity and irrotationality and has not considered the boundary conditions in theanalysis. Lastly, the paper determines the pressure distribution and the solutions contain a set of constants.

scholarly journals Incompressible Fluid flow through free andporous areas

2021 ◽  
pp. 99-102
Author(s):  
Mohamed Saif AlDien ◽  
Hussam M.Gubara
Keyword(s):  
Fluid Flow ◽  
Boundary Conditions ◽  
Incompressible Fluid ◽  
Continuity Equation ◽  
Flow Problem ◽  
Darcy’S Law ◽  
Darcy's Law ◽  
Incompressible Fluid Flow ◽  
Flow Through

In this paper we discussedincompressiblefluid flow problem through free and porous areas by using Darcy's law and continuity equation, by apply the boundary conditions required to specify the solutio

GPU-Accelerated Simulation of Two-Phase Incompressible Fluid Flow Using a Level-Set Method for Interface Capturing

2009 ◽  
Author(s):  
Jesse Kelly
Keyword(s):  
Fluid Dynamics ◽  
Fluid Flow ◽  
Incompressible Fluid ◽  
Level Set Method ◽  
Level Set ◽  
Incompressible Fluid Flow ◽  
Visual Effects ◽  
Two Phase ◽  
Flow Solver ◽  
Collocated Grid

Computational fluid dynamics has seen a surge of popularity as a tool for visual effects animators over the past decade since Stam’s seminal Stable Fluids paper [1]. Complex fluid dynamics simulations can often be prohibitive to run due to the time it takes to perform all of the necessary computations. This project proposes an accelerated two-phase incompressible fluid flow solver implemented on programmable graphics hardware. Modern graphics-processing units (GPUs) are highly parallel computing devices, and in problems with a large potential for parallel computation the GPU may vastly out-perform the CPU. This project will use the potential parallelism in the solution of the Navier-Stokes equations in writing a GPU-accelerated flow solver. NVIDIA’s Compute-Unified-Device-Architecture (CUDA) language will be used to program the parallel portions of the solver. CUDA is a C-like language introduced by the NVIDIA Corporation with the goal of simplifying general-purpose computing on the GPU. CUDA takes advantage of data-parallelism by executing the same or near-same code on different data streams simultaneously, so the algorithms used in the flow solver will be designed to be highly data-parallel. Most finite difference-based fluid solvers for computer graphics applications have used the traditional staggered marker-and-cell (MAC) grid, introduced by Harlow and Welsh [2]. The proposed approach improves upon the programmability of solvers such as these by using a non-staggered (collocated) grid. An efficient technique is implemented to smooth the pressure oscillations that often result from the use of a collocated grid in the simulation of incompressible flows. To be appropriate for visual effects use, a fluid solver must have some means of tracking fluid interfaces in order to have a renderable fluid surface. This project uses the level-set method [3] for interface tracking. The level set is treated as a scalar property, and so its propagation in time is computed using the same transport algorithm used in the main fluid flow solver.

A model of unsteady subsonic flow with acoustics excluded

1997 ◽  
Vol 334 ◽  
pp. 135-155 ◽  
Author(s):  
A. T. FEDORCHENKO
Keyword(s):  
Fluid Flow ◽  
Boundary Conditions ◽  
Incompressible Fluid ◽  
Compressible Fluid ◽  
Fluid Motion ◽  
General System ◽  
Initial Boundary ◽  
Heat Fluxes ◽  
Closed Volume ◽  
Sound Waves

Diverse subsonic initial-boundary-value problems (flows in a closed volume initiated by blowing or suction through permeable walls, flows with continuously distributed sources, viscous flows with substantial heat fluxes, etc.) are considered, to show that they cannot be solved by using the classical theory of incompressible fluid motion which involves the equation div u = 0. Application of the most general theory of compressible fluid flow may not be best in such cases, because then we encounter difficulties in accurately resolving the complex acoustic phenomena as well as in assigning the proper boundary conditions. With this in mind a new non-local mathematical model, where div u ≠ 0 in the general case, is proposed for the simulation of unsteady subsonic flows in a bounded domain with continuously distributed sources of mass, momentum and entropy, also taking into account the effects of viscosity and heat conductivity when necessary. The exclusion of sound waves is one of the most important features of this model which represents a fundamental extension of the conventional model of incompressible fluid flow. The model has been built up by modifying both the general system of equations for the motion of compressible fluid (viscous or inviscid as required) and the appropriate set of boundary conditions. Some particular cases of this model are discussed. A series of exact time-dependent solutions, one- and two-dimensional, is presented to illustrate the model.

scholarly journals Mathematical Modelling and Simulation for One Dimensional - Two-Phase Flow Equation in Petroleum Reservoir: A Matlab Algorithm Approach

2021 ◽  
Vol 16 ◽  
pp. 213-221
Author(s):  
Jwngsar Brahma
Keyword(s):  
Mass Transfer ◽  
Fluid Flow ◽  
Boundary Conditions ◽  
Pressure Distribution ◽  
Two Phase Flow ◽  
Flow Equation ◽  
Phase Flow ◽  
Petroleum Reservoir ◽  
Two Phase ◽  
One Dimensional

The reservoir behaviors described by a set of differential equation those results from combining Darcy’s law and the law of mass conservation for each phase in the system. The one-dimensional two-phase flow equation is implicit in the pressure and saturation and explicit in relative permeability. A mathematical model of a physical system is a set of partial differential equations together with an appropriate set of boundary conditions, which describes the significant physical processes taking place in that system. The processes occurring in petroleum reservoirs are fluid flow and mass transfer. Two immiscible phases (water& oil) flow simultaneously while mass transfer may take place among the phases. Gravity, capillary, and viscous forces play a role in the fluid-flow process. The model equations must account for all these forces and should also take into account an arbitrary reservoir description with respect to heterogeneity and geometry. Finally, one-dimensional two-phase flow equation through porous media is formulated by considering above reservoir parameters and forces. A numerical method based on finite difference scheme is implemented to get the solutions of one-dimensional two-phase flow equation. A MATLAB algorithm is used to solve the equation with mathematical analysis resulting in upper and lower bounds for the ratio of time step to mesh. The MATLAB algorithm is modified as per the model with appropriate initial and boundary conditions. The algorithm is applied to two-phase water flooding problems in laboratory size cores, and resulting saturation and pressure distribution are presented graphically. The saturation and pressure distribution of two-phase flow model is in agreement with the prediction of the Buckley Leveret theory. The numerical solution is used as a base for evaluating the numerical methods with respect to machine time requirement and allowable tie step for fixed mesh spacing.

Axisymmetric flow near the critical point on the moving boundary

2010 ◽  
Vol 7 ◽  
pp. 182-190
Author(s):  
I.Sh. Nasibullayev ◽  
E.Sh. Nasibullaeva
Keyword(s):  
Fluid Flow ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Axial Velocity ◽  
Moving Boundary ◽  
Axisymmetric Flow ◽  
Boundary Motion ◽  
Newton Raphson ◽  
Raphson Method

In this paper the investigation of the axisymmetric flow of a liquid with a boundary perpendicular to the flow is considered. Analytical equations are derived for the radial and axial velocity and pressure components of fluid flow in a pipe of finite length with a movable right boundary, and boundary conditions on the moving boundary are also defined. A numerical solution of the problem on a finite-difference grid by the iterative Newton-Raphson method for various velocities of the boundary motion is obtained.

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