scholarly journals Slow Viscous Flow in a Syringe

1986 ◽  
Vol 108 (4) ◽  
pp. 317-323 ◽  
Author(s):  
L. T. Watson ◽  
S. C. Billups ◽  
C.-Y. Wang ◽  
E. A. Everett
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Viscous Flow ◽  
Stokes Equation ◽  
Governing Equations ◽  
Slow Viscous Flow ◽  
Pressure Profiles ◽  
Nonstandard Finite Difference

The slow viscous flow in a syringe is modeled by the quasi-steady axisymmetric Stokes equation with a point sink for the needle hole. The governing equations are approximated using nonstandard finite difference formulas optimized for the boundary conditions, and solved numerically using a SOR technique. Streamlines and pressure profiles are computed for a variety of syringe configurations.

A Noniterative Numerical Solution of Poisson’s and Laplace’s Equations With Applications to Slow Viscous Flow

1966 ◽  
Vol 88 (4) ◽  
pp. 725-733 ◽  
Author(s):  
M. L. Booy
Keyword(s):  
Boundary Conditions ◽  
Viscous Flow ◽  
Computational Effort ◽  
Linear Boundary ◽  
Simultaneous Solution ◽  
Slow Viscous Flow ◽  
Flow Problems ◽  
Engineering Problems ◽  
Iterative Procedures ◽  
Multiple Boundary Conditions

A noniterative finite-difference method for solution of Poisson’s and Laplace’s equations for linear boundary conditions is given. The method is simpler and more accurate than iterative procedures. It is limited in the number of meshes that can be used, but that number is adequate to obtain accurate solutions to many engineering problems. The computational effort is reduced vastly when one differential equation must be solved in a family of domains for the same boundary condition. The same applies to calculations of the integral of the function in the domain. Examples are given for simultaneous solution in Laplace’s and Poisson’s equations and for problems with multiple boundary conditions. The results of several slow viscous-flow problems are discussed.

Development of Three-Dimensional PML Boundary Conditions for Aeroacoustics Applications

2002 ◽  
Vol 1 (3) ◽  
pp. 307-327
Author(s):  
J-F. Dietiker ◽  
K.A. Hoffmann ◽  
M. Papadakis ◽  
R. Agarwal
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Three Dimensional ◽  
Perfectly Matched Layer ◽  
Optimum Combination ◽  
Curvilinear Coordinates ◽  
Main Program ◽  
Governing Equations ◽  
Compact Finite Difference ◽  
Finite Difference Formulation

Perfectly Matched Layer (PML) boundary conditions are derived in generalized curvilinear coordinates for three-dimensional aeroacoustic applications. The resulting governing equations are solved numerically by a four-stage Runge-Kutta scheme, with 4th/6th order compact finite difference formulation. The PML equations are programmed in a subroutine, which is easily incorporated to the main program LINEULER (Linearized Euler's equation solver). Two and three-dimensional benchmarks problems are solved to investigate the efficiency and accuracy of the PML boundary conditions. Investigations on the PML parameters have been conducted to determine the optimum combination of parameters used in the computations.

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.

scholarly journals Vibration of rotating circular cylindrical shells with distributed springs

2021 ◽  
Vol 37 ◽  
pp. 346-358
Author(s):  
Fuchun Yang ◽  
Xiaofeng Jiang ◽  
Fuxin Du
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Shell Theory ◽  
Rotation Speed ◽  
Cylindrical Shells ◽  
Free Vibrations ◽  
Governing Equations ◽  
Natural Response ◽  
Circular Cylindrical Shells ◽  
The Galerkin Method

Abstract Free vibrations of rotating cylindrical shells with distributed springs were studied. Based on the Flügge shell theory, the governing equations of rotating cylindrical shells with distributed springs were derived under typical boundary conditions. Multicomponent modal functions were used to satisfy the distributed springs around the circumference. The natural responses were analyzed using the Galerkin method. The effects of parameters, rotation speed, stiffness, and ratios of thickness/radius and length/radius, on natural response were also examined.

Biharmonic navigation using radial basis functions

Robotica ◽  
2021 ◽  
pp. 1-12
Author(s):  
Xu-Qian Fan ◽  
Wenyong Gong
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Radial Basis Functions ◽  
Real World ◽  
Biharmonic Equation ◽  
Finite Difference Methods ◽  
Basis Functions ◽  
Large Size ◽  
Radial Basis ◽  
Difference Methods

Abstract Path planning has been widely investigated by many researchers and engineers for its extensive applications in the real world. In this paper, a biharmonic radial basis potential function (BRBPF) representation is proposed to construct navigation fields in 2D maps with obstacles, and it therefore can guide and design a path joining given start and goal positions with obstacle avoidance. We construct BRBPF by solving a biharmonic equation associated with distance-related boundary conditions using radial basis functions (RBFs). In this way, invalid gradients calculated by finite difference methods in large size grids can be preventable. Furthermore, paths constructed by BRBPF are smoother than paths constructed by harmonic potential functions and other methods, and plenty of experimental results demonstrate that the proposed method is valid and effective.

Thermal Modeling of Unlooped and Looped Pulsating Heat Pipes

2001 ◽  
Vol 123 (6) ◽  
pp. 1159-1172 ◽  
Author(s):  
Mohammad B. Shafii ◽  
Amir Faghri ◽  
Yuwen Zhang
Keyword(s):  
Heat Transfer ◽  
Finite Difference ◽  
Heat Pipes ◽  
Analytical Models ◽  
Charge Ratio ◽  
Sensible Heat ◽  
Governing Equations ◽  
Heating Wall ◽  
Heat Mode ◽  
Explicit Finite Difference

Analytical models for both unlooped and looped Pulsating Heat Pipes (PHPs) with multiple liquid slugs and vapor plugs are presented in this study. The governing equations are solved using an explicit finite difference scheme to predict the behavior of vapor plugs and liquid slugs. The results show that the effect of gravity on the performance of top heat mode unlooped PHP is insignificant. The effects of diameter, charge ratio, and heating wall temperature on the performance of looped and unlooped PHPs are also investigated. The results also show that heat transfer in both looped and unlooped PHPs is due mainly to the exchange of sensible heat.

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