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.

Numerical Boundary Conditions for Viscous Flow Problems

AIAA Journal ◽  
1976 ◽  
Vol 14 (8) ◽  
pp. 1042-1049 ◽  
Author(s):  
J.C. Wu
Keyword(s):  
Boundary Conditions ◽  
Viscous Flow ◽  
Flow Problems

On Boundary Conditions on Solid Walls in Viscous Flow Problems

2021 ◽  
Vol 13 (4) ◽  
pp. 591-603
Author(s):  
A. P. Duben ◽  
I. V. Abalakin ◽  
V. O. Tsvetkova
Keyword(s):  
Boundary Conditions ◽  
Viscous Flow ◽  
Flow Problems ◽  
Solid Walls

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.

Molecular Dynamics Using Non-Variational Polarizable Force Fields: Theory, Periodic Boundary Conditions Implementation and Application to the Bond Capacity Model

2019 ◽  
Author(s):  
Pier Paolo Poier ◽  
Louis Lagardere ◽  
Jean-Philip Piquemal ◽  
Frank Jensen
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Force Fields ◽  
Periodic Boundary Conditions ◽  
Computational Effort ◽  
Polarizable Force Fields ◽  
Energy Models ◽  
Capacity Model ◽  
Energy Gradient ◽  
Polarization Models

<div> <div> <div> <p>We extend the framework for polarizable force fields to include the case where the electrostatic multipoles are not determined by a variational minimization of the electrostatic energy. Such models formally require that the polarization response is calculated for all possible geometrical perturbations in order to obtain the energy gradient required for performing molecular dynamics simulations. </p><div> <div> <div> <p>By making use of a Lagrange formalism, however, this computational demanding task can be re- placed by solving a single equation similar to that for determining the electrostatic variables themselves. Using the recently proposed bond capacity model that describes molecular polarization at the charge-only level, we show that the energy gradient for non-variational energy models with periodic boundary conditions can be calculated with a computational effort similar to that for variational polarization models. The possibility of separating the equation for calculating the electrostatic variables from the energy expression depending on these variables without a large computational penalty provides flexibility in the design of new force fields. </p><div><div><div> </div> </div> </div> <p> </p><div> <div> <div> <p>variables themselves. Using the recently proposed bond capacity model that describes molecular polarization at the charge-only level, we show that the energy gradient for non-variational energy models with periodic boundary conditions can be calculated with a computational effort similar to that for variational polarization models. The possibility of separating the equation for calculating the electrostatic variables from the energy expression depending on these variables without a large computational penalty provides flexibility in the design of new force fields. </p> </div> </div> </div> </div> </div> </div> </div> </div> </div>

Boundary conditions for gas flow problems from anisotropic scattering kernels

2015 ◽  
Vol 56 (10) ◽  
pp. 103101 ◽  
Author(s):  
Quy-Dong To ◽  
Van-Huyen Vu ◽  
Guy Lauriat ◽  
Céline Léonard
Keyword(s):  
Boundary Conditions ◽  
Gas Flow ◽  
Anisotropic Scattering ◽  
Flow Problems
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