A general method for deriving boundary conditions associated with reduced distribution functions

1983 ◽  
Vol 52 (3) ◽  
pp. 247-252 ◽  
Author(s):  
S. Chaturvedi ◽  
G. S. Agarwal
Keyword(s):  
Boundary Conditions ◽  
Distribution Functions ◽  
Reduced Distribution Functions ◽  
General Method

Wigner distribution and reduced distribution functions

1973 ◽  
Vol 58 (11) ◽  
pp. 5120-5124 ◽  
Author(s):  
D. Shalitin
Keyword(s):  
Wigner Distribution ◽  
Distribution Functions ◽  
Reduced Distribution Functions

Stress Distribution in a Uniformly Rotating Equilateral Triangular Shaft

1955 ◽  
Vol 22 (2) ◽  
pp. 255-259
Author(s):  
H. T. Johnson
Keyword(s):  
Approximate Solution ◽  
Stress Distribution ◽  
Boundary Conditions ◽  
Plane Strain ◽  
Cross Section ◽  
Plane Stress ◽  
Biharmonic Equation ◽  
Approximate Solutions ◽  
Distribution Of Stresses ◽  
General Method

Abstract An approximate solution for the distribution of stresses in a rotating prismatic shaft, of triangular cross section, is presented in this paper. A general method is employed which may be applied in obtaining approximate solutions for the stress distribution for rotating prismatic shapes, for the cases of either generalized plane stress or plane strain. Polynomials are used which exactly satisfy the biharmonic equation and the symmetry conditions, and which approximately satisfy the boundary conditions.

scholarly journals Monte Carlo Calculations of the Radial Distribution Functions for a Proton?Electron Plasma

1965 ◽  
Vol 18 (2) ◽  
pp. 119 ◽  
Author(s):  
AA Barker
Keyword(s):  
Monte Carlo ◽  
Crystal Lattice ◽  
Radial Distribution ◽  
Lattice Theory ◽  
Electron Plasma ◽  
Distribution Functions ◽  
Radial Distribution Functions ◽  
Monte Carlo Calculations ◽  
Wide Range ◽  
General Method

A general method is presented for computation of radial distribution functions for plasmas over a wide range of temperatures and densities. The method uses the Monte Carlo technique applied by Wood and Parker, and extends this to long-range forces using results borrowed from crystal lattice theory. The approach is then used to calculate the radial distribution functions for a proton-electron plasma of density 1018 electrons/cm3 at a temperature of 104 OK. The results show the usefulness of the method if sufficient computing facilities are available.

scholarly journals Collisionless distribution functions for force-free current sheets: using a pressure transformation to lower the plasma beta

2018 ◽  
Vol 84 (3) ◽  
Author(s):  
F. Wilson ◽  
T. Neukirch ◽  
O. Allanson
Keyword(s):  
Distribution Function ◽  
Current Sheet ◽  
Plasma Phys ◽  
Distribution Functions ◽  
Hermite Functions ◽  
Slow Convergence ◽  
Nonlinear Force ◽  
Free Current ◽  
Transformed Distribution ◽  
General Method

So far, only one distribution function giving rise to a collisionless nonlinear force-free current sheet equilibrium allowing for a plasma beta less than one is known (Allansonet al.,Phys. Plasmas, vol. 22 (10), 2015, 102116; Allansonet al.,J. Plasma Phys., vol. 82 (3), 2016a, 905820306). This distribution function can only be expressed as an infinite series of Hermite functions with very slow convergence and this makes its practical use cumbersome. It is the purpose of this paper to present a general method that allows us to find distribution functions consisting of a finite number of terms (therefore easier to use in practice), but which still allow for current sheet equilibria that can, in principle, have an arbitrarily low plasma beta. The method involves using known solutions and transforming them into new solutions using transformations based on taking integer powers ($N$) of one component of the pressure tensor. The plasma beta of the current sheet corresponding to the transformed distribution functions can then, in principle, have values as low as$1/N$. We present the general form of the distribution functions for arbitrary$N$and then, as a specific example, discuss the case for$N=2$in detail.

Truncation procedure for high order reduced distribution functions

1978 ◽  
Vol 90 (3-4) ◽  
pp. 587-596 ◽  
Author(s):  
V.S. Vikhrenko ◽  
G.S. Bokun
Keyword(s):  
Distribution Functions ◽  
High Order ◽  
Reduced Distribution Functions

On a General Method of Unsteady Potential Calculation Applied to the Compression Stages of a Turbomachine—Part I: Theoretical Approach

2001 ◽  
Vol 123 (4) ◽  
pp. 780-786 ◽  
Author(s):  
F. Bakir ◽  
S. Kouidri ◽  
T. Belamri ◽  
R. Rey
Keyword(s):  
Boundary Conditions ◽  
Centrifugal Pump ◽  
Theoretical Approach ◽  
Axial Fan ◽  
Variable Pitch ◽  
Singularity Method ◽  
Parametric Studies ◽  
The Mean ◽  
The Impact ◽  
General Method

An algorithm using the singularity method was developed. It allows taking into account the interaction between fixed and mobile cascades. Its principle is based on the summation of discrete vortices distributed periodically on the rotor and stator profiles. The overall matrix, obtained by applying the boundary conditions, takes into account the complexity of the studied cascade geometry (presence or not of splitter blades, possibly variable pitch of the profiles, etc…) To illustrate the interest and the impact of the algorithm, two parametric studies on turbomachines cascade are presented: Planes cascade made up of a rotor and a stator (at the mean radius of an axial fan). Circular cascade made up of impeller and a volute (peripheral cascade of a centrifugal pump).

scholarly journals Convective Boundary Conditions Effect on Cylindrical Media with Transient Heat Transfer

2021 ◽  
Vol 82 (2) ◽  
pp. 146-156
Author(s):  
Raoudha Chaabane ◽  
Nor Azwadi Che Sidik ◽  
Abdelmajid Jemni
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Convective Boundary Condition ◽  
Distribution Functions ◽  
Convective Boundary ◽  
Thermal Fields ◽  
Fortran 90 ◽  
Boltzmann Method ◽  
Transfer Problems ◽  
Good Agreement

Lattice Boltzmann method is used to solve inside a cylindrical cavity with convective boundary condition is highlighted in this paper. Because of its simple, stable, accurate, efficient and ease for parallelization, we use the thermal Single Relaxation Time Bhatnagar Gross Krook (SRT BGK) mesoscopic approach in order to solve the energy equation. Thermal fields are simulated using D2Q9 scheme. We introduce and demonstrate numerically some usual cases (Dirichlet, Newmann) of Boundary conditions (Bcs). After validation, we extend the present work to the convective case. At the wall of the cavity, the unknown Thermal Distribution Functions (TDF) are exposed to the bounce back concept which is determined consistently by one of the imposed BCs. An in-house Fortran 90 code is used to analyze a variety of BCs inside a two-dimensional cavity. In validation, obtained results highlight a good agreement with literature. The present study is extended to deal with convective boundary condition for conduction transfer problems inside an axisymmetric cylindrical media subjected to heat generation and Newman boundary conditions.

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