High-order thermal lattice Boltzmann models derived by means of Gauss quadrature in the spherical coordinate system

2012 ◽  
Vol 86 (1) ◽  
Author(s):  
Victor Eugen Ambruş ◽  
Victor Sofonea
Keyword(s):  
Coordinate System ◽  
Lattice Boltzmann ◽  
High Order ◽  
Spherical Coordinate System ◽  
Gauss Quadrature ◽  
Spherical Coordinate ◽  
Lattice Boltzmann Models ◽  
Thermal Lattice Boltzmann

scholarly journals A Lattice Boltzmann Scheme for Diffusion Equation in Spherical Coordinate

2018 ◽  
Vol 1 (4) ◽  
Author(s):  
Debabrata Datta ◽  
T K Pal
Keyword(s):  
Diffusion Equation ◽  
Coordinate System ◽  
Lattice Boltzmann ◽  
Spherical Coordinate System ◽  
Cartesian Coordinate System ◽  
Spherical Coordinate ◽  
Cartesian Coordinate ◽  
Lattice Boltzmann Models ◽  
Boltzmann Method ◽  
Good Agreement

Lattice Boltzmann models for diffusion equation are generally in Cartesian coordinate system. Very few researchers have attempted to solve diffusion equation in spherical coordinate system. In the lattice Boltzmann based diffusion model in spherical coordinate system extra term, which is due to variation of surface area along radial direction, is modeled as source term. In this study diffusion equation in spherical coordinate system is first converted to diffusion equation which is similar to that in Cartesian coordinate system by using proper variable. The diffusion equation is then solved using standard lattice Boltzmann method. The results obtained for the new variable are again converted to the actual variable. The numerical scheme is verified by comparing the results of the simulation study with analytical solution. A good agreement between the two results is established.

scholarly journals GAUSS QUADRATURES – THE KEYSTONE OF LATTICE BOLTZMANN MODELS

2013 ◽  
Vol 25 (01) ◽  
pp. 1340016 ◽  
Author(s):  
BENJAMIN PIAUD ◽  
STÉPHANE BLANCO ◽  
RICHARD FOURNIER ◽  
VICTOR EUGEN AMBRUŞ ◽  
VICTOR SOFONEA
Keyword(s):  
Coordinate System ◽  
Lattice Boltzmann ◽  
Equilibrium Distribution ◽  
Temperature Jump ◽  
Equilibrium Distribution Function ◽  
Maximum Order ◽  
Spherical Coordinate ◽  
Gauss Hermite Quadrature ◽  
Cartesian Coordinate ◽  
Lattice Boltzmann Models

In this paper, we compare two families of Lattice Boltzmann (LB) models derived by means of Gauss quadratures in the momentum space. The first one is the HLB (N;Qx,Qy,Qz) family, derived by using the Cartesian coordinate system and the Gauss–Hermite quadrature. The second one is the SLB (N;K,L,M) family, derived by using the spherical coordinate system and the Gauss–Laguerre, as well as the Gauss–Legendre quadratures. These models order themselves according to the maximum order N of the moments of the equilibrium distribution function that are exactly recovered. Microfluidics effects (slip velocity, temperature jump, as well as the longitudinal heat flux that is not driven by a temperature gradient) are accurately captured during the simulation of Couette flow for Knudsen number (kn) up to 0.25.

Comparison Considerations Toward Investigating the Factors of Load and Age Group on the Maximum Reach Envelope

2020 ◽  
pp. 001872082096501
Author(s):  
Heather Johnston ◽  
Colleen Dewis ◽  
John Kozey
Keyword(s):  
Coordinate System ◽  
Three Dimensional ◽  
Spherical Coordinate System ◽  
Upper Body ◽  
Group Differences ◽  
Anthropometric Measures ◽  
Younger Adults ◽  
Present Measurement ◽  
Spherical Coordinate ◽  
Cylindrical Coordinate

Objective The objectives were to compare cylindrical and spherical coordinate representations of the maximum reach envelope (MRE) and apply these to a comparison of age and load on the MRE. Background The MRE is a useful measurement in the design of workstations and quantifying functional capability of the upper body. As a dynamic measure, there are human factors that impact the size, shape, and boundaries of the MRE. Method Three-dimensional reach measures were recorded using a computerized potentiometric system for anthropometric measures (CPSAM) on two adult groups (aged 18–25 years and 35–70 years). Reach trials were performed holding .0, .5, and 1 kg. Results Three-dimensional Cartesian coordinates were transformed into cylindrical ( r, θ , Z) and spherical ( r, θ, ϕ) coordinates. Median reach distance vectors were calculated for 54 panels within the MRE as created by incremented banding of the respective coordinate systems. Reach distance and reach area were compared between the two groups and the loaded conditions using a spherical coordinate system. Both younger adults and unloaded condition produced greater reach distances and reach areas. Conclusions Where a cylindrical coordinate system may reflect absolute reference for design, a normalized spherical coordinate system may better reflect functional range of motion and better compare individual and group differences. Age and load are both factors that impact the MRE. Application These findings present measurement considerations for use in human reach investigation and design.

Optimal Design and Structural Precision Analysis for a Spherical Coordinate System 3D Scanner Guiding Device

2014 ◽  
Vol 705 ◽  
pp. 164-168
Author(s):  
Sang Wook Park ◽  
Hee Young Maeng ◽  
Ju Wook Park
Keyword(s):  
Optimal Design ◽  
Data Collection ◽  
Reverse Engineering ◽  
Coordinate System ◽  
Fem Analysis ◽  
Spherical Coordinate System ◽  
3D Scanner ◽  
Spherical Coordinate ◽  
Overall Performance ◽  
Improved Design

Recently, automatic 3D scanning devices are commonly researched and developed for better productivity of the reverse engineering fields. In this paper, a 3D scanner utilizing a spherical coordinate system was designed and analyzed using FEM analysis. The system was designed for optimal performance, high precision, minimal deflection, and speed of data collection. FEM analysis allowed us to properly design the system to achieve these goals, with focus on the deflection of the cantilever arm. Results of the FEM analysis and figures showing the apparatus design are provided. Successive prototypes are shown to increase in overall performance and reliability through improved design and analysis.

A linear model for relative motion in an elliptical orbit based on a spherical coordinate system

2019 ◽  
Vol 157 ◽  
pp. 465-476 ◽  
Author(s):  
Chao Han ◽  
Huan Chen ◽  
Gustavo Alonso ◽  
Yinrui Rao ◽  
Javier Cubas ◽  
...  
Keyword(s):  
Coordinate System ◽  
Linear Model ◽  
Relative Motion ◽  
Spherical Coordinate System ◽  
Elliptical Orbit ◽  
Spherical Coordinate
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