Affecting the Relaxation Parameter in the Multifrontal Method

2020 ◽  
pp. 215-224
Author(s):  
Tomoki Nakano ◽  
Mitsuo Yokokawa ◽  
Yusaku Yamamoto ◽  
Takeshi Fukaya
Keyword(s):  
Relaxation Parameter ◽  
Multifrontal Method

scholarly journals Numerical Study of a Cooling System Using Phase Change of a Refrigerant in a Thermosyphon

Energies ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3634
Author(s):  
Grzegorz Czerwiński ◽  
Jerzy Wołoszyn
Keyword(s):  
Mass Transfer ◽  
Phase Change ◽  
Heat Dissipation ◽  
Cooling System ◽  
Numerical Study ◽  
Relaxation Parameter ◽  
Phase Changes ◽  
Transfer Time ◽  
Two Phase ◽  
Time Relaxation

With the increasing trend toward the miniaturization of electronic devices, the issue of heat dissipation becomes essential. The use of phase changes in a two-phase closed thermosyphon (TPCT) enables a significant reduction in the heat generated even at high temperatures. In this paper, we propose a modification of the evaporation–condensation model implemented in ANSYS Fluent. The modification was to manipulate the value of the mass transfer time relaxation parameter for evaporation and condensation. The developed model in the form of a UDF script allowed the introduction of additional source equations, and the obtained solution is compared with the results available in the literature. The variable value of the mass transfer time relaxation parameter during condensation rc depending on the density of the liquid and vapour phase was taken into account in the calculations. However, compared to previous numerical studies, more accurate modelling of the phase change phenomenon of the medium in the thermosyphon was possible by adopting a mass transfer time relaxation parameter during evaporation re = 1. The assumption of ten-fold higher values resulted in overestimated temperature values in all sections of the thermosyphon. Hence, the coefficient re should be selected individually depending on the case under study. A too large value may cause difficulties in obtaining the convergence of solutions, which, in the case of numerical grids with many elements (especially three-dimensional), significantly increases the computation time.

Elastic Effects on Rayleigh-Be´nard-Marangoni Convection in Liquids With Temperature-Dependent Viscosity

2009 ◽  
Author(s):  
G. N. Sekhar ◽  
G. Jayalatha
Keyword(s):  
Stress Relaxation ◽  
Variable Viscosity ◽  
Relaxation Parameter ◽  
Oscillatory Convection ◽  
Tight Coupling ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Dependent Viscosity ◽  
Viscoelastic Liquids ◽  
Retardation Parameter

A linear stability analysis of convection in viscoelastic liquids with temperature-dependent viscosity is studied using normal modes and Galerkin method. Stationary convection is shown to be the preferred mode of instability when the ratio of strain retardation parameter to stress relaxation parameter (elasticity ratio) is greater than unity. When the ratio is less than unity the possibility of oscillatory convection is shown to arise. Oscillatory convection is studied numerically for Rivlin-Ericksen, Walters B′, Maxwell and Jeffreys liquids by considering free-free and rigid-free isothermal/adiabatic boundaries. It is found that there is a tight coupling between the Rayleigh and Marangoni numbers, with an increase in one resulting in a decrease in the other. The effect of variable viscosity parameter is shown to destabilize the system. The problem reveals the stabilizing nature of strain retardation parameter and destabilizing nature of stress relaxation parameter, on the onset of convection. The Maxwell liquids are found to be more unstable than the one subscribing to Jeffreys description whereas the Rivlin-Ericksen and Walters B′ liquids are comparatively more stable. Rigid-free adiabatic boundary combination is found to give rise to a most stable system, whereas the free isothermal free adiabatic combination gives rise to a most unstable system. The problem has applications in non-isothermal systems having viscoelastic liquids as working media.

A computational process for choosing the relaxation parameter in nonlinear SOR

Computing ◽  
1986 ◽  
Vol 37 (1) ◽  
pp. 19-29 ◽  
Author(s):  
M. E. Brewster ◽  
R. Kannan
Keyword(s):  
Relaxation Parameter ◽  
Computational Process

ENHANCING ADEQUACY OF GRADING STUDY PROJECTS ON THE BASE OF PARAMETRIC RELAXATION OF PAIRWISE COMPARISONS

2021 ◽  
Vol 1 ◽  
pp. 122-133
Author(s):  
Alexey V. Oletsky ◽  
◽  
Mikhail F. Makhno ◽  
◽  
Keyword(s):  
Center Of Mass ◽  
Estimation Algorithm ◽  
Relaxation Parameter ◽  
Connected Components ◽  
Pairwise Comparisons ◽  
Strongly Connected Components ◽  
Standard Scale ◽  
Relaxation Parameters ◽  
Strongly Connected ◽  
The One

A problem of automated assessing of students’ study projects is regarded. A heuristic algorithm based on fuzzy estimating of projects and on pairwise comparisons among them is proposed. For improving adequacy and naturalness of grades, an approach based on introducing a parameter named relaxation parameter was suggested in the paper. This enables to reduce the spread between maximum and minimum values of projects in comparison with the one in the standard scale suggested by T. Saati. Reasonable values of this parameter were selected experimentally. For estimating the best alternative, a center of mass of a fuzzy max-min composition should be calculated. An estimation algorithm for a case of non-transitive preferences based on getting strongly connected components and on pairwise comparisons between them is also suggested. In this case, relaxation parameters should be chosen separately for each subtask. So the combined technique of evaluating alternatives proposed in the paper depends of the following parameters: relaxation parameters for pairwise comparisons matrices within each strongly connected components; relaxation parameter for pairwise comparisons matrices among strongly connected components; membership function for describing the best alternative.

SOR-like Methods with Optimization Model for Augmented Linear Systems

2017 ◽  
Vol 7 (1) ◽  
pp. 101-115 ◽  
Author(s):  
Rui-Ping Wen ◽  
Su-Dan Li ◽  
Guo-Yan Meng
Keyword(s):  
Linear Systems ◽  
Linear Equations ◽  
Optimization Technique ◽  
Relaxation Parameter ◽  
Convergence Theory ◽  
Optimization Models ◽  
System Of Linear Equations ◽  
Augmented System ◽  
New Methods ◽  
Outstanding Work

AbstractThere has been a lot of study on the SOR-like methods for solving the augmented system of linear equations since the outstanding work of Golub, Wu and Yuan (BIT 41(2001)71-85) was presented fifteen years ago. Based on the SOR-like methods, we establish a class of accelerated SOR-like methods for large sparse augmented linear systems by making use of optimization technique, which will find the optimal relaxation parameter ω by optimization models. We demonstrate the convergence theory of the new methods under suitable restrictions. The numerical examples show these methods are effective.

Darcy-Forchheimer flow with variable thermal conductivity and Cattaneo-Christov heat flux

2016 ◽  
Vol 26 (8) ◽  
pp. 2355-2369 ◽  
Author(s):  
T. Hayat ◽  
Taseer Muhammad ◽  
Saleh Al-Mezal ◽  
S.J. Liao
Keyword(s):  
Thermal Conductivity ◽  
Temperature Field ◽  
Velocity Field ◽  
Thermal Relaxation ◽  
Heat Transfer Process ◽  
Relaxation Parameter ◽  
Content Type ◽  
Opposite Behavior ◽  
Non Linear System ◽  
Forchheimer Flow

Purpose The objectives of present communication are threefolds. First is to model and analyze the two-dimensional Darcy-Forchheimer flow of Maxwell fluid induced by a stretching surface. Temperature-dependent thermal conductivity is taken into account. Second is to examine the heat transfer process through non-classical flux by Cattaneo-Christov theory. Third is to derive convergent homotopic solutions for velocity and temperature distributions. The paper aims to discuss these issues. Design/methodology/approach The resulting non-linear system is solved through the homotopy analysis method. Findings An increment in Deborah number β causes a reduction in velocity field f′(η) while opposite behavior is observed for temperature field θ(η). Velocity field f′(η) and thickness of momentum boundary layer are decreased when the authors enhance the values of porosity parameter λ while opposite behavior is noticed for temperature profile θ(η). Temperature field θ(η) is inversely proportional to the thermal relaxation parameter γ. The numerical values of temperature gradient at the sheet − θ′(0) are higher for larger values of thermal relaxation parameter γ. Originality/value To the best of author’s knowledge, no such consideration has been given in the literature yet.

Multifrontal Method

2011 ◽  
pp. 1209-1216 ◽  
Author(s):  
David Padua ◽  
Amol Ghoting ◽  
John A. Gunnels ◽  
Mark S. Squillante ◽  
José Meseguer ◽  
...  
Keyword(s):  
Multifrontal Method

MAGNETO-CONVECTIVE INSTABILITY IN A HORIZONTAL VISCOELASTIC NANOFLUID SATURATED POROUS LAYER

2016 ◽  
Vol 78 (12-3) ◽  
Author(s):  
Norazuwin Najihah Mat Tahir ◽  
Fuziyah Ishak ◽  
Seripah Awang Kechil
Keyword(s):  
Magnetic Field ◽  
Stress Relaxation ◽  
Differential Equations ◽  
Porous Layer ◽  
Closed Form Solution ◽  
Relaxation Parameter ◽  
Linear Stability Theory ◽  
Weighted Residuals ◽  
Viscoelastic Nanofluid ◽  
Retardation Parameter

Nanofluids have been shown experimentally to have high thermal conductivity. In this study, the convective instabilities in a horizontal viscoelastic nanofluid saturated by porous layer under the influences of gravity and magnetic field are investigated. The linear stability theory is used for the transformation of the partial differential equations to system of ordinary differential equations through infinitesimal perturbations, scaling, linearization and method of normal modes with two-dimensional periodic waves. The system is solved analytically for the closed form solution of the thermal Darcy-Rayleigh number by using the Galerkin-type weighted residuals method to investigate the onset of both stationary and oscillatory convection. The effects of the scaled stress relaxation parameter, scaled strain retardation parameter and Chandrasekhar number on the stability of the system are investigated. The scaled strain retardation parameter stabilizes while the scaled stress relaxation parameter destabilizes the nanofluid system. The system in the presence of magnetic field is more stable than the system in the absence of magnetic field. 

T1 and T2* mapping of the human quadriceps and patellar tendons using ultra-short echo-time (UTE) imaging and bivariate relaxation parameter-based volumetric visualization

2019 ◽  
Vol 63 ◽  
pp. 29-36 ◽  
Author(s):  
M. Krämer ◽  
M.B. Maggioni ◽  
N.M. Brisson ◽  
S. Zachow ◽  
U. Teichgräber ◽  
...  
Keyword(s):  
T2 Mapping ◽  
Relaxation Parameter ◽  
Echo Time ◽  
T1 And T2 ◽  
Short Echo Time
Sign in / Sign up

Export Citation Format

Share Document