Modeling spatial and temporal frost formation with distributed properties on a flat plate using the orthogonal collocation method

2017 ◽  
Vol 76 ◽  
pp. 193-205 ◽  
Author(s):  
Teresa Benítez ◽  
S.A. Sherif
Keyword(s):  
Flat Plate ◽  
Collocation Method ◽  
Orthogonal Collocation ◽  
Frost Formation

Solution of the Pellet Equation by use of the Orthogonal Collocation and Least Squares Methods: Effects of Different Orthogonal Jacobi Polynomials

2012 ◽  
Vol 10 (1) ◽  
Author(s):  
Jannike Solsvik ◽  
Hugo Jakobsen
Keyword(s):  
Numerical Methods ◽  
Least Squares ◽  
Collocation Method ◽  
Jacobi Polynomial ◽  
Jacobi Polynomials ◽  
Least Squares Method ◽  
Condition Numbers ◽  
Orthogonal Collocation ◽  
Point Distribution ◽  
Boundary Points

Two numerical methods in the family of weighted residual methods; the orthogonal collocation and least squares methods, are used within the spectral framework to solve a linear reaction-diffusion pellet problem with slab and spherical geometries. The node points are in this work taken as the roots of orthogonal polynomials in the Jacobi family. Two Jacobi polynomial parameters, alpha and beta, can be used to tune the distribution of the roots within the domain. Further, the internal points and the boundary points of the boundary-value problem can be given according to: i) Gauss-Lobatto-Jacobi points, or ii) Gauss-Jacobi points plus the boundary points. The objective of this paper is thus to investigate the influence of the distribution of the node points within the domain adopting the orthogonal collocation and least squares methods. Moreover, the results of the two numerical methods are compared to examine whether the methods show the same sensitivity and accuracy to the node point distribution. The notifying findings are as follows: i) The Legendre polynomial, i.e., alpha=beta=0, is a very robust Jacobi polynomial giving the better condition number of the coefficient matrix and the polynomial also give good behavior of the error as a function of polynomial order. This polynomial gives good results for small and large gradients within both slab and spherical pellet geometries. This trend is observed for both of the weighted residual methods applied. ii) Applying the least squares method the error decreases faster with increasing polynomial order than observed with the orthogonal collocation method. However, the orthogonal collocation method is not so sensitive to the choice of Jacobi polynomial and the method also obtains lower error values than the least squares method due to favorable lower condition numbers of the coefficient matrices. Thus, for this particular problem, the orthogonal collocation method is recommended above the least squares method. iii) The orthogonal collocation method show minor differences between Gauss-Lobatto-Jacobi points and Gauss-Jacobi plus boundary points.

Simulation of transient gas flow using the orthogonal collocation method

2012 ◽  
Vol 90 (11) ◽  
pp. 1701-1710 ◽  
Author(s):  
Edris Ebrahimzadeh ◽  
Mahdi Niknam Shahrak ◽  
Bahamin Bazooyar
Keyword(s):  
Collocation Method ◽  
Gas Flow ◽  
Orthogonal Collocation

scholarly journals Cubic Hermite Collocation Method for Solving Boundary Value Problems with Dirichlet, Neumann, and Robin Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Ishfaq Ahmad Ganaie ◽  
Shelly Arora ◽  
V. K. Kukreja
Keyword(s):  
Boundary Value Problems ◽  
Collocation Method ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Spline Method ◽  
Orthogonal Collocation ◽  
Nonlinear Boundary Value Problems ◽  
B Spline ◽  
Linear And Nonlinear ◽  
Volume Method

Cubic Hermite collocation method is proposed to solve two point linear and nonlinear boundary value problems subject to Dirichlet, Neumann, and Robin conditions. Using several examples, it is shown that the scheme achieves the order of convergence as four, which is superior to various well known methods like finite difference method, finite volume method, orthogonal collocation method, and polynomial and nonpolynomial splines and B-spline method. Numerical results for both linear and nonlinear cases are presented to demonstrate the effectiveness of the scheme.

A semi-empirical transient method for modelling frost formation on a flat plate

1993 ◽  
Vol 16 (5) ◽  
pp. 321-329 ◽  
Author(s):  
S.A Sherif ◽  
S.P Raju ◽  
M.M Padki ◽  
A.B Chan
Keyword(s):  
Flat Plate ◽  
Transient Method ◽  
Frost Formation ◽  
Semi Empirical

scholarly journals A computationally efficient technique for the solution of pulp washing models

2021 ◽  
Author(s):  
Satinder pal Kaur ◽  
◽  
Dr. Ajay Kumar Mittal ◽  
Keyword(s):  
Collocation Method ◽  
Present Method ◽  
Numerical Technique ◽  
Hermite Polynomials ◽  
Solute Concentration ◽  
Breakthrough Curves ◽  
Point Boundary ◽  
Convergence Criteria ◽  
Computationally Efficient ◽  
Orthogonal Collocation

An efficient numerical technique for the solution of the pulp washing model is proposed in this study. Two linear and one nonlinear model are explained with quintic Hermite collocation method. In this technique, quintic Hermite polynomials (C2 continuous) are used as a basis function and orthogonal collocation method is applied within each element of the partitioned domain. For accuracy and applicability of the method, a comparison of the numerical results with analytic ones is made. The method is found to be stable using stability analysis and convergence criteria. The effect of Peclet number on exit solute concentration and other parameters is presented in the form of breakthrough curves. The results are derived for a broad range of parameters and the present method is found to be more useful and refined for solving the two-point boundary value problems.

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