Papers by Keyword: Collocation Method

Abstract: Entropy generation minimization is a method that helps to improve the efficiency of real processes and devices. This study investigates the heat transfer in an electrically conducting Casson fluid flow between parallel plates under the influence of thermal radiation and convective boundary conditions. The thermodynamics first and second laws were employed to examine the problem. The present study provides a fast convergent method on the finite parallel plates, namely the Optimal Homotopy Analysis method (OHAM) and Collocation Method (CM) are used to analyzes the fluid flow, heat, transport. The impacts of governing parameters on Casson flow velocity, temperature profile, local skin friction, and Nusselt number were analysed. The obtained solutions were used to determine the heat transfer irreversibility and bejan number of the model. The method employed in this paper offers excellently convergence solutions with good accuracy. The results of the computation show that the effect of thermophysical properties such as thermal radiation parameter, suction/injection parameter, magnetic field parameter, radiation parameter, and Eckert number has a significant influence on Skin friction coefficient (Cf) and local Nusselt number (Nu) when compared to the Newtonian fluid. The application of this work can be found in polymer synthesis, metallic processing, and electromagnetic crucible systems.

Abstract: Fluid flow in internally finned tubes is a very important problem from a practical point of view. In the literature there are many different numerical methods which were used for analysis this problem. However to the best knowledge of the authors of the present paper there are no so many papers in which meshless methods were applied for this purpose. The main advantages of these methods are: easy implementation, semi-analytical form of the approximate solution and no need for mesh generation. In the paper these meshless methods are compared in application for analysis of incompressible, fully-developed, Newtonian fluid flow in an internally finned tube.

Abstract: A barycentric interpolation Newton-Raphson iterative method for solving nonlinear beam bending problems is presented in this article. The nonlinear governing differential equation of beam bending problem is discretized by barycentric interpolation collocation method to form a system of nonlinear algebraic equations. Newton-Raphson iterative method is applied to solve the system of nonlinear algebraic equations. The Jacobian derivative matrix in Newton-Raphson iterative method is formulated by the Hadamard product of vectors. Some numerical examples are given to demonstrate the validity and accuracy of proposed method.

Abstract: A meshless, barycentric interpolation collocation method for numerical approximation of Darcy flows is proposed. The barycentric Lagrange interpolation and its differentiation matrices are basic tool to discretize governing equations, Dirichlet and Neumann boundary conditions. For Darcy flows in irregular domains, embedding the irregular domain into a rectangular, the barycentric interpolation collocation method can be directly applied. The resultant saddle-point systems come from combining the discretized governing equations and boundary conditions, such that we can deal easy with all kinds of boundary condition either regular or irregular domains. Some numerical examples are given to illustrate the accuracy, stability and robust of presented method.

Abstract: This paper starts with the principle and operation approaches of Collocation orbit integration method, analyzing the integration process and initialization value of motion equation and variation equation. Through different integration lengths and polynomial degrees, this paper discussed the impact to orbit precision. It also compares the results to the scientific orbit which were offered by GFZ, through the analysis of this method; we also find the appropriate integration length and polynomial degree and validate the validity of this method.

Abstract: In this paper, a forging problem is analyzed by using the overrange collocation method (ORCM), which is a new meshless method. By introducing some collocation points, which are located out of domain of the analyzed body, unsatisfactory issue of the positivity conditions of boundary points in collocation methods can be avoided. Because the overrange points are used only in interpolating calculation, no overconstrain occurs in partial differential equations on the solved problems.

Abstract: An accurate prediction of the dynamic stability of a cutting system involves the implementation of tool geometry and cutting conditions on any model used for such purpose. This study presents a dynamic cutting force model based on the collocation method by Chebyshev polynomials taking advantage from its ability to consider tool geometry and cutting parameters. In the paper, a simple 1DOF model is used to forecast chatter vibrations due to the workpiece and tool, which are distinguished in separate sections. The proposed model is verified positively against experimental dynamic tests.

Abstract: This paper deals with the solutions of lateral heat loss equation by using collocation method with cubic B-splines finite elements. The stability analysis of this method is investigated by considering Fourier stability method. The comparison of the numerical solutions obtained by using this method with the analytic solutions is given by the tables and the figure.

Abstract: In this paper, an upsetting problem is analyzed by using a new meshless method called the overrange collocation method (ORCM). By introducing some collocation points, which are located at outside of domain of the analyzed body, unsatisfactory issue of the positivity conditions of boundary points in collocation methods can be avoided. Because the overrange points are used only in interpolating calculation, no over-constrain condition is imposed into solved boundary value problems.

Abstract: In this paper, a forging problem is analyzed by using the overrange collocation method (ORCM), which is a new meshless method. By introducing some collocation points, which are located out of domain of the analyzed body, unsatisfactory issue of the positivity conditions of boundary points in collocation methods can be avoided. Because the overrange points are used only in interpolating calculation, no overconstrain occurs in partial differential equations on the solved problems.