Newton’s iterative technique is commonly used in solving a system of non-linear equations. The advantage of using Newton’s method is that it gives local quadratic convergence leading to high computational efficiency. Specifically, Newton’s method has been applied to finite volume formulation for convective-diffusive transport processes. A direct solution method is adopted. Development of sparse direct solvers has significantly reduced the computation time of direct solution methods. Here UMFPACK (Unsymmetric Multi-Frontal method), has been used to solve the resulting linear system obtained from Newton’s step. A simple damping strategy is applied to ensure the global convergence of the system of equations during the first few iterations. The efficiency of this method is compared to that of Picard’s iterative procedure and the SIMPLE procedure for convective-diffusive transport processes. A modified Newton technique is also analyzed which lead to significant reduction in total CPU time.
Skip Nav Destination
ASME 2005 Summer Heat Transfer Conference collocated with the ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems
July 17–22, 2005
San Francisco, California, USA
Conference Sponsors:
- Heat Transfer Division and Electronic and Photonic Packaging Division
ISBN:
0-7918-4733-0
PROCEEDINGS PAPER
Application of Direct Newton’s Methods for Efficient Solution to Convective-Diffusive Transport Processes
Mandhapati P. Raju
Mandhapati P. Raju
Case Western Reserve University, Cleveland, OH
Search for other works by this author on:
Mandhapati P. Raju
Case Western Reserve University, Cleveland, OH
Paper No:
HT2005-72210, pp. 847-851; 5 pages
Published Online:
March 9, 2009
Citation
Raju, MP. "Application of Direct Newton’s Methods for Efficient Solution to Convective-Diffusive Transport Processes." Proceedings of the ASME 2005 Summer Heat Transfer Conference collocated with the ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems. Heat Transfer: Volume 3. San Francisco, California, USA. July 17–22, 2005. pp. 847-851. ASME. https://doi.org/10.1115/HT2005-72210
Download citation file:
6
Views
Related Proceedings Papers
Related Articles
Discussion on “Vibration Analysis of Non-Classically Damped Linear Systems”
J. Vib. Acoust (February,2005)
Efficient Dynamic Analysis of a Nonlinear Wave Energy Harvester Model
J. Offshore Mech. Arct. Eng (August,2016)
Related Chapters
Application of the Ergodic Algorithm for Solving Nonlinear Equations and Tridiagonal Linear Equations
International Conference on Mechanical Engineering and Technology (ICMET-London 2011)
Some Laws to Affect the Results in Numerical Calculus
International Conference on Advanced Computer Theory and Engineering, 4th (ICACTE 2011)
The Solutions for the Equations with Localized Consistent Blow-Up Rate
International Conference on Computer Technology and Development, 3rd (ICCTD 2011)