Computationally inexpensive and revised normalized weighting factor method for segregated solvers

ABSTRACT

A new methodology for the implementation of high-resolution (HR) scheme is being presented. The proposed method is a revision of the existing normalized weighting factor (NWF) method and henceforth, it is termed as revised normalized weighting factor (RNWF) method. Unlike the previous method which is penta-diagonal in nature, the RNWF method generates tri-diagonal system of linear equations and is expected to be computationally inexpensive and robust to use. Further to assess the performance of this method, iterations required for the convergence of HR schemes and to configure the CPU clock time, pure advection tests (viz. Step, Double-Step and Sine) were performed. These results were then compared with the existing methods such as, deferred correction (DC) and NWF which suggested that the proposed RNWF method is 4 times faster than DC and 1.3 times faster than NWF on uniform grids. To further evaluate the performance of this method, assessment tests for incompressible, newtonian fluid using the segregated solver (SIMPLE algorithm) are also detailed. Results suggest that RNWF method delivers computationally inexpensive and convergent numerical solutions when compared to the existing methods. Moreover, this method outperforms the NWF as it has been successfully applied for segregated solvers.

KEYWORDS:

• High-resolution schemes
• normalized variable diagram
• revised normalized weighting factor
• TDMA
• numerical convergence

AMS SUBJECT CLASSIFICATION:

• 74S10

Acknowledgments

The author is grateful to Indian Institute of Technology Indore (IITI) for providing with the research facilities. Also, author is thankful to Dr S. Dhinakaran, Dr D. Deshmukh and Dr S. S. Ahmad for their valuable support.

Disclosure statement

No potential conflict of interest was reported by the authors.