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Numerical Analysis of Fluid Flow Behaviour in Four-Sided Square Lid-Driven Cavity Using the Finite Volume Technique

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Abstract

In the present study, numerical simulations of two-dimensional steady-state incompressible Newtonian fluid flow in one-sided and four-sided lid-driven square cavities are reported. For the one-sided lid-driven cavity, the upper wall is moved to the right with up to 5000 Reynolds numbers under a grid size of up to \( 501\times 501\). This lends support to previous findings in the literature. Two cases are used in this article for the four-sided lid-driven square cavity specifically. In case-I, the top and lower walls are moved to the right, while the left and right walls are moved upward and downward, respectively. In case II, the top wall is moved to the left, the lower wall to the right, the left wall is moved upward, and the right wall is moved downward, with all three walls moving at the same speed one and the bottom wall moving at two. Conventional numerical solutions show that the unique solutions exist for all Reynolds numbers for both the geometries. All possible flow solutions are studied in the present article, as velocity profiles and streamline contours for the same Reynolds number using a finite volume SIMPLE technique. The work done in this paper includes flow properties such as the location of primary and secondary vortices, velocity components, and numerical values for benchmarking purposes, and it is in excellent agreement with previous findings in the literature. A PARAM Shavak, high-performance computing computer, was used to execute the calculations.

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Data Availability

All data generated or analyzed during this study are included in this article.

Abbreviations

2D :

Two dimensional

SIMPLE:

Semi implicit method for pressure linked equation

HPC:

High performance computing

FVM:

Finite volume technique

PV:

Primary vortex

Right-SV:

Right secondary vortex

Left-SV:

Left secondary vortex

Left-USV:

Left upper secondary vortex

UPV:

Upper primary vortex

LPV:

Left primary vortex

RPV:

Right primary vortex

BPV:

Bottom primary vortex

BSV:

Bottom secondary vortex

u :

x-axis velocity component (m/s)

\(u^*\) :

x-axis approximate velocity component (m/s)

\(u^\prime \) :

x-axis correction velocity component (m/s)

v :

y-axis velocity component (m/s)

\(v^*\) :

y-axis approximate velocity component (m/s)

\(v^\prime \) :

y-axis correction velocity component (m/s)

p :

Pressure (\(\mathrm{N/m}^2\))

\(p^*\) :

Guessed pressure (\(\mathrm{N/m}^2\))

\(p^\prime \) :

Correction pressure (\(\mathrm{N/m}^2\))

i :

x-direction node location

j :

y-direction node location

Re :

Reynolds number

\(\Delta x\) :

x-direction spatial step

\(\Delta y\) :

y-direction spatial step

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Acknowledgements

The authors would like to express our special thanks and gratitude to DST, Gujcost, and C-DAC high-performance computing clusters, PARAM Shavak of KSV.

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Authors and Affiliations

  1. Department of Mathematics, LDRP Institute of Technology and Research, Kadi Sarva Vishwavidyalaya, Gandhinagar, Gujarat, 382015, India

    Manoj R. Patel & Vijay K. Patel

  2. Department of Mathematics, Sarvajanik College of Engineering and Technology, Gujarat Technological University, Surat, Gujarat, 395001, India

    Jigisha U. Pandya

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  1. Manoj R. Patel
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Patel, M.R., Pandya, J.U. & Patel, V.K. Numerical Analysis of Fluid Flow Behaviour in Four-Sided Square Lid-Driven Cavity Using the Finite Volume Technique. Int. J. Appl. Comput. Math 8, 153 (2022). https://doi.org/10.1007/s40819-022-01353-x

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