<abstract xmlns="http://www.w3.org/1999/xhtml">

Numerical simulations of an unsteady laminar lid-driven cavity Newtonian flow are executed to demonstrate formation of eddies under different aspect ratios and steady-state criteria. A couple of nonlinear unsteady partial differential equations (PDEs) of Navier Stokes satisfying a set of boundary conditions is examined with both inclusions of no-slip and free-slip effects. Finite difference method (FDM) is employed to solve the vorticity-stream function using a self-developed Matlab® code embedded in a GUI to ease the cavity problem analysis by the end users. Four models are studied where Ansys Fluent® employing finite element method is used to verify the present FDM steady-state results produced for the first model. It is observed that the value of stream function begins to drop and streamline distribution changes shape when <italic>e</italic> ≤ 10−5. Refrainment of merging of secondary eddies also happens until the free-slip boundary condition effect passes the threshold value. Stretching effect with free-slip BC in the fourth model regulates the fluid dynamics to reach the entire cavity sufficiently with no room for eddy formation by increasing the slip length to an intense value. Free-slip simulates free surface applications in geophysical occurrences (river and glacier), spilling dynamics, ship hull designs, technologies of coating and fuel spraying/injection.
</abstract>

Numerical simulations of an unsteady laminar lid-driven cavity Newtonian flow are executed to demonstrate formation of eddies under different aspect ratios and steady-state criteria. A couple of nonlinear unsteady partial differential equations (PDEs) of Navier Stokes satisfying a set of boundary conditions is examined with both inclusions of no-slip and free-slip effects. Finite difference method (FDM) is employed to solve the vorticity-stream function using a self-developed Matlab® code embedded in a GUI to ease the cavity problem analysis by the end users. Four models are studied where Ansys Fluent® employing finite element method is used to verify the present FDM steady-state results produced for the first model. It is observed that the value of stream function begins to drop and streamline distribution changes shape when e ≤ 10−5. Refrainment of merging of secondary eddies also happens until the free-slip boundary condition effect passes the threshold value. Stretching effect with free-slip BC in the fourth model regulates the fluid dynamics to reach the entire cavity sufficiently with no room for eddy formation by increasing the slip length to an intense value. Free-slip simulates free surface applications in geophysical occurrences (river and glacier), spilling dynamics, ship hull designs, technologies of coating and fuel spraying/injection.

Variant slip effects, aspect ratios and steady-state criteria in unsteady cavities with direct PDE simulation of eddies

Institute of Mathematical Sciences, Faculty of Science

Department of Applied Mathematics and Statistics

International Journal of Mathematics and Computer in Engineering

This work is licensed under the Creative Commons Attribution 4.0 International License.

Numerical simulations of an unsteady laminar lid-driven cavity Newtonian flow are executed to demonstrate formation of eddies under different aspect ratios and...

Variant slip effects, aspect ratios and steady-state criteria in unsteady cavities with direct PDE simulation of eddies

Article Category: Original Study

Published Online: Jun 02, 2024

Page range: -

Received: Jul 12, 2023

Accepted: Jan 21, 2024

DOI: https://doi.org/10.2478/ijmce-2025-0006

Keywords
Numerical finite difference, vorticity-stream function, slip effects, eddies simulation, Matlab

© 2025 Hon Fei Wong et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Variant slip effects, aspect ratios and steady-state criteria in unsteady cavities with direct PDE simulation of eddies

Article Category: Original Study

Published Online: Jun 02, 2024

Page range: -

Received: Jul 12, 2023

Accepted: Jan 21, 2024

DOI: https://doi.org/10.2478/ijmce-2025-0006

KeywordsNumerical finite difference, vorticity-stream function, slip effects, eddies simulation, Matlab

© 2025 Hon Fei Wong et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Numerical finite difference, vorticity-stream function, slip effects, eddies simulation, Matlab