Numerical Investigation of Vertical Oscillations of a Buoyant Object in a Stratified Fluid

Fathya Rabiatunisa; Diki Fernandi; Ikha Magdalena

doi:10.37905/euler.v14i1.37621

Numerical Investigation of Vertical Oscillations of a Buoyant Object in a Stratified Fluid

Fathya Rabiatunisa, Diki Fernandi, Ikha Magdalena

Abstract

This study explores the vertical oscillation dynamics of a buoyant object in a linearly stratified fluid and assesses the accuracy of a first-order finite difference scheme used for numerical simulation. The mathematical formulation, derived from the harmonic motion equation, was solved analytically through linearization around the equilibrium position and numerically to evaluate the scheme’s stability and precision. A sensitivity analysis with respect to the time step (∆t) revealed that numerical accuracy strongly depends on temporal resolution: at ∆t = 1 s, the numerical results closely matched the analytical solution, whereas larger ∆t values caused noticeable phase errors and reduced precision. As ∆t increased, phase errors became noticeable, with discrepancies appearing more clearly at ∆t = 5 s and beyond, highlighting a trade-off between computational efficiency and precision. The model was further extended by incorporating a quadratic damping term (R), enabling the simulation of damped oscillatory motion. Results showed that the decay rate of oscillations increases proportionally with R, where higher friction coefficients (R = 0.2) lead to faster energy dissipation and stabilization compared to smaller ones (R = 0.05). These outcomes demonstrate the robustness and reliability of the proposed numerical approach in reproducing both undamped and damped oscillation behaviors. This study provides a reliable framework for simulating buoyant object oscillations in stratified fluids, though further development is needed to incorporate more complex hydrodynamic effects for enhanced predictive accuracy.

Keywords

Vertical Oscillations; Buoyant Object; Finite Difference Method; Brunt–Vaisala Frequency

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DOI: https://doi.org/10.37905/euler.v14i1.37621