Taylor-Green vortex simulation using CABARET scheme in a weakly compressible formulation

Area of Science:

• Computational fluid dynamics
• Numerical analysis
• Fluid mechanics

Background:

• The Taylor-Green vortex problem is a standard benchmark for numerical methods in fluid dynamics.
• Understanding vortex dynamics is crucial for various engineering applications.
• Weakly compressible formulations offer advantages in certain flow regimes.

Purpose of the Study:

• To implement and assess a novel CABARET numerical scheme for the Taylor-Green vortex problem.
• To analyze the scheme's performance in both laminar and turbulent vortex decay.
• To evaluate the accuracy and efficiency of the numerical method across different resolutions and Reynolds numbers.

Main Methods:

• In-house implementation of the CABARET numerical scheme.
• Simulations conducted using a weakly compressible formulation.
• Utilized a sequence of refined grids ([Formula: see text], [Formula: see text], [Formula: see text] cells).
• Investigated various Reynolds numbers for laminar ([Formula: see text]) and turbulent ([Formula: see text]) scenarios.

Main Results:

• The CABARET scheme accurately captures key features of vortex decay.
• Analysis of kinetic energy dissipation rate and integral enstrophy curves.
• Temporal evolution of spanwise vorticity, energy spectra, and spatial correlation functions were examined.
• Performance was evaluated across different grid resolutions and Reynolds numbers.

Conclusions:

• The CABARET numerical scheme is a viable tool for simulating the Taylor-Green vortex problem.
• The method demonstrates robustness in capturing both laminar and turbulent vortex dynamics.
• The study provides insights into the scheme's capabilities for fluid flow simulations.