November 30, 2025

Reformulation of the ω Equation of the k−ω Model

Key Points

Numerical solution adjustment leads to enhanced accuracy in high-Mach-number flows, particularly in boundary layers.
Singular solution consistency allows for effective mapping to nonsingular solutions over varying speeds.
Assessment of the model indicates superior results in high-Mach scenarios compared to traditional methods at low speeds.
Implications highlight the potential to refine modeling approaches in various fluid dynamics applications.

Abstract

The standard Formula: see text model uses a singular solution to the Formula: see text equation. That is not attractive for numerical discretization. Also, the singular solution does not comply with high-Mach-number wall scaling. A procedure is introduced to map a nonsingular numerical solution into the singular solution. The mapping is consistent with high-Mach-number scaling. It is shown that this procedure provides virtually the same results as the singular solution in low-speed flow and significantly better results in high-Mach-number boundary layers.

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