Ktheta

Ktheta, or the k-theta turbulence model, is a two-equation model used in computational fluid dynamics to predict turbulent flows. It provides a simplified yet robust framework for capturing turbulence characteristics in a variety of wall-bounded and separated flows, and has historically served as an alternative to the more widely used k-ε and k-ω models.

The model introduces two transport equations: one for the turbulent kinetic energy k and one for the dissipation rate-like variable θ, which is related to the dissipation of turbulence and is often defined such that θ ≈ ε/k. The turbulent (eddy) viscosity is typically closed with μ_t = ρ C_μ k / θ, leading to an effective viscosity μ_eff = μ + μ_t. The transport equations include terms for production of turbulence, dissipation through θ, and diffusion via turbulent and molecular mechanisms. Boundary conditions near walls often use wall functions or low-Reynolds-number formulations, depending on the variant.

Variants of the k-theta model differ in the exact form of the production and dissipation terms and the near-wall treatment. It is valued for its relative simplicity and numerical robustness, especially in flows with strong swirl or separation. However, it can underperform for certain complex flows compared with more modern models such as k-ε, k-ω, or shear-stress transport (SST) models, which have more extensive validation across a wider range of conditions.

In practice, the k-theta model remains part of many legacy CFD codes and educational contexts. It is chosen when a balance between computational efficiency and reasonable accuracy is desired, particularly for industrial engineering applications where rapid qualitative insight is more important than high-fidelity turbulence prediction.