The recent 1/2-equation model of turbulence is a simplification of the standard Kolmogorov-Prandtl 1-equation URANS model. Surprisingly, initial numerical tests indicated that the 1/2-equation model produces comparable velocity statistics at reduced cost. It is also a test problem and first step for developing numerical analysis to address a full 1-equation model. This report begins the numerical analysis of the 1/2 equation model. Stability, convergence and error estimates are proven for a semi-discrete and fully discrete approximation. Finally, numerical tests are conducted to validate our convergence theory.

翻译：近期提出的湍流1/2方程模型是标准Kolmogorov-Prandtl单方程URANS模型的简化形式。令人惊讶的是，初步数值试验表明该1/2方程模型能以更低的计算成本获得可比较的速度统计量。该模型同时可作为测试问题，并为发展针对完整单方程模型的数值分析提供了首要步骤。本报告开启了1/2方程模型的数值分析研究。针对半离散与全离散近似格式，我们证明了其稳定性、收敛性及误差估计。最后，通过数值试验验证了所提出的收敛理论。