Previous studies (Watt et al. in J Eng Math 75(1):1, 2012; Cartwright and Falle in J Eng Math 115(1):157, 2019) have shown that a streamline based approach to modelling of steady state detonations can produce good results for rate laws which have maximal reaction at the shock. In this paper we consider a Variational Streamline Approximation (VSA) which introduces streamline curvature. Comparing results with Direct Numerical Simulations (DNS) and the existing Straight Streamline Approximation (SSA) model, we find that the VSA improves the predictive accurary of streamlines modelling compared to DNS calculations, capturing the shock front and sonic surfaces with greater accuracy than SSA.

先前的研究（Watt 等人在 J Eng Math 75(1):1, 2012 中；Cartwright 和 Falle 在 J Eng Math 115(1):157, 2019 中）表明，基于流线的稳态爆炸建模方法可以对在冲击时具有最大反应的速率定律产生良好的结果。在本文中，我们考虑引入流线曲率的变分流线近似 (VSA)。将结果与直接数值模拟 (DNS) 和现有的直线流线近似 (SSA) 模型进行比较，我们发现与 DNS 计算相比，VSA 提高了流线建模的预测精度，比 SSA 更准确地捕获了激波前沿和声波表面。