An improved embedded-manifold/Navier–Stokes numerical methodology is developed to simulate the propagation of premixed flames within the context of the hydrodynamic theory. The method is computationally tractable, permitting calculations to not only be extended to larger physical domains but also to span a broader parametric space of physicochemical parameters. The focus of this paper is to examine the susceptibility of centrally ignited, freely propagating and outwardly expanding circular flames to small amplitude disturbances and observe the flame's development through the onset of the hydrodynamic instability. The numerical simulations, validated by a linear stability analysis, show that for mixtures with Lewis numbers above criticality, thermo-diffusive effects exert stabilising influences which dominate at small flame radii, initially suppressing the growth of all disturbances. Consistent with the linear theory, simulations show the flame initially remaining stable and demonstrate the existence of a particular mode which is the first to grow. This mode is said to dictate the cellular pattern observed experimentally at the onset of instability. The variation in critical flame radius with respect to the Markstein length and thermal expansion coefficients are in quantitative agreement with these analytical results.

开发了一种改进的嵌入式歧管/纳维-斯托克斯数值方法，以在流体动力学理论的背景下模拟预混火焰的传播。该方法在计算上易于处理，不仅可以将计算扩展到更大的物理域，还可以跨越更广泛的物理化学参数参数空间。本文的重点是检查集中点燃、自由传播和向外扩展的圆形火焰对小振幅扰动的敏感性，并通过流体动力学不稳定的开始观察火焰的发展。通过线性稳定性分析验证的数值模拟表明，对于路易斯数高于临界值的混合物，热扩散效应会产生稳定影响，在小火焰半径下占主导地位，最初抑制了所有干扰的增长。与线性理论一致，模拟显示火焰最初保持稳定，并证明存在第一个增长的特定模式。据说这种模式决定了在不稳定开始时通过实验观察到的细胞模式。临界火焰半径相对于 Markstein 长度和热膨胀系数的变化与这些分析结果在定量上一致。