论文标题
交错压力校正数值方案，以在部分混合物中计算行进的反应性界面
A staggered pressure correction numerical scheme to compute a travelling reactive interface in a partially premixed mixture
论文作者
论文摘要
我们在本文中解决了模拟工业应用中湍流典当的模型。该流程由可变组合混合物的Euler方程控制，燃烧建模基于现象学方法：火焰传播由燃烧区的特征功能的转运表示，其中化学反应已完成；在该区域之外，气氛保持新鲜状态。从数值上讲，我们通过类似惩罚的方法来近似此问题，即使用有限的转换率，其特征时间趋于与空间和时间步骤为零。数值方案可用于交错的，可能是非结构化的网格。时间构建算法是隔离的类型，包括在第一步求解化学物种质量平衡，然后在第二步中质量，动量和能量平衡。对于算法的后一个阶段，我们使用压力校正技术，并为所谓的明智的焓而不是总能量平衡解决平衡方程，并具有纠正术语以保持一致性。该方案显示出与连续问题相同的稳定性的满足：化学物种质量分数保持在[0，1]间隔中，密度和明智的内部能量保持正向，并且在离散总能量的计算域上保持了不可或缺的整体。此外，我们表明该方案实际上是保守的，即其解决方案满足保守的离散总能量平衡方程，并具有空间和时间离散化，这在Lax-Wendroff意义上是不寻常但一致的。最后，我们从数值上观察到惩罚程序会收敛，即使化学时间尺度倾向于零允许将目标收敛到目标（无限快速化学）连续问题的求解。测试还证明了该方案的准确性极大地取决于化学物种质量平衡中对流操作员的离散化。 2020年10月14日。
We address in this paper a model for the simulation of turbulent deflagrations in industrial applications. The flow is governed by the Euler equations for a variable composition mixture and the combustion modelling is based on a phenomenological approach: the flame propagation is represented by the transport of the characteristic function of the burnt zone, where the chemical reaction is complete; outside this zone, the atmosphere remains in its fresh state. Numerically, we approximate this problem by a penalization-like approach, i.e. using a finite conversion rate with a characteristic time tending to zero with the space and time steps. The numerical scheme works on staggered, possibly unstructured, meshes. The time-marching algorithm is of segregated type, and consists in solving in a first step the chemical species mass balances and then, in a second step, mass, momentum and energy balances. For this latter stage of the algorithm, we use a pressure correction technique, and solve a balance equation for the so-called sensible enthalpy instead of the total energy balance, with corrective terms for consistency. The scheme is shown to satisfy the same stability properties as the continuous problem: the chemical species mass fractions are kept in the [0, 1] interval, the density and the sensible internal energy stay positive and the integral over the computational domain of a discrete total energy is conserved. In addition, we show that the scheme is in fact conservative, i.e. that its solution satisfy a conservative discrete total energy balance equation, with space and time discretizations which are unusual but consistent in the Lax-Wendroff sense. Finally, we observe numerically that the penalization procedure converges, i.e. that making the chemical time scale tend to zero allows to converge to the solution of the target (infinitely fast chemistry) continuous problem. Tests also evidence that the scheme accuracy dramatically depends on the discretization of the convection operator in the chemical species mass balances. October 14, 2020.
