In this work, a mathematical formulation for the calculation of the sensitivity of manifold-based simplified chemistry with respect to the scalar gradient is derived. This methodology allows to answer how important the scalar gradient is for the Reaction–Diffusion Manifolds (REDIM) reduced chemistry and how sensitive the reduced scheme is with respect to the gradient estimate. Based on the governing REDIM evolution equation, the sensitivity equation is derived in form of a linear in-homogeneous partial differential equation system of second order with non-constant coefficients. Some examples including simple reaction systems and real combustion systems are shown to validate the approach. Moreover, the developed sensitivity analysis can also be used in other manifold-based methods.

在这项工作中，导出了用于计算基于流形的简化化学对标量梯度的敏感性的数学公式。该方法可以回答标量梯度对于反应-扩散歧管 (REDIM) 还原化学的重要性以及还原方案对梯度估计的敏感程度。基于控制的REDIM演化方程，以具有非恒定系数的二阶线性非齐次偏微分方程组的形式导出灵敏度方程。展示了一些示例，包括简单的反应系统和真实的燃烧系统，以验证该方法。此外，开发的敏感性分析也可以用于其他基于流形的方法。