AI 中文总结
研究原始和连续伴随流求解器中动量加权插值的求解器诱导依赖性问题，提出简单修正去除压力驱动项对角动量系数的此类贡献，经实验评估，修正公式在多参数下结果更一致。
AI 中文摘要
动量加权插值（MWI）是同位格单元中心有限体积法中压力-速度耦合方案的关键组成部分，用于原始和连续伴随公式。在许多实际实现中，MWI依赖于包含欠松弛和时间离散化贡献的对角动量系数。这导致原始感兴趣量和伴随灵敏度可能对求解器参数表现出非物理依赖性。本文基于离散一致MWI公式的先前发展，提出一种简单修正，去除压力驱动项中对角动量系数的求解器诱导贡献。所得公式保留原始离散化，消除对松弛和时间步长参数的人为依赖性，并一致应用于原始和伴随系统。以结构化、类似配方的方式给出推导以便应用。通过二维层流圆柱流和三维湍流船体流配置评估该修正。未修正公式在改变求解器参数时会导致力、尾流相关量和形状灵敏度的显著变化，而修正公式在宽范围的松弛因子和时间步长下产生一致结果。
英文摘要
Momentum-Weighted Interpolation (MWI) is a key component in pressure--velocity coupling schemes on collocated cell-centered finite-volume methods for both primal and continuous adjoint formulations. In many practical implementations, MWI relies on diagonal momentum coefficients that include contributions from under-relaxation and time discretization. As a result, both primal quantities of interest and adjoint sensitivities may exhibit a non-physical dependence on solver parameters such as relaxation factors and time-step size, and no well-defined limit is obtained as these parameters approach zero. In this work, building on previous developments in discrete-consistent MWI formulations, a simple correction is proposed that removes solver-induced contributions from the diagonal momentum coefficients in the pressure-driven term. The resulting formulation preserves the original discretization while eliminating artificial dependencies on relaxation and time-stepping parameters and is applied consistently to both primal and adjoint systems. To facilitate its application, the derivation is presented in a structured, recipe-like manner that can be readily followed and transferred to different finite volume-based solver configurations. The proposed modification is assessed for a two-dimensional laminar cylinder flow and a three-dimensional turbulent ship hull flow configuration. In both cases, the uncorrected formulation leads to significant variations in forces, wake-related quantities, and shape sensitivities when solver parameters are altered, despite all simulations being iterated to converged residual levels and stable integral quantities. In contrast, the corrected formulation yields consistent results across a wide range of relaxation factors and time-step sizes.
