The eigensystem of the Pulliam-Chaussee diagonalized form of the approximate-factorization algorithm for the three-dimensional Euler and Navier-Stokes equations is revisited to remove an apparent dimensional inconsistency. The original set of eigenvectors in curvilinear coordinates were derived systematically and has been widely used and referenced. Although mathematically correct, the original eigenvectors for the advected modes appear dimensionally inconsistent and yield a set of matrices with large condition numbers for some flows. A new set of eigenvectors is presented that remove the inconsistency and improves the robustness of the diagonalized scheme.

再次探讨了三维Euler和Navier-Stokes方程的近似分解算法的Pulliam-Chaussee对角化形式的本征系统，以消除明显的尺寸不一致。系统地推导了曲线坐标系中的原始特征向量集，并得到了广泛的应用和参考。尽管在数学上是正确的，但平移模式的原始特征向量在尺寸上似乎不一致，并为某些流生成了一组具有大条件数的矩阵。提出了一组新的特征向量，该特征向量消除了不一致性并提高了对角化方案的鲁棒性。