A Lower-Upper/Approximate-Factorization (LU/AF) scheme is developed for the incompressible Navier-Stokes equations. The LU/AF scheme is to be used in conjunction with linearized implicit approximations and artificial compressibility to compute steady solutions, and within sub-iterations to compute unsteady solutions. The LU/AF scheme contains an iteration parameter that can be adjusted to improve iterative convergence rate. For one choice of the parameter (alpha = 1) this scheme is equivalent to symmetric Gauss-Seidel relaxation; for another choice (alpha = 0), the factorization is an LU analog of that used in ADI schemes. Optimal convergence behavior is found to occur at an intermediate value of the parameter.
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机译：针对不可压缩的Navier-Stokes方程，开发了一种下-上/近似因子化（LU / AF）方案。 LU / AF方案将与线性化隐式近似和人工可压缩性结合使用，以计算稳定解，并在子迭代内计算非稳定解。 LU / AF方案包含一个迭代参数，可以对其进行调整以提高迭代收敛速度。对于参数（alpha = 1）的一种选择，此方案等效于对称高斯-塞德尔松弛。对于另一个选择（alpha = 0），因式分解是ADI方案中使用的LU模拟。发现最佳收敛行为发生在参数的中间值。
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