CFD中统计误差的数值精度分析

在计算流体力学（CFD）的算法研究中经常会对离散误差进行数值精度分析，通常以统计误差的各范数为研究对象，最常用的统计误差范数为L₁范数、L₂范数和L_∞范数，一般认为各范数在数值精度上具有等价性。实际上，由于流场局部存在间断、网格局部不连续或者是在极值点附近采用非线性加权插值等可能使数值方法存在局部降阶问题，导致统计误差各范数所表达的数值精度并不一致。通过详细的理论分析，揭示了统计误差各范数所表达的数值精度之间的关系，并通过相应的数值试验予以验证。研究结果不仅能够指导CFD算法的数值精度验证工作，而且也可为更为复杂流动模拟的数值精度判定提供理论依据。

Accuracy analysis of numerical error with statistical forms in CFD

Generally, the accuracy of an algorithm should be validated numerically in Computational Fluid Dynamics(CFD), and the research object is composed by statistical norms of numerical error, which is usually represented by the L₁ norm, the L₂ norm, and the L_∞ norm based on the hypothesis that each norm is equivalent in accuracy order. In reality, there are locally discontinuities of flow variables, non-smoothness of mesh, and nonlinear interpolations near critical points that will result in the loss in accuracy of numerical algorithm, causing different numerical orders of accuracy of each norm of numerical error. By carrying out detailed theoretical analysis, the relationship of different error norms in accuracy order is exhibited in this paper and is soon validated by numerical experiments. The research results in this paper can not only serve as a guide to the validation of the accuracy order in a CFD algorithm, but also theoretically support the judgement of numerical simulation order with more complex flow.