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首页> 外文期刊>Transactions of the Japan society for aeronautical and space sciences >Actual Numerical Accuracy of an Iterative Scheme for Solving Evolution Equations with Application to Boundary-Layer Flow
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Actual Numerical Accuracy of an Iterative Scheme for Solving Evolution Equations with Application to Boundary-Layer Flow

机译：求解演化方程的迭代方案的实际数值精度及其在边界层流中的应用

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摘要

Actual numerical accuracy of an arbilrary-high-order accurate scheme with inner iterations which has been developed by the author is assessed in this paper. The scheme is based on a δ~κ-form of the algorithm for the κth-order accuracy in evolutional direction. The κth-order accuracy in evolutional direction is shown to be achieved with at most κ of times of inner iterations. In this paper the scheme is applied to boundary-layer equations, since the δ~κ-form of the algorithm can be applied to any type of evolution equations and the boundary-layer equations are a typical system of evolution equations. Assessment of actual numerical accuracy by grid refienement studies is performed for practical third-order accuracy using a laminar boundary-layer flow problem. The numerical experiment shows that the actual numerical accuracy agrees with theoretical accuracy.
机译：本文评估了作者开发的内部迭代的任意高阶精度方案的实际数值精度。该方案基于算法的δ〜κ形式，用于进化方向上的κ阶精度。在进化方向上的κ阶精度被证明最多可以进行内部迭代的κ倍。本文将该方案应用于边界层方程，因为该算法的δ〜κ形式可以应用于任何类型的演化方程，并且边界层方程是一个典型的演化方程系统。使用层状边界层流动问题，通过网格参考研究对实际数值精度进行评估，以获得实用的三阶精度。数值实验表明，实际数值精度与理论精度一致。

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