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首页> 外文期刊>Journal of Computational Physics >AN EXTENDED LAGRANGIAN METHOD
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AN EXTENDED LAGRANGIAN METHOD

机译：扩展的拉格朗日方法

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A unique formulation of describing fluid motion is presented. The method, referred to as ''extended Lagrangian method,'' is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the Eulerian description. The present method and the Arbitrary Lagrangian-Eulerian (ALE) method have a similarity in spirit-eliminating the cross-streamline numerical diffusion. For this purpose, we suggest a simple grid constraint condition and utilize an accurate discretization procedure. This grid constraint is only applied to the transverse cell face parallel to the local stream velocity, and hence our method for the steady state problems naturally reduces to the streamline-curvature method, without explicitly solving the steady streamline-coordinate equations formulated a priori. Unlike the Lagrangian method proposed by Loh and Hui which is valid only for steady supersonic flows, the present method is general and capable of treating subsonic flows and supersonic flows as well as unsteady flows, simply by invoking in the same code an appropriate grid constraint suggested in this paper. The approach is found to be robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multi-dimensional discontinuities with a high level of accuracy, similar to that found in one-dimensional problems. (c) 1995 Academic Press. Inc. [References: 24]
机译：提出了描述流体运动的独特公式。从理论和数值角度来看，该方法都被称为“扩展拉格朗日方法”。通过避免在欧拉描述中通量混合引起的数值扩散，该公式提供了数值解的准确性。本方法与任意拉格朗日-欧拉（ALE）方法在消除跨流线数值扩散的精神上具有相似之处。为此，我们提出了一个简单的网格约束条件，并利用了精确的离散化程序。该网格约束仅适用于平行于局部流速度的横向单元面，因此，我们针对稳态问题的方法自然会简化为流线曲率法，而无需明确求解先验公式化的稳态流线坐标方程。不同于Loh和Hui提出的拉格朗日方法仅适用于稳定的超音速流，本方法是通用的并且能够处理亚音速流和超音速流以及非稳态流，只需在同一代码中调用建议的适当网格约束即可。在本文中。发现该方法是鲁棒且稳定的。它可以自动适应流量特征，而无需借助聚类，从而在整个过程中以及较长的时间间隔内保持相当均匀的网格间距。此外，该方法已显示出可以解决多维不连续性的高精度问题，类似于一维问题。 （c）1995年学术出版社。 Inc. [参考：24]

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