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首页> 外文期刊>Computer Methods in Applied Mechanics and Engineering >Discrete Hamilton's equations for arbitrary Lagrangian-Eulerian dynamics of viscous compressible flow
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Discrete Hamilton's equations for arbitrary Lagrangian-Eulerian dynamics of viscous compressible flow

机译：粘性可压缩流的任意拉格朗日-欧拉动力学的离散汉密尔顿方程

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摘要

A number of different arbitrary Lagrangian-Eulerian (ALE) formulations of continuum fluid and solid dynamics problems have been developed, to address applications where more conventional Lagrangian or Eulerian modeling techniques are difficult to apply. In general these ALE formulations are based on finite difference or weighted residual finite element solutions of the partial differential equations for the system. An alternative, energy based ALE model for fluid dynamics simulations may be obtained, by direct application of Hamilton's canonical equations to a finite element discretization of an open, deforming control volume. Formulated in terms of convected coordinates and incorporating an adaptive mesh scheme, this modeling approach yields a simple but general description of viscous compressible flows. Numerical application of the method demonstrates accurate results in the solution of several shock problems, whether the calculations are performed using a Lagrangian, an Eulerian, or an ALE mesh.
机译：已经开发了许多不同的连续流体和固体动力学问题的任意拉格朗日-欧拉（ALE）公式，以解决难以应用更常规的拉格朗日或欧拉建模技术的应用。通常，这些ALE公式基于系统偏微分方程的有限差分或加权剩余有限元解。通过将汉密尔顿正则方程直接应用于开放的，变形的控制体积的有限元离散化，可以获得用于流体动力学模拟的替代的基于能量的ALE模型。根据对流坐标表示并结合自适应网格方案，此建模方法可对粘性可压缩流进行简单但通用的描述。不管是使用拉格朗日，欧拉还是ALE网格进行计算，该方法的数值应用都证明了在解决多个冲击问题方面的准确结果。

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