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Remapping-free ALE-type kinetic method for flow computations

机译：用于计算流量的免重映射ALE型动力学方法

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Based on the integral form of the fluid dynamic equations, a finite volume kinetic scheme with arbitrary control volume and mesh velocity is developed. Different from the earlier unified moving mesh gas-kinetic method [C.Q.Jin, K. Xu, An unified moving grid gas-kinetic method in Eulerian space for viscous flow computation, J. Comput. Phys. 222 (2007) 155175], the coupling of the fluid equations and geometrical conservation laws has been removed in order to make the scheme applicable for any quadrilateral or unstructured mesh rather than parallelogram in 2D case. Since a purely Lagrangian method is always associated with mesh entangling, in order to avoid computational collapsing in multidimensional flow simulation, the mesh velocity is constructed by considering both fluid velocity (Lagrangian methodology) and diffusive velocity (Regenerating Eulerian mesh function). Therefore, we obtain a generalized Arbitrary-Lagrangian-Eulerian (ALE) method by properly designing a mesh velocity instead of re-generating a new mesh after distortion. As a result, the remapping step to interpolate flow variables from old mesh to new mesh is avoided. The current method provides a general framework, which can be considered as a remapping-free ALE-type method. Since there is great freedom in choosing mesh velocity, in order to improve the accuracy and robustness of the method, the adaptive moving mesh method [H.Z. Tang, T. Tang, Adaptive mesh methods for one-and two-dimensional hyperbolic conservation laws, SIAM J. Numer. Anal. 41 (2003) 487-515] can be also used to construct a mesh velocity to concentrate mesh to regions with high flow gradients. (C) 2009 Elsevier Inc. All rights reserved.
机译：基于流体动力学方程的积分形式，提出了具有任意控制体积和网格速度的有限体积动力学方案。与早期的统一移动网格气体动力学方法[C.Q.Jin，K. Xu，在欧拉空间中用于粘性流计算的统一移动网格气体动力学方法不同，J。Comput。物理222（2007）155175]，已删除了流体方程和几何守恒定律的耦合，以使该方案适用于任何四边形或非结构化网格，而不适用于二维情况下的平行四边形。由于纯粹的拉格朗日方法始终与网格缠结相关联，因此，为了避免多维流模拟中的计算崩溃，必须同时考虑流体速度（拉格朗日方法）和扩散速度（重新生成欧拉网格函数）来构造网格速度。因此，我们通过适当设计网格速度而不是在变形后重新生成新网格来获得广义的任意拉格朗日欧拉（ALE）方法。结果，避免了将流量变量从旧网格插入到新网格的重新映射步骤。当前方法提供了一种通用框架，可以将其视为免重映射ALE类型的方法。由于在选择网格速度方面有很大的自由度，因此为了提高该方法的准确性和鲁棒性，自适应运动网格方法[H.Z． Tang，T。Tang，《一维和二维双曲守恒律的自适应网格方法》，SIAM J. Numer。肛门41（2003）487-515]也可用于构造网格速度以将网格集中到具有高流动梯度的区域。 （C）2009 Elsevier Inc.保留所有权利。

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