A SECOND-ORDER ADAPTIVE ARBITRARY LAGRANGIAN–EULERIAN METHOD FOR THE COMPRESSIBLE EULER EQUATIONS
A SECOND-ORDER ADAPTIVE ARBITRARY LAGRANGIAN–EULERIAN METHOD FOR THE COMPRESSIBLE EULER EQUATIONS
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DOI：
10.1142/s0217984909017923
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发表时间：
2009-02
影响因子：
1.9
通讯作者：
Yu-Han Wang;N. Zhao;Chun-Wei Wang;Donghong Wang
中科院分区：
文献类型：
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作者：
Yu-Han Wang;N. Zhao;Chun-Wei Wang;Donghong Wang
任意拉格朗日-欧拉（ALE）方法中的有限体积格式大多是在交错网格上构造的，其中动量定义在节点处，其他变量（密度、压力和比内能）以网格为中心。然而，这类方案必须使用两次以单元为中心的重映射算法，这是非常低效的。此外，有不一致的处理的动能和内能。1最近，一类新的细胞中心拉格朗日格式的二维可压缩流问题已被提出在参考文献。该算法的主要新功能是在每个边缘上引入四个压力，每个节点在边缘的每一侧上两个。该方案仅具有一阶精度。本文利用ENO型方法构造了一个二阶中心守恒ENO拉格朗日格式，以扩展空间二阶精度。时间离散是基于一个二阶龙格-库塔格式。将守恒插值（重映射）方法3，4与二阶Lagrange格式相结合，可以得到一种以单元为中心的二阶ALE方法。用该方法进行了数值试验。结果表明，该方法是有效的，具有二阶精度。最后，为了进一步提高激波区域的分辨率，我们采用了基于变分原理的自适应网格生成方法作为一类自适应ALE方法的重分区策略。数值实验验证了该方法的有效性。
Most of finite volume schemes in the Arbitrary Lagrangian–Eulerian (ALE) method are constructed on the staggered mesh, where the momentum is defined at the nodes and the other variables (density, pressure and specific internal energy) are cell-centered. However, this kind of schemes must use a cell-centered remapping algorithm twice which is very inefficient. Furthermore, there is inconsistent treatment of the kinetic and internal energies.1 Recently, a new class of cell-centered Lagrangian scheme for two-dimensional compressible flow problems has been proposed in Ref. 2. The main new feature of the algorithm is the introduction of four pressures on each edge, two for each node on each side of the edge. This scheme is only first-order accurate. In this paper, a second-order cell-centered conservative ENO Lagrangian scheme is constructed by using an ENO-type approach to extend the spatial second-order accuracy. Time discretization is based on a second-order Runge–Kutta scheme. Combining a conservative interpolation (remapping) method3,4 with the second-order Lagrangian scheme, a kind of cell-centered second-order ALE methods can be obtained. Some numerical experiments are made with this method. All results show that our method is effective and have second-order accuracy. At last, in order to further increase the resolution of shock regions, we use an adaptive mesh generation based on the variational principle5 as a rezoned strategy for developing a class of adaptive ALE methods. Numerical experiments are also presented to valid the performance of the proposed method.