Arbitrary-Lagrangian-Eulerian One-Step WENO Finite Volume Schemes on Unstructured Triangular Meshes
Arbitrary-Lagrangian-Eulerian One-Step WENO Finite Volume Schemes on Unstructured Triangular Meshes
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DOI：
10.4208/cicp.181012.010313a
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发表时间：
2013-02
期刊：
影响因子：
--
通讯作者：
W. Boscheri;M. Dumbser
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文献类型：
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作者：
W. Boscheri;M. Dumbser
本文提出了一类新的高精度ALE一步韦诺有限体积格式，在移动的二维非结构三角形网格上求解非线性双曲型守恒律方程组.采用韦诺重建算法实现空间高阶精度，采用局部时空Galerkin预报器实现时间高阶一步离散。为此，一个新的元素-当地弱制定的管理PDE上移动的空间-时间元素。考虑通过一组预定义的节点的拉格朗日插值多项式的时空基和测试函数。此外，由相同的局部时空基函数定义的多项式映射的PDE的弱解被用来映射到一个时空参考元素的运动的物理时空元素。为了保持算法的简单性，最终的ALE一步有限体积格式使用直边移动三角形网格。这在ALE框架中是可能的，其允许不同于局部流体速度的局部网格速度。我们提出了本文提出的方案的数值收敛速度高达六阶精度的空间和时间，并显示了一些经典的数值试验问题的二维欧拉方程的可压缩气体动力学。
In this article we present a new class of high order accurate Arbitrary-Eulerian-Lagrangian (ALE) one-step WENO finite volume schemes for solving nonlinear hyperbolic systems of conservation laws on moving two dimensional unstructured triangular meshes. A WENO reconstruction algorithm is used to achieve high order accuracy in space and a high order one-step time discretization is achieved by using the local space-time Galerkin predictor. For that purpose, a new element--local weak formulation of the governing PDE is adopted on moving space--time elements. The space-time basis and test functions are obtained considering Lagrange interpolation polynomials passing through a predefined set of nodes. Moreover, a polynomial mapping defined by the same local space-time basis functions as the weak solution of the PDE is used to map the moving physical space-time element onto a space-time reference element. To maintain algorithmic simplicity, the final ALE one-step finite volume scheme uses moving triangular meshes with straight edges. This is possible in the ALE framework, which allows a local mesh velocity that is different from the local fluid velocity. We present numerical convergence rates for the schemes presented in this paper up to sixth order of accuracy in space and time and show some classical numerical test problems for the two-dimensional Euler equations of compressible gas dynamics.