Conservation with moving meshes over orography
Conservation with moving meshes over orography
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DOI：
10.1016/j.jcp.2022.111217
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发表时间：
2021-08
期刊：
影响因子：
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通讯作者：
H. Yamazaki;H. Weller;C. Cotter;P. Browne
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文献类型：
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作者：
H. Yamazaki;H. Weller;C. Cotter;P. Browne
自适应网格有可能通过在最需要的地方提高分辨率来提高大气建模的准确性和效率。网格重分布或r-自适应通过移动网格而不更改连接来进行自适应。这避免了h-自适应（添加和删除点）的一些挑战：解决方案不需要在网格之间映射，这可能是昂贵的并引入错误，并且在并行计算机上没有负载平衡问题。一个长期存在的问题，这两种形式的自适应性已经改变的体积的域的分辨率变化在不均匀的边界。我们提出了一个解决方案，实现精确的局部守恒和保持一个统一的标量场，而网格的体积变化，因为它在地形移动。通过引入一个体积修正参数来跟踪单元体积，而不需要使用昂贵的守恒映射。本文描述了运动网格上地形上平流方程的有限体积解，并给出了计算结果，证明了运动网格的使用提高了计算精度。证明了均匀标量场的精确局部守恒和保持，并保持了正确的网格体积，我们使用最优输运生成的网格保证不缠结，并关于一个监控函数是等分布的。这导致了一个Monge-Ampère方程，该方程用牛顿解算器求解。牛顿解算器优于其他技术的证明在附录中。然而，牛顿解算器只有在应用于蒙赫-安培方程的左手侧并在右手侧进行定点迭代时才有效。
Adaptive meshes have the potential to improve the accuracy and efficiency of atmospheric modelling by increasing resolution where it is most needed. Mesh re-distribution, or r-adaptivity, adapts by moving the mesh without changing the connectivity. This avoids some of the challenges with h-adaptivity (adding and removing points): the solution does not need to be mapped between meshes, which can be expensive and introduces errors, and there are no load balancing problems on parallel computers. A long standing problem with both forms of adaptivity has been changes in volume of the domain as resolution changes at an uneven boundary. We propose a solution which achieves exact local conservation and maintains a uniform scalar field while the mesh changes volume as it moves over orography. This is achieved by introducing a volume correction parameter which tracks the cell volumes without using expensive conservative mapping.A finite volume solution of the advection equation over orography on moving meshes is described and results are presented demonstrating improved accuracy for cost using moving meshes. Exact local conservation and maintenance of uniform scalar fields is demonstrated and the correct mesh volume is preserved.We use optimal transport to generate meshes which are guaranteed not to tangle and are equidistributed with respect to a monitor function. This leads to a Monge-Ampère equation which is solved with a Newton solver. The superiority of the Newton solver over other techniques is demonstrated in the appendix. However the Newton solver is only efficient if it is applied to the left hand side of the Monge-Ampère equation with fixed point iterations for the right hand side.