论文标题
混合模拟频谱元素的彼得 - 加加尔金助剂升至地球物理流动问题
Petrov-Galerkin flux upwinding for mixed mimetic spectral elements, and its application to geophysical flow problems
论文作者
论文摘要
描述并分析了上弯的质量通量，以使用混合模拟频谱元素离散地离散。这涉及彼得罗夫 - 盖尔金配方，通过该公式在下游位置沿速度特征评估质量通量测试函数。至于原始的混合模拟频谱元素对流操作员，上弯的质量通量对流操作员是保守的，但是与原始的对流算子不同，纯粹是双曲线的原始对流操作员，尖锐的对流操作员增加了耗散，这偏向于高波数。上弯的对流操作员还消除了原始对流操作员分散关系中存在的光谱差距。至于原始的对流运算符，可以通过类似地向示踪剂梯度的试验函数构建材料形式的对流操作员。两种方法都允许通过偏斜的制剂为不可压缩的流场恢复精确的能源保护。但是，这些偏斜的对称配方再次是纯粹的双曲线算子，不会抑制振荡。该方案是在球体上的浅水法中实施的，以诊断和插入潜在的涡度。在没有其他耗散术语的情况下，证明它可以为压缩不稳定的标准测试用例产生更连贯的结果。
Upwinded mass fluxes are described and analysed for advection operators discretised using mixed mimetic spectral elements. This involves a Petrov-Galerkin formulation by which the mass flux test functions are evaluated at downstream locations along velocity characteristics. As for the original mixed mimetic spectral element advection operator, the upwinded mass flux advection operator is conservative, however unlike the original advection operator, which is purely hyperbolic, the upwinded advection operator adds dissipation which is biased towards high wave numbers. The upwinded advection operator also removes the spectral gaps present in the dispersion relation for the original advection operator. As for the original advection operator, a material form advection operator may be constructed by similarly downwinding the trial functions of the tracer gradients. Both methods allow for the recovery of exact energy conservation for an incompressible flow field via skew-symmetric formulations. However these skew-symmetric formulations are once again purely hyperbolic operators which do not suppress oscillations. The scheme is implemented within a shallow water code on the sphere in order to diagnose and interpolate the potential vorticity. In the absence of other dissipation terms, it is shown to yield more coherent results for a standard test case of barotropic instability.
