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.

描述并分析了使用混合模拟频谱元素离散化的对流算子的迎风质量通量。这涉及Petrov-Galerkin公式，通过该公式，可以沿速度特性在下游位置评估质量通量测试功能。对于原始的混合模拟频谱元素对流算子，上风的质量通量对流算子是保守的，但是与原始的对流算子纯粹是双曲线的不同，上风的对流算子增加了向高波数偏置的耗散。上流对流算子还为原始对流算子消除了色散关系中存在的光谱间隙。至于原先的平流算子 可以通过类似地降低示踪梯度的试验函数来构造材料形式的对流算子。两种方法都可以通过偏斜对称公式为不可压缩的流场恢复精确的能量守恒。但是，这些偏斜对称公式仍然是纯双曲算子，不会抑制振荡。该方案是在球体上的浅水代码内实施的，以便诊断和内插潜在的涡度。在没有其他耗散项的情况下，对于正压不稳定性的标准测试案例，它显示出更一致的结果。但是，这些偏斜对称公式仍然是纯双曲算子，不会抑制振荡。该方案是在球体上的浅水代码内实施的，以便诊断和内插潜在的涡度。在没有其他耗散项的情况下，对于正压不稳定性的标准测试案例，它显示出更一致的结果。但是，这些偏斜对称公式仍然是纯双曲算子，不会抑制振荡。该方案是在球体上的浅水代码内实施的，以便诊断和内插潜在的涡度。在没有其他耗散项的情况下，对于正压不稳定性的标准测试案例，它显示出更一致的结果。