AI 中文总结
研究粘性旋转浅水方程非对称内罚 DG 离散化中内罚参数标度的影响，通过局部 Lax--Friedrichs 通量近似双曲项，比较$\beta = 1$和$\beta = 3$，建立相关性质，经测试表明标准标度在精度-成本折衷上表现更好。
AI 中文摘要
我们研究了内罚参数的标度如何影响地势变量下粘性旋转浅水方程的非对称内罚伽辽金（NIPG）离散化。双曲项由局部 Lax--Friedrichs 通量近似，粘性通过罚律$\mu_e=\sigma h_e^{-\beta}$作用于动量变量。将标准选择$\beta = 1$和超罚选择$\beta = 3$与对称内罚伽辽金参考进行比较。对于扩散形式，我们建立了$\beta\geq1$时的一致性、连续性以及动量 DG 半范数下的精确强制性恒等式。制造解测试表明，超罚可以恢复预期的动量$L^2$精度，而耦合的地势变量不一定有相同提升。旋转和地形感知测试进一步表明，对于这里考虑的显式实现，标准标度通常能给出更好的精度-成本折衷。
英文摘要
We investigate how the scaling of the interior-penalty parameter affects nonsymmetric interior-penalty Galerkin (NIPG) discretizations of the viscous rotating shallow-water equations in geopotential variables. The hyperbolic terms are approximated by a local Lax--Friedrichs flux, while viscosity acts on the momentum variables through a penalty law $μ_e=σh_e^{-β}$. The standard choice $β=1$ and the super-penalized choice $β=3$ are compared with a symmetric interior-penalty Galerkin reference. For the diffusion form, we establish consistency, continuity for $β\ge 1$, and an exact coercivity identity in the momentum DG seminorm. Manufactured-solution tests show that super-penalization can recover the expected momentum $L^2$ accuracy, whereas the coupled geopotential variable need not exhibit the same improvement. Rotating and topography-aware tests further show that the standard scaling generally gives the better accuracy-cost compromise for the explicit implementation considered here.
