论文标题
水平/垂直隐式非静态气氛中能量交流的确切空间和时间平衡
Exact spatial and temporal balance of energy exchanges within a horizontally explicit/vertically implicit non-hydrostatic atmosphere
论文作者
论文摘要
引入了一种新的水平水平/垂直隐式（HEVI）时间分配方案，用于大气建模，为此，在隐式垂直替代中应用了水平差异项。新的HEVI方案是与混合模拟频谱元件空间离散和半平移垂直时间步进方案一起实施的，该方案既保留了运动方程式的非经典汉密尔顿形式的偏斜对称结构。在这种情况下，新的HEVI方案允许在时空中所有能量交流的确切平衡。但是，由于满足此平衡的水平通量的选择与时间级结束时的水平速度不一致，因此该方案仍然承认了时间节能误差。线性化特征值分析表明，与完全隐式的方法相似，新的HEVI方案对于所有浮力模式都是中性稳定的，而且与二阶梯形HEVI方案不同，对于以下所有水平CFL数量的所有声学模式，梯形HEVI方案都是稳定的。该方案针对行星和非静水状态的标准测试用例进行了验证。对于行星尺度的斜压力不稳定性测试案例，新的配方表现出二次振荡的潜力，具有动能功率交换的潜力，时间频率约为四倍，而水平三阶则表现出大约四次，垂直二阶二阶梯形方案。对于非静态测试案例，显示潜在温度诊断方程的垂直上风显示可减少虚假振荡而不改变溶液的能量，因为这种向后的趋势是以能量一致的方式进行的。对于在仿射几何形状上配置的测试用例，能量交换的确切平衡使模型可以稳定运行而无需任何形式的耗散。
A new horizontally explicit/vertically implicit (HEVI) time splitting scheme for atmospheric modelling is introduced, for which the horizontal divergence terms are applied within the implicit vertical substep. The new HEVI scheme is implemented in conjunction with a mixed mimetic spectral element spatial discretisation and semi-implicit vertical time stepping scheme that both preserve the skew-symmetric structure of the non-canonical Hamiltonian form of the equations of motion. Within this context the new HEVI scheme allows for the exact balance of all energetic exchanges in space and time. However since the choice of horizontal fluxes for which this balance is satisfied is not consistent with the horizontal velocity at the end of the time level the scheme still admits a temporal energy conservation error. Linearised eigenvalue analysis shows that similar to a fully implicit method, the new HEVI scheme is neutrally stable for all buoyancy modes, and unlike a second order trapezoidal HEVI scheme is stable for all acoustic modes below a certain horizontal CFL number. The scheme is validated against standard test cases for both planetary and nonhydrostatic regimes. For the planetary scale baroclinic instability test case, the new formulation exhibits a secondary oscillation in the potential to kinetic energy power exchanges, with a temporal frequency approximately four times that exhibited by a horizontally third order, vertically second order trapezoidal scheme. For the nonhydrostatic test case, the vertical upwinding of the potential temperature diagnostic equation is shown to reduce spurious oscillations without altering the energetics of the solution, since this upwinding is performed in an energetically consistent manner. For this test case, which is configured on an affine geometry, the exact balance of energy exchanges allows the model to run stably without any form of dissipation.
