Numerical methods for entrainment and detrainment in the multi-fluid Euler equations for convection
Numerical methods for entrainment and detrainment in the multi-fluid Euler equations for convection
复制标题
对流多流体欧拉方程中夹带和脱附的数值方法
DOI：
10.1002/qj.3728
复制
发表时间：
2020
影响因子：
8.9
通讯作者：
McIntyre W
中科院分区：
文献类型：
--
作者：
McIntyre W
对流方案是全球天气和气候模型中误差的一大来源，现代分辨率通常太精细而无法对对流进行参数化，但仍然太粗糙而无法完全解析它。最近，人们提出了多流体方程的数值解，以更灵活和一致地处理亚网格尺度对流，包括对流和非平衡动力学的净质量传递。该技术涉及将大气分成多种流体。例如，大气可以分为活跃的上升气流和稳定的区域。流体通过共同的压力、阻力和质量传递（夹带和脱出）相互作用。关于流体之间的传质项的数值特性知之甚少。我们推导了重新标记流体的质量传递项，并推导了传递方案的数值属性，包括同位网格上的有界性、动量守恒和能量守恒。使用 C 网格对多流体欧拉方程进行数值模拟，在解析良好的双流体干对流测试案例上使用稳定和不稳定的传输处理。我们发现两种方案对于大时间步来说是保守的、稳定的和有界的，并且在交错网格上保持了它们的数值特性。
Convection schemes are a large source of error in global weather and climate models, and modern resolutions are often too fine to parametrize convection, but are still too coarse to fully resolve it. Recently, numerical solutions of multi‐fluid equations have been proposed for a more flexible and consistent treatment of subgrid‐scale convection, including net mass transport by convection and non‐equilibrium dynamics. The technique involves splitting the atmosphere into multiple fluids. For example, the atmosphere could be divided into buoyant updraughts and stable regions. The fluids interact through a common pressure, drag and mass transfers (entrainment and detrainment). Little is known about the numerical properties of mass transfer terms between the fluids. We derive mass transfer terms which relabel the fluids and derive numerical properties of the transfer schemes, including boundedness, momentum conservation and energy conservation on a co‐located grid. Numerical simulations of the multi‐fluid Euler equations using a C‐grid are presented using stable and unstable treatments of the transfers on a well‐resolved two‐fluid dry convection test case. We find two schemes which are conservative, stable and bounded for large time steps, and maintain their numerical properties on staggered grids.