多流体对流欧拉方程中卷吸和分离的数值方法
Numerical methods for entrainment and detrainment in the multi-fluid Euler equations for convection
摘要：
对流方案是全球天气和气候模式中的一个很大的误差来源，现代分辨率往往太精细，对流参数化，但仍然太粗糙，完全solves. Recently，数值解的多流体方程已经提出了一个更灵活和一致的处理亚网格尺度对流，包括净质量输送对流和非平衡动力学。这项技术涉及将大气层分裂成多种流体。例如，大气层可以分为浮力上升区和稳定区。流体通过共同的压力、阻力和质量传递（夹带和去除）相互作用。关于流体之间的传质项的数值特性知之甚少。我们推导出的质量传递项，重新标记的流体，并获得数值性质的传输计划，包括有界性，动量守恒和能量守恒。采用稳定和不稳定的处理方法，在一个高分辨率的两流体干对流试验情况下，使用C-网格的多流体欧拉方程的数值解。我们找到了两个格式，这是保守的，稳定的和有界的大时间步长，并保持其数值性质交错网格。
英文摘要：
Convection schemes are a large source of error in global weather and climate models, and modern resolutions are often too fine to parameterise 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 sub-grid 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 updrafts 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. Numerical solutions 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 timesteps, and maintain their numerical properties on staggered grids.
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