We present a discontinuous Galerkin method for moist atmospheric dynamics, with and without warm rain. By considering a combined density for water vapour and cloud water, we avoid the need to model and compute a source term for condensation. We recover the vapour and cloud densities by solving a pointwise non-linear problem each time step. Consequently, we enforce the requirement for the water vapour not to be supersaturated implicitly. Together with an explicit time-stepping scheme, the method is highly parallelisable and can utilise high-performance computing hardware. Furthermore, the discretisation works on structured and unstructured meshes in two and three spatial dimensions. We illustrate the performance of our approach using several test cases in two and three spatial dimensions. In the case of a smooth, exact solution, we illustrate the optimal higher-order convergence rates of the method.

翻译：我们提出了一种适用于湿大气动力学（含与不含暖雨过程）的间断伽辽金方法。通过将水汽和云水的密度合并考虑，我们无需建模和计算凝结源项。在每个时间步，通过逐点求解非线性问题来恢复水汽和云水密度，从而隐式强制执行水汽不出现过饱和的约束条件。结合显式时间推进格式，该方法具有高度并行性，可充分利用高性能计算硬件。此外，该离散方案适用于二维和三维空间中的结构化和非结构化网格。我们通过多个二维和三维空间测试案例验证了方法的性能。在存在光滑精确解的情况下，展示了该方法的最优高阶收敛率。