A HEVI time-integration scheme for idealized non-hydrostatic compressible atmosphere flow [video]
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When entering the non-hydrostatic regime of the atmospheric modeling, the time-integration is one of the challenges for constructing an efficient dynamical core. A high aspect ratio between horizontal and vertical spacial discretization is common in the mesoscale community and it imposes a stringent restriction on time step size. While an explicit time solver is still acceptable for the evolving horizontal propagation, a semi-implicit or full-implicit time integration scheme is highly encouraged for the vertical dynamics. Discontinuous Galerkin (DG) method, a conservative, high-order and excellently scalable numerical method is employed for the spatial discretization. To overcome the aforementioned limitations, a horizontal-expilict-vertical-implicit (HEVI) time integration based DG is studied in the present work. The time-step size can be relaxed to the horizontal propagation only and the utilization of the horizontal domain decomposition can greatly improve the computational efficiency. An efficient implicit solver, which results in a block-tridiagonal system, is also introduced to accelerate the vertical dynamics. The performance of the proposed scheme will be presented.