Horizontally Explicit and Vertically Implicit (HEVI) Time Discretization Scheme for a Discontinuous Galerkin Nonhydrostatic Model

AbstractA two-dimensional nonhydrostatic (NH) atmospheric model based on the compressible Euler system has been developed in the (x, z) Cartesian domain. The spatial discretization is based on a nodal discontinuous Galerkin (DG) method with exact integration. The orography is handled by the terrain-following height-based coordinate system. The time integration uses the horizontally explicit and vertically implicit (HEVI) time-splitting scheme, which is introduced to address the stringent restriction on the explicit time step size due to a high aspect ratio between the horizontal (x) and vertical (z) spatial discretization. The HEVI scheme is generally based on the Strang-type operator-split approach, where the horizontally propagating waves in the Euler system are solved explicitly while the vertically propagating waves are treated implicitly. As a consequence, the HEVI scheme relaxes the maximum allowed time step to be mainly determined by the horizontal grid spacing. The accuracy of the HEVI scheme is r...

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