o3o3: A Variant of Spectral Elements with a Regular Collocation Grid

• DOI: 10.1175/mwr-d-18-0288.1
• Publication Date: 2019-03-22T18:21:34Z
• Authors: J. Steppeler; J. Li; F. Fang; J. Zhu; P. A. Ullrich
• Keywords: Collocation (remote sensing); Quadrature (astronomy); Sparse grid

Abstract In this study, an alternative local Galerkin method (LGM), the o3o3 scheme, is proposed. a variant or generalization of third-order spectral element (SEM3). It uses piecewise polynomials for representation field and third-degree fluxes. For discretization, SEM3 irregular Legendre–Gauss–Lobatto grid while regular collocation grid. can be regarded as inhomogeneous finite-difference scheme on uniform grid, which means that equations are different each group with three points. A particular version set example many possibilities to construct LGM schemes polynomial spaces in basis functions used continuous at corner points function having derivatives shortly discussed. We propose standard alternatives using quadrature approximation. These two selected were chosen ease implementation rather than optimal performance. one dimension, compared SEM3, has larger CFL condition benefiting from use While This considered advantage physical parameterizations. The shortest resolved wave marginally smaller SEM3. dimensions, implemented sparse where only part underlying forecasting.