A conservative multi-tracer transport scheme for spectral-element spherical grids

• Published in: Journal of computational physics Vol. 256; pp. 118 - 134
• Main Authors: Erath, Christoph, Nair, Ramachandran D.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.01.2014
• Subjects: Algorithms; Characteristic semi-Lagrangian; Computation; Computer simulation; Conservative semi-Lagrangian; Cubed sphere; Discretization; Flux-corrected transport; Mathematical models; Multi-moment reconstruction; Multi-tracer transport; Parallelization; Reconstruction; Scalability; Spectra; Spectral-element grid; Transport; Flux-corrected transport; Conservative semi-Lagrangian; Scalability; Multi-tracer transport; Cubed sphere; Characteristic semi-Lagrangian; Spectral-element grid; Multi-moment reconstruction; Parallelization
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2013.08.050

Atmospheric models used for practical climate simulation must be capable handling the transport of hundreds of tracers. For computational efficiency conservative multi-tracer semi-Lagrangian type transport schemes are appropriate. Global models based on high-order Galerkin approach employ highly non-uniform spectral-element grids, and semi-Lagrangian transport is a challenge on those grids. A conservative semi-Lagrangian scheme (SPELT — SPectral-Element Lagrangian Transport) employing a multi-moment compact reconstruction procedure is developed for non-uniform quadrilateral grids. The scheme is based on a characteristic semi-Lagrangian method that avoids complex and expensive upstream area computations. The SPELT scheme has been implemented in the High-Order Method Modeling Environment (HOMME), which is based on a cubed-sphere grid with spectral-element spatial discretization. Additionally, we show the (strong) scalability and multi-tracer efficiency using several benchmark tests. The SPELT solution can be made monotonic (positivity preserving) by combining the flux-corrected transport algorithm, which is demonstrated on a uniform resolution grid. In particular, SPELT can be efficiently used for non-uniform grids and provides accurate and stable results for high-resolution meshes.