Apply a positivity-preserving limiter of spectral element method to KIM

Abstract

 As for a tracer transport scheme, the spectral element method (SEM) has a good accuracy in the  L2-norm error analysis since it uses relatively high-order continuous polynomials. However, the fact  that the basis functions for SEM are globally continuous makes it difficult to preserve important property such as positivity of tracer advection, which results in oscillations in numerical solutions. Moreover, this may cause difficulties in maintaining conservation of mass in long-term integration. Therefore, in many studies, many efforts have been made to reduce or eliminate these oscillations. Among them, this study attempts to apply a positivity-preserving limiter used in finite volume and discontinuous finite element method to SEM. It was proposed by Zhang and Shu (2010) in the highorder positivity-preserving discontinuous Galerkin schemes without losing local conservation or high-order accuracy.  The Korean Integrated Model (KIM) is employing SEM for a tracer transport scheme and has a kind of sign-preserving limiter to reduce oscillations currently (Guba et al.). The limiter prevents all undershoots up to machine precision in a highly deformational advection test case. As a primary result, this study aims to analyze the numerical results in terms of accuracy, mass conservation, oscillation magnitude, comparing to two types of limiters (positivity-preserving limiter & sign-preserving limiter) with original one of KIM.