Developement and test of a positive definite method for the Wicker-Skamarock-advection scheme
Responsible: Lennart Böske?
Project type: bachelor thesis
Duration: November 2011- May 2012

The 5^th order advection scheme of Wicker and Skamarock (2002) as it is implemented in PALM - hereafter WS5 - is neither positive definite nor monotonic. In case of sharp gradients of a transported scalar, discretisation errors of WS5 can lead to non-physical negative values or unwanted amplification of initial extrema. In order to achieve positive definiteness or monotonicity so-called flux limiters can be used to correct the solutions given by WS5 (Skamarock, 2006; Wang et al., 2009). In this thesis two low-order flux limiters (positive definite and monotonic) for WS5 are investigated using 1D-simulations, focusing on shape preserving qualities of the modified scheme. With regard to a potential future implementation in PALM the increase in computing time caused by the flux limiters is evaluated.

Download: bachelor thesis​ (in German)