局所細密化節点による低気圧を模した渦の再現性

Abstract

Accuracy of advection on the sphere with refined nodes was investigated in a test case with a known exact solution, in which two vortices at the North and South poles roll-up. Flyer and Lehto (2010) investigated the accuracy with refined nodes and showed that the node refinement improves accuracy in the test case. They made refined nodes from minimum energy (ME) nodes using electrostatic repulsion, but this algorithm may not be useful because generation of refined nodes can be slow and inaccurate. Thus, we adopt an alternative node refinement algorithm, the Schmidt transformation of quasi-uniform nodes. We obtained more accurate results with refined nodes than those with quasi-uniform nodes. To achieve normalized root mean square error (ℓ2) of about 1.0 × 10(−5), 4096 node are needed in the quasi-uniform case compared to 1849 nodes with refined nodes.