Paul Aaron Ullrich, Peter Hjort Lauritzen and Christiane Jablonowski Some considerations for high-order ‘incremental remap’-based transport schemes: edges, reconstructions, and area integration International Journal for Numerical Methods in Fluids 71
The problem of tracer advection on the sphere is extremely important in modeling of the atmosphere and oceans. This paper examines the popular ‘incremental remap’ family of schemes, which are capable of reaching high-order accuracy without the need for multistage integration in time. Specifically, we show that in the presence of strong nonlinear, shear upstream edges must be treated with quadratic accuracy or else significant errors will arise.
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