Leibniz MMS Days 2023 - Abstract

Knoth, Oswald

Improved advection schemes for continuous spectral methods

Spectral methods are nowadays a common tool in numerical weather prediction. However for the accompanying tracer transport equations the method has to be stabilized to guarantee positivity and monotonicity of these values. We will discuss two different methods different in nature to overcome these limitations. The first one is a posteriori inside a time integration method and reshuffles the tracer data locally via small optimization problems to preserve the data properties. The optimization problems includes as constraints mass preservation and bound constraints. The second method blends the higher order spectral method with a lower order finite volume method by a convex combination of both methods a priori to each time step. The low order method has the desired properties and is only used in troubled regions with usually steep gradients of the tracer variables. The blending is possible by rewriting the higher order method as a local flux method having the same structure as the low order method. Both methods are implemented in the Julia code CGDycore.jl. Numerical results are presented for tracer transport examples on the sphere from the DCMIP test suite.