Masters Thesis Defense by Danny Høgsholt – Niels Bohr Institutet - Københavns Universitet

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Masters Thesis Defense by Danny Høgsholt

Application of a non-hydrostatic, semi-Lagrangian scheme on convective dynamics.

ABSTRACT: A non-hydrostatic, semi-Lagrangian transport scheme is proposed. The scheme is able to solve the fully-compressible Euler equations with a minimum of filtering and approximation, allowing high-speed waves such as acoustic waves. Acoustic waves put severe limitations on the maximum time step that can be taken, ensuring stability by not violating the Courant-Friedrich-Lewy criterion. Therefore, a time-split technique is incorporated, such that the pressure type waves are treated with an Eulerian forward-backward method and the advective part is treated with a semi-Lagrangian method. The scheme is able to reliably simulate convective thermals in both neutrally and stably stratified environments, including features as gravity wave oscillations and Kelvin-Helmholtz instability. A review of Eulerian and semi-Lagrangian methods is given, along with a discussion of previous methods used in compressible models. Qualitative comparisons to earlier non-hydrostatic model studies are made.