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Titel |
Hamiltonian approaches to spatial and temporal discretization of fully compressible equations |
VerfasserIn |
Thomas Dubos, Sarvesh Dubey |
Konferenz |
EGU General Assembly 2017
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Medientyp |
Artikel
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Sprache |
en
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Digitales Dokument |
PDF |
Erschienen |
In: GRA - Volume 19 (2017) |
Datensatznummer |
250146762
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Publikation (Nr.) |
EGU/EGU2017-10803.pdf |
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Zusammenfassung |
The fully compressible Euler (FCE) equations are the most accurate for representing atmospheric motion, compared to approximate systems like the hydrostatic, anelastic or pseudo-incompressible systems. The price to pay for this accuracy is the presence of additional degrees of freedom and high-frequency acoustic waves that must be treated implicitly.
In this work we explore a Hamiltonian approach to the issue of stable spatial and temporal discretization of the FCE using a non-Eulerian vertical coordinate. For scalability, a horizontally-explicit, vertically-implicit (HEVI) time discretization is adopted. The Hamiltonian structure of the equations is used to obtain the spatial finite-difference discretization and also in order to identify those terms of the equations of motion that need to be treated implicitly. A novel treatment of the lower boundary condition in the presence of orography is introduced: rather than enforcing a no-normal-flow boundary condition, which couples the horizontal and vertical velocity components and interferes with the HEVI structure, the ground is treated as a flexible surface with arbitrarily large stiffness, resulting in a decoupling of the horizontal and vertical dynamics and yielding a simple implicit problem which can be solved efficiently. Standard test cases performed in a vertical slice configuration suggest that an effective horizontal acoustic Courant number close to 1 can be achieved. |
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