2018
DOI: 10.1175/mwr-d-18-0043.1
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Finite Elements Used in the Vertical Discretization of the Fully Compressible Core of the ALADIN System

Abstract: The finite-element method with B splines is used for definition of vertical operators in the nonhydrostatic fully compressible dynamical core of the ALADIN system. It represents a generalization of the same method used in the hydrostatic dynamical core shared by the ALADIN system and the global forecast system ARPEGE/IFS. The method is shown to be robust enough in idealized academic tests and real simulations. Its theoretical superiority is shown when compared with the finite-difference method.

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Cited by 7 publications
(5 citation statements)
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“…This has been done in the finite difference discretization, but unfortunately, the C1 constraint is not guaranteed in the construction of the finite element operators. An iterative method was developed by (Vivoda and Smolíková 2013) in order to relax the C1 constraint. Based on this approach a theoretical development to solve the C1 constraint was proposed by Subias (2015), which has been tested in HARMONIE-AROME in cycle 40h1.1.…”
Section: A Dynamicsmentioning
confidence: 99%
“…This has been done in the finite difference discretization, but unfortunately, the C1 constraint is not guaranteed in the construction of the finite element operators. An iterative method was developed by (Vivoda and Smolíková 2013) in order to relax the C1 constraint. Based on this approach a theoretical development to solve the C1 constraint was proposed by Subias (2015), which has been tested in HARMONIE-AROME in cycle 40h1.1.…”
Section: A Dynamicsmentioning
confidence: 99%
“…The vertical discretization is based on finite differences (Simmons and Burridge, 1981) or finite elements. For the latter the implementation of B-splines of either linear or cubic order (Untch and Hortal, 2004) can be used in the hydrostatic case only, while in the nonhydrostatic case B-splines of general order are introduced according to Vivoda and Smolíková (2013). Unlike the hydrostatic case, in the ALADIN-NH dynamical core not only the integral operators but also the vertical derivatives need to be discretized since they appear in the set of basic equations.…”
Section: The Aladin-nh Nonhydrostatic Dynamical Corementioning
confidence: 99%
“…In the HPE case, it uses cubic B-splines as basis functions (Untch and Hortal 2004). In the nonhydrostatic EE core, a more general scheme was introduced, enhancing accuracy to an arbitrary order (Vivoda and Smolíková 2013).…”
Section: Randd Highlightsmentioning
confidence: 99%