dorsal/arxiv
View SchemaStability of leap-frog constant-coefficients semi-implicit schemes for the fully elastic system of Euler equations. Flat-terrain case
| Authors | Pierre Benard, Rene Laprise, Jozef Vivoda, Petra Smolikova |
|---|---|
| Categories | |
| ArXiv ID | physics/0311123 |
| URL | https://arxiv.org/abs/physics/0311123 |
| DOI | 10.1175/1520-0493(2004)132<1306:SOLCSS>2.0.CO;2 |
Abstract
The aim of this paper is to investigate the response of this system/scheme in terms of stability in presence of explicitly treated residual terms, as it inevitably occurs in the reality of NWP. This sudy is restricted to the impact of thermal and baric residual terms (metric residual terms linked to the orography are not considered here). It is shown that conversely to what occurs with Hydrostatic Primitive Equations, the choice of the prognostic variables used to solve the system in time is of primary importance for the robustness with Euler Equations. For an optimal choice of prognostic variables, unconditionnally stable schemes can be obtained (with respect to the length of the time-step), but only for a smaller range of reference states than in the case of Hydrostatic Primitive Equations. This study also indicates that: (i) vertical coordinates based on geometrical height and on mass behave similarly in terms of stability for the problems examined here, and (ii) hybrid coordinates induce an intrinsic instability, the practical importance of which is however not completely elucidated in the theoretical context of this paper.
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"abstract": "The aim of this paper is to investigate the response of this system/scheme in\nterms of stability in presence of explicitly treated residual terms, as it\ninevitably occurs in the reality of NWP. This sudy is restricted to the impact\nof thermal and baric residual terms (metric residual terms linked to the\norography are not considered here). It is shown that conversely to what occurs\nwith Hydrostatic Primitive Equations, the choice of the prognostic variables\nused to solve the system in time is of primary importance for the robustness\nwith Euler Equations. For an optimal choice of prognostic variables,\nunconditionnally stable schemes can be obtained (with respect to the length of\nthe time-step), but only for a smaller range of reference states than in the\ncase of Hydrostatic Primitive Equations. This study also indicates that: (i)\nvertical coordinates based on geometrical height and on mass behave similarly\nin terms of stability for the problems examined here, and (ii) hybrid\ncoordinates induce an intrinsic instability, the practical importance of which\nis however not completely elucidated in the theoretical context of this paper.",
"arxiv_id": "physics/0311123",
"authors": [
"Pierre Benard",
"Rene Laprise",
"Jozef Vivoda",
"Petra Smolikova"
],
"categories": [
"physics.ao-ph"
],
"doi": "10.1175/1520-0493(2004)132\u003c1306:SOLCSS\u003e2.0.CO;2",
"title": "Stability of leap-frog constant-coefficients semi-implicit schemes for the fully elastic system of Euler equations. Flat-terrain case",
"url": "https://arxiv.org/abs/physics/0311123"
},
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