Show simple item record

dc.contributor.authorGiraldo, F.X.
dc.contributor.authorRestelli, M.
dc.date.accessioned2013-01-18T19:11:44Z
dc.date.available2013-01-18T19:11:44Z
dc.date.issued2008
dc.identifier.citationJournal of Computational Physics / Volume 227, Issue 8, 3849-3877
dc.identifier.urihttp://hdl.handle.net/10945/25519
dc.descriptionThe article of record as published may be located at http://dx.doi.org/10.1016/j.jcp.2007.12.009en_US
dc.description.abstractWe present spectral element (SE) and discontinuous Galerkin (DG) solutions of the Euler and compressible Navier-Stokes (NS) equations for stratified fluid flow which are of importance in nonhydrostatic mesoscale atmospheric modeling. We study three different forms of the governing equations using seven test cases. Three test cases involve flow over mountains which require the implementation of non-reflecting boundary conditions, while one test requires viscous terms (density current). Including viscous stresses into finite difference, finite element, or spectral element models poses no additional challenges; however, including these terms to either finite volume or discontinuous Galerkin models requires the introduction of additional machinery because these methods were originally designed for first-order operators. We use the local discontinuous Galerkin method to overcome this obstacle. The seven test cases show that all of our models yield good results. The main conclusion is that equation set 1 (non-conservation form) does not perform as well as sets 2 and 3 (conservation forms). For the density current (viscous), the SE and DG models using set 3 (mass and total energy) give less dissipative results than the other equation sets; based on these results we recommend set 3 for the development of future multiscale research codes. In addition, the fact that set 3 conserves both mass and energy up to machine precision motives us to pursue this equation set for the development of future mesoscale models. For the bubble and mountain tests, the DG models performed better. Based on these results and due to its conservation properties we recommend the DG method. In the worst case scenario, the DG models are 50% slower than the non-conservative SE models. In the best case scenario, the DG models are just as efficient as the conservative SE models. Published by Elsevier Inc.en_US
dc.rightsThis publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.en_US
dc.titleA study of spectral element and discontinuous Galerkin methods for the Navier-Stokes equations in nonhydrostatic mesoscale atmospheric modeling: Equation sets and test casesen_US
dc.typeArticleen_US
dc.contributor.departmentApplied Mathematics


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record