Comparison between adaptive and uniform discontinuous Galerkin simulations in dry 2D bubble experiments

JOURNAL OF COMPUTATIONAL PHYSICS

卷:235

Article

Mueller, Andreas¹  Behrens, Joern²  Giraldo, Francis X.¹  Wirth, Volkmar³ 

[1] USN, Postgrad Sch, Dept Appl Math, Monterey, CA 93943 USA

[2] Univ Hamburg, D-20144 Hamburg, Germany

[3] Johannes Gutenberg Univ Mainz, Inst Atmospher Phys, D-55127 Mainz, Germany

关键词: Adaptive mesh refinement;    Discontinuous Galerkin;    IMEX;    Meteorology;    Dry warm air bubble;   

DOI  :  10.1016/j.jcp.2012.10.038

来源: Elsevier

【 摘 要 】

Adaptive mesh refinement generally aims to increase computational efficiency without compromising the accuracy of the numerical solution. However it is an open question in which regions the spatial resolution can actually be coarsened without affecting the accuracy of the result. This question is investigated for a specific example of dry atmospheric convection, namely the simulation of warm air bubbles. For this purpose a novel numerical model is developed that is tailored towards this specific application. The compressible Euler equations are solved with a discontinuous Galerkin method. Time integration is done with an IMEX-method and the dynamic grid adaptivity uses space filling curves via the AMATOS function library. So far the model is able to simulate dry flow in two-dimensional geometry without subgrid-scale modeling. The model is tested with three standard test cases. An error indicator is introduced for a warm air bubble test case which allows one to compare the accuracy between different choices of refinement regions without knowing the exact solution. Essentially this is done by comparing features of the solution that are strongly sensitive to spatial resolution. For the rising warm air bubble the additional error by using adaptivity is smaller than 1% of the total numerical error if the average number of elements used for the adaptive simulation is about a factor of two times smaller than the number used for the simulation with the uniform fine-resolution grid. Correspondingly the adaptive simulation is almost two times faster than the uniform simulation. Furthermore the adaptive simulation is more accurate than a uniform simulation when both use the same CPU-time. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free