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A Variational Multiscale Stabilized Finite Element Method to solve the Euler Equations for Nonhydrostatic Stratified Benchmarks

Wednesday 26th September 2012 - 09:50 to 10:15
INI Seminar Room 1
Session Title: 
Vertical Session
In this talk we present a Variational Multiscale Stabilization (VMS) for Compressible Euler Equations applied to the Finite Element (FE) solution of nonhydrostatic stratified flows. The VMS method was firstly presented by Hughes and co-workers [1] in the context of incompressible flows. In the present work, recentely presented in [3], we extend these concepts to Compressible Flows. In the framework of nonhydrostatic atmospheric dynamics, we test the algorithm for problems at low Mach numbers. A general version of the current compressible VMS technique was originally devised for Computational Fluid Dynamics (CFD) of compressible flows without stratification [2]. The present work is justified by the previously observed good performance of VMS and by the advantages that an element-based Galerkin formulation offers on massively parallel architectures, a challange for both CFD and Numerical Weather Prediction (NWP). Unphysical vertical oscillations that may appear for not well-balanced approximations are a relevant problem in NWP, especially in the proximity of steep topography. In that respect, to properly discretize the dominant hydrostatics, a particular interpolation technique is proposed. To evaluate the performance of the method in this context, some standard test cases of stratified environments are presented.

References [1] T. Hughes, Multiscale Phenomena: Green’s functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods, CMAME 127 (1995) 387–401.

[2] M. Moragues, M. V´azquez, G. Houzeaux, R. Aubry, Variational Multiscale Stabilization of Compressible flows in Parallel Architectures, Parallel CFD 2010, Taiwan, May 2010.

[3] S. Marras, M. Moragues, M. V´azquez, O. Jorba, G. Houzeaux, A Variational Multiscale Stabilized Finite Element Method for the Solution of the Euler Equations of Nonhydrostatic Stratified Flows, J. Comput. Phys. (submitted 2012)
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Presentation Material: 
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons