A Variational Multiscale Stabilized Finite Element Method to solve the Euler Equations for Nonhydrostatic Stratified Benchmarks
Seminar Room 1, Newton Institute
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  in the context
of incompressible flows. In the present work, recentely presented in , 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 .
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.
 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)
 M. Moragues, M. V´azquez, G. Houzeaux, R. Aubry, Variational Multiscale Stabilization of Compressible flows in Parallel Architectures, Parallel CFD 2010, Taiwan, May 2010.
 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)