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| Titel |
A Massive Parallel Variational Multiscale FEM Scheme Applied to Nonhydrostatic Atmospheric Dynamics |
| VerfasserIn |
Mariano Vazquez, Simone Marras, Margarida Moragues, Oriol Jorba, Guillaume Houzeaux, Romain Aubry |
| Konferenz |
EGU General Assembly 2010
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 12 (2010) |
| Datensatznummer |
250039599
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| Zusammenfassung |
| The solution of the fully compressible Euler equations of stratified flows is approached from
the point of view of Computational Fluid Dynamics techniques. Specifically, the main aim of
this contribution is the introduction of a Variational Multiscale Finite Element (CVMS-FE)
approach to solve dry atmospheric dynamics effectively on massive parallel architectures
with more than 1000 processors. The conservation form of the equations of motion is
discretized in all directions with a Galerkin scheme with stabilization given by the
compressible counterpart of the variational multiscale technique of Hughes [1] and
Houzeaux et al. [2]. The justification of this effort is twofold: the search of optimal
parallelization characteristics and linear scalability trends on petascale machines is one.
The development of a numerical algorithm whose local nature helps maintaining
minimal the communication among the processors implies, in fact, a large leap
towards efficient parallel computing. Second, the rising trend to global models and
models of higher spatial resolution naturally suggests the use of adaptive grids
to only resolve zones of larger gradients while keeping the computational mesh
properly coarse elsewhere (thus keeping the computational cost low). With these two
hypotheses in mind, the finite element scheme presented here is an open option
to the development of the next generation Numerical Weather Prediction (NWP)
codes.
This methodology is as new in Computational Fluid Dynamics for compressible flows at
low Mach number as it is in Numerical Weather Prediction (NWP). We however mean to
show its ability to maintain stability in the solution of thermal, gravity-driven flows in a
stratified environment in the specific context of dry atmospheric dynamics. Standard two
dimensional benchmarks are implemented and compared against the reference literature. In
the context of thermal and gravity-driven flows in a neutral atmosphere, we present: (1) the
density current evolution from a smooth initial cold disturbance as in Straka et al. [3]. (2) The
warm raising anomaly of initial smooth distribution (i.e. Wicker and Skamarock [4]; Ahmad
and Lindeman [5]) run on a structured grid of quadrilaterals first, and on a fully unstructured
next; and (3) the interaction of a small cold anomaly falling and a raising warm
bubble raising (Robert [6]). Problems in a stably stratified environment are also
described and compared with (1) the hydrostatic and non-hydrostatic, linear and non
linear mountain wave problems for flows over different sets of topographic features.
The definitions and results of Smith [7], Bonaventura [8], Mayr and Gohm [9],
and Schär [10] are taken as reference. The parallel performances of the algorithm
were tested for the solution of the fully compressible Navier-Stokes equations in a
three dimensional boundary layer problem. The scalability in the strong sense was
measured for runs on 1, 1000, 2000, and 5000 processors, exploiting a combination of
message passing interface (MPI) with automatic domain partition, and threads using
OpenMP.
Keywords: Numerical Weather Prediction, Computational Fluid Dynamics, Low Mach,
Compressible Flows, High Performance Computing
References
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Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins
of stabilized methods" Comp. Methods Appl. Mech. and Eng. 127, 387-401
[2]Â Â Â G. Houzeaux and M. Vázquez and R. Aubry (2009), "A Parallel
Incompressible Navier-Stokes Solver for Large Scale Supercomputers" J.
Comput. Phys., In press
[3]Â Â Â J. Straka and R. Wilhelmson and L. Wicker and J. Anderson and K.
Droegemeier (1993), "Numerical solution of a nonlinear density current: a
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