3,997 research outputs found
Adaptive time-stepping for incompressible flow. Part II: Navier-Stokes equations
We outline a new class of robust and efficient methods for solving the Navier- Stokes equations. We describe a general solution strategy that has two basic building blocks: an implicit time integrator using a stabilized trapezoid rule with an explicit Adams-Bashforth method for error control, and a robust Krylov subspace solver for the spatially discretized system. We present numerical experiments illustrating the potential of our approach. © 2010 Society for Industrial and Applied Mathematics
A "poor man's" approach for high-resolution three-dimensional topology optimization of natural convection problems
This paper treats topology optimization of natural convection problems. A
simplified model is suggested to describe the flow of an incompressible fluid
in steady state conditions, similar to Darcy's law for fluid flow in porous
media. The equations for the fluid flow are coupled to the thermal
convection-diffusion equation through the Boussinesq approximation. The coupled
non-linear system of equations is discretized with stabilized finite elements
and solved in a parallel framework that allows for the optimization of high
resolution three-dimensional problems. A density-based topology optimization
approach is used, where a two-material interpolation scheme is applied to both
the permeability and conductivity of the distributed material. Due to the
simplified model, the proposed methodology allows for a significant reduction
of the computational effort required in the optimization. At the same time, it
is significantly more accurate than even simpler models that rely on convection
boundary conditions based on Newton's law of cooling. The methodology discussed
herein is applied to the optimization-based design of three-dimensional heat
sinks. The final designs are formally compared with results of previous work
obtained from solving the full set of Navier-Stokes equations. The results are
compared in terms of performance of the optimized designs and computational
cost. The computational time is shown to be decreased to around 5-20% in terms
of core-hours, allowing for the possibility of generating an optimized design
during the workday on a small computational cluster and overnight on a high-end
desktop
ParMooN - a modernized program package based on mapped finite elements
{\sc ParMooN} is a program package for the numerical solution of elliptic and
parabolic partial differential equations. It inherits the distinct features of
its predecessor {\sc MooNMD} \cite{JM04}: strict decoupling of geometry and
finite element spaces, implementation of mapped finite elements as their
definition can be found in textbooks, and a geometric multigrid preconditioner
with the option to use different finite element spaces on different levels of
the multigrid hierarchy. After having presented some thoughts about in-house
research codes, this paper focuses on aspects of the parallelization for a
distributed memory environment, which is the main novelty of {\sc ParMooN}.
Numerical studies, performed on compute servers, assess the efficiency of the
parallelized geometric multigrid preconditioner in comparison with some
parallel solvers that are available in the library {\sc PETSc}. The results of
these studies give a first indication whether the cumbersome implementation of
the parallelized geometric multigrid method was worthwhile or not.Comment: partly supported by European Union (EU), Horizon 2020, Marie
Sk{\l}odowska-Curie Innovative Training Networks (ITN-EID), MIMESIS, grant
number 67571
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