16,326 research outputs found
The LifeV library: engineering mathematics beyond the proof of concept
LifeV is a library for the finite element (FE) solution of partial
differential equations in one, two, and three dimensions. It is written in C++
and designed to run on diverse parallel architectures, including cloud and high
performance computing facilities. In spite of its academic research nature,
meaning a library for the development and testing of new methods, one
distinguishing feature of LifeV is its use on real world problems and it is
intended to provide a tool for many engineering applications. It has been
actually used in computational hemodynamics, including cardiac mechanics and
fluid-structure interaction problems, in porous media, ice sheets dynamics for
both forward and inverse problems. In this paper we give a short overview of
the features of LifeV and its coding paradigms on simple problems. The main
focus is on the parallel environment which is mainly driven by domain
decomposition methods and based on external libraries such as MPI, the Trilinos
project, HDF5 and ParMetis.
Dedicated to the memory of Fausto Saleri.Comment: Review of the LifeV Finite Element librar
A high-order semi-explicit discontinuous Galerkin solver for 3D incompressible flow with application to DNS and LES of turbulent channel flow
We present an efficient discontinuous Galerkin scheme for simulation of the
incompressible Navier-Stokes equations including laminar and turbulent flow. We
consider a semi-explicit high-order velocity-correction method for time
integration as well as nodal equal-order discretizations for velocity and
pressure. The non-linear convective term is treated explicitly while a linear
system is solved for the pressure Poisson equation and the viscous term. The
key feature of our solver is a consistent penalty term reducing the local
divergence error in order to overcome recently reported instabilities in
spatially under-resolved high-Reynolds-number flows as well as small time
steps. This penalty method is similar to the grad-div stabilization widely used
in continuous finite elements. We further review and compare our method to
several other techniques recently proposed in literature to stabilize the
method for such flow configurations. The solver is specifically designed for
large-scale computations through matrix-free linear solvers including efficient
preconditioning strategies and tensor-product elements, which have allowed us
to scale this code up to 34.4 billion degrees of freedom and 147,456 CPU cores.
We validate our code and demonstrate optimal convergence rates with laminar
flows present in a vortex problem and flow past a cylinder and show
applicability of our solver to direct numerical simulation as well as implicit
large-eddy simulation of turbulent channel flow at as well as
.Comment: 28 pages, in preparation for submission to Journal of Computational
Physic
An optimal order interior penalty discontinuous Galerkin discretization of the compressible Navier-Stokes equations
In this article we propose a new symmetric version of the
interior penalty discontinuous Galerkin finite element
method for the numerical approximation
of the compressible Navier-Stokes equations. Here, particular
emphasis is devoted to the construction of an optimal numerical
method for the evaluation of certain target functionals of practical
interest, such as the lift and drag coefficients of a body immersed in a
viscous fluid. With this in mind, the key ingredients in the
construction of the method include: (i) An adjoint consistent imposition of
the boundary conditions; (ii) An adjoint consistent reformulation of the
underlying target functional of practical interest; (iii) Design of appropriate
interior--penalty stabilization terms. Numerical experiments presented
within this article clearly indicate the optimality of the proposed
method when the error is measured in terms of both the L2-norm, as well as
for certain target functionals. Computational comparisons with
other discontinuous Galerkin schemes proposed in the literature,
including the second scheme
of Bassi and Rebay, the standard SIPG method
outlined in [Hartmann,Houston-2006], and an NIPG variant of the new scheme
will be undertaken
Domain Decomposition Based High Performance Parallel Computing\ud
The study deals with the parallelization of finite element based Navier-Stokes codes using domain decomposition and state-ofart sparse direct solvers. There has been significant improvement in the performance of sparse direct solvers. Parallel sparse direct solvers are not found to exhibit good scalability. Hence, the parallelization of sparse direct solvers is done using domain decomposition techniques. A highly efficient sparse direct solver PARDISO is used in this study. The scalability of both Newton and modified Newton algorithms are tested
- …