13 research outputs found
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
High-order DG solvers for under-resolved turbulent incompressible flows: A comparison of and (div) methods
The accurate numerical simulation of turbulent incompressible flows is a
challenging topic in computational fluid dynamics. For discretisation methods
to be robust in the under-resolved regime, mass conservation as well as energy
stability are key ingredients to obtain robust and accurate discretisations.
Recently, two approaches have been proposed in the context of high-order
discontinuous Galerkin (DG) discretisations that address these aspects
differently. On the one hand, standard -based DG discretisations enforce
mass conservation and energy stability weakly by the use of additional
stabilisation terms. On the other hand, pointwise divergence-free
-conforming approaches ensure exact mass conservation
and energy stability by the use of tailored finite element function spaces. The
present work raises the question whether and to which extent these two
approaches are equivalent when applied to under-resolved turbulent flows. This
comparative study highlights similarities and differences of these two
approaches. The numerical results emphasise that both discretisation strategies
are promising for under-resolved simulations of turbulent flows due to their
inherent dissipation mechanisms.Comment: 24 pages, 13 figure
A weakly compressible hybridizable discontinuous Galerkin formulation for fluid-structure interaction problems
A scheme for the solution of fluid-structure interaction (FSI) problems with
weakly compressible flows is proposed in this work. A novel hybridizable
discontinuous Galerkin (HDG) method is derived for the discretization of the
fluid equations, while the standard continuous Galerkin (CG) approach is
adopted for the structural problem. The chosen HDG solver combines robustness
of discontinuous Galerkin (DG) approaches in advection-dominated flows with
higher order accuracy and efficient implementations. Two coupling strategies
are examined in this contribution, namely a partitioned Dirichlet-Neumann
scheme in the context of hybrid HDG-CG discretizations and a monolithic
approach based on Nitsche's method, exploiting the definition of the numerical
flux and the trace of the solution to impose the coupling conditions. Numerical
experiments show optimal convergence of the HDG and CG primal and mixed
variables and superconvergence of the postprocessed fluid velocity. The
robustness and the efficiency of the proposed weakly compressible formulation,
in comparison to a fully incompressible one, are also highlighted on a
selection of two and three dimensional FSI benchmark problems.Comment: 49 pages, 20 figures, 2 table