1,226 research outputs found
On the stability of projection methods for the incompressible Navier-Stokes equations based on high-order discontinuous Galerkin discretizations
The present paper deals with the numerical solution of the incompressible
Navier-Stokes equations using high-order discontinuous Galerkin (DG) methods
for discretization in space. For DG methods applied to the dual splitting
projection method, instabilities have recently been reported that occur for
coarse spatial resolutions and small time step sizes. By means of numerical
investigation we give evidence that these instabilities are related to the
discontinuous Galerkin formulation of the velocity divergence term and the
pressure gradient term that couple velocity and pressure. Integration by parts
of these terms with a suitable definition of boundary conditions is required in
order to obtain a stable and robust method. Since the intermediate velocity
field does not fulfill the boundary conditions prescribed for the velocity, a
consistent boundary condition is derived from the convective step of the dual
splitting scheme to ensure high-order accuracy with respect to the temporal
discretization. This new formulation is stable in the limit of small time steps
for both equal-order and mixed-order polynomial approximations. Although the
dual splitting scheme itself includes inf-sup stabilizing contributions, we
demonstrate that spurious pressure oscillations appear for equal-order
polynomials and small time steps highlighting the necessity to consider inf-sup
stability explicitly.Comment: 31 page
A coupled approximate deconvolution and dynamic mixed scale model for large-eddy simulation
Large-eddy simulations of incompressible Newtonian fluid flows with
approximate deconvolution models based on the van Cittert method are reported.
The Legendre spectral element method is used for the spatial discretization to
solve the filtered Navier--Stokes equations. A novel variant of approximate
deconvolution models blended with a mixed scale model using a dynamic
evaluation of the subgrid-viscosity constant is proposed. This model is
validated by comparing the large-eddy simulation with the direct numerical
simulation of the flow in a lid-driven cubical cavity, performed at a Reynolds
number of 12'000. Subgrid modeling in the case of a flow with coexisting
laminar, transitional and turbulent zones such as the lid-driven cubical cavity
flow represents a challenging problem. Moreover, the coupling with the spectral
element method having very low numerical dissipation and dispersion builds a
well suited framework to analyze the efficiency of a subgrid model. First- and
second-order statistics obtained using this new model are showing very good
agreement with the direct numerical simulation. Filtering operations rely on an
invertible filter applied in a modal basis and preserving the C0-continuity
across elements. No clipping on dynamic parameters was needed to preserve
numerical stability
Hermite regularization of the Lattice Boltzmann Method for open source computational aeroacoustics
The lattice Boltzmann method (LBM) is emerging as a powerful engineering tool
for aeroacoustic computations. However, the LBM has been shown to present
accuracy and stability issues in the medium-low Mach number range, that is of
interest for aeroacoustic applications. Several solutions have been proposed
but often are too computationally expensive, do not retain the simplicity and
the advantages typical of the LBM, or are not described well enough to be
usable by the community due to proprietary software policies. We propose to use
an original regularized collision operator, based on the expansion in Hermite
polynomials, that greatly improves the accuracy and stability of the LBM
without altering significantly its algorithm. The regularized LBM can be easily
coupled with both non-reflective boundary conditions and a multi-level grid
strategy, essential ingredients for aeroacoustic simulations. Excellent
agreement was found between our approach and both experimental and numerical
data on two different benchmarks: the laminar, unsteady flow past a 2D cylinder
and the 3D turbulent jet. Finally, most of the aeroacoustic computations with
LBM have been done with commercial softwares, while here the entire theoretical
framework is implemented on top of an open source library (Palabos).Comment: 34 pages, 12 figures, The Journal of the Acoustical Society of
America (in press
THREE-DIMENSIONAL FREE SURFACE NON-HYDROSTATIC MODELING OF PLUNGING WATER WITH TURBULENCE AND AIR ENTRAINED TRANSPORT
The advance in computational fluid dynamics in recent years has provided the opportunity for many fluid dynamic problems to be analyzed numerically. One such problem concerns the modeling of plunging water into a still water body, often encountered in pump stations. Air bubbles introduced into the system by the plunging jet can be a significant problem, especially when consumed into operating pumps. The classical approach to investigate the hydrodynamics of plunging jet in pump stations is by physical model studies. This approach is time consuming, tedious and costly. The availability of computational power today, along with appropriate numerical techniques, allows such phenomenon to be studied in a greater level of detail and more cost efficient. Despite the advantages of numerical studies, little attention has been devoted to solve the plunging jet and air transport problem numerically.
In this current work, a 3-dimensional finite volume, Large Eddy Simulation (LES) code is developed to simulate these flow conditions. For turbulent flow, the large scale quantities were numerically resolved while the dynamic sub-grid scale model is used to model the small scale energy dissipations. The code also has the capability to handle free surface deformation, an important aspect in simulating the impact section of an impinging jet.
Modeling of the air entrainment is performed numerically utilizing the information obtained from the hydrodynamics. Migration of air bubbles is modeled using the scalar transport equation, modified to account for the buoyancy of the bubbles. Instead of the typical Lagrangian schemes, which track individual air bubbles, air bubble dynamics are modeled in the form of concentrations. Modeling air bubbles in this manner is computational efficient and simpler to implement. For the air entrainment simulations, standard numerical boundaries conditions and empirical entrainment equations are used to provide the necessary boundary conditions. The developed model is compared with the literature, producing satisfactory results, suggesting that the code has an excellent potential of extending its application to practical industry practices
A matrix-free high-order discontinuous Galerkin compressible Navier-Stokes solver: A performance comparison of compressible and incompressible formulations for turbulent incompressible flows
Both compressible and incompressible Navier-Stokes solvers can be used and
are used to solve incompressible turbulent flow problems. In the compressible
case, the Mach number is then considered as a solver parameter that is set to a
small value, , in order to mimic incompressible flows.
This strategy is widely used for high-order discontinuous Galerkin
discretizations of the compressible Navier-Stokes equations. The present work
raises the question regarding the computational efficiency of compressible DG
solvers as compared to a genuinely incompressible formulation. Our
contributions to the state-of-the-art are twofold: Firstly, we present a
high-performance discontinuous Galerkin solver for the compressible
Navier-Stokes equations based on a highly efficient matrix-free implementation
that targets modern cache-based multicore architectures. The performance
results presented in this work focus on the node-level performance and our
results suggest that there is great potential for further performance
improvements for current state-of-the-art discontinuous Galerkin
implementations of the compressible Navier-Stokes equations. Secondly, this
compressible Navier-Stokes solver is put into perspective by comparing it to an
incompressible DG solver that uses the same matrix-free implementation. We
discuss algorithmic differences between both solution strategies and present an
in-depth numerical investigation of the performance. The considered benchmark
test cases are the three-dimensional Taylor-Green vortex problem as a
representative of transitional flows and the turbulent channel flow problem as
a representative of wall-bounded turbulent flows
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