5,583 research outputs found
The anisotropic averaged Euler equations
The purpose of this paper is to derive the anisotropic averaged Euler
equations and to study their geometric and analytic properties. These new
equations involve the evolution of a mean velocity field and an advected
symmetric tensor that captures the fluctuation effects. Besides the derivation
of these equations, the new results in the paper are smoothness properties of
the equations in material representation, which gives well-posedness of the
equations, and the derivation of a corrector to the macroscopic velocity field.
The numerical implementation and physical implications of this set of equations
will be explored in other publications.Comment: 24 pages, 1 figur
Arbitrary-Lagrangian-Eulerian discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes
We present a new family of high order accurate fully discrete one-step
Discontinuous Galerkin (DG) finite element schemes on moving unstructured
meshes for the solution of nonlinear hyperbolic PDE in multiple space
dimensions, which may also include parabolic terms in order to model
dissipative transport processes. High order piecewise polynomials are adopted
to represent the discrete solution at each time level and within each spatial
control volume of the computational grid, while high order of accuracy in time
is achieved by the ADER approach. In our algorithm the spatial mesh
configuration can be defined in two different ways: either by an isoparametric
approach that generates curved control volumes, or by a piecewise linear
decomposition of each spatial control volume into simplex sub-elements. Our
numerical method belongs to the category of direct
Arbitrary-Lagrangian-Eulerian (ALE) schemes, where a space-time conservation
formulation of the governing PDE system is considered and which already takes
into account the new grid geometry directly during the computation of the
numerical fluxes. Our new Lagrangian-type DG scheme adopts the novel a
posteriori sub-cell finite volume limiter method, in which the validity of the
candidate solution produced in each cell by an unlimited ADER-DG scheme is
verified against a set of physical and numerical detection criteria. Those
cells which do not satisfy all of the above criteria are flagged as troubled
cells and are recomputed with a second order TVD finite volume scheme. The
numerical convergence rates of the new ALE ADER-DG schemes are studied up to
fourth order in space and time and several test problems are simulated.
Finally, an application inspired by Inertial Confinement Fusion (ICF) type
flows is considered by solving the Euler equations and the PDE of viscous and
resistive magnetohydrodynamics (VRMHD).Comment: 39 pages, 21 figure
Numerical simulation of separated flows
A new numerical method, based on the Vortex Method, for the simulation of two-dimensional separated flows, was developed and tested on a wide range of gases. The fluid is incompressible and the Reynolds number is high. A rigorous analytical basis for the representation of the Navier-Stokes equation in terms of the vorticity is used. An equation for the control of circulation around each body is included. An inviscid outer flow (computed by the Vortex Method) was coupled with a viscous boundary layer flow (computed by an Eulerian method). This version of the Vortex Method treats bodies of arbitrary shape, and accurately computes the pressure and shear stress at the solid boundary. These two quantities reflect the structure of the boundary layer. Several versions of the method are presented and applied to various problems, most of which have massive separation. Comparison of its results with other results, generally experimental, demonstrates the reliability and the general accuracy of the new method, with little dependence on empirical parameters. Many of the complex features of the flow past a circular cylinder, over a wide range of Reynolds numbers, are correctly reproduced
Modeling and Simulation of a Fluttering Cantilever in Channel Flow
Characterizing the dynamics of a cantilever in channel flow is relevant to
applications ranging from snoring to energy harvesting. Aeroelastic flutter
induces large oscillating amplitudes and sharp changes with frequency that
impact the operation of these systems. The fluid-structure mechanisms that
drive flutter can vary as the system parameters change, with the stability
boundary becoming especially sensitive to the channel height and Reynolds
number, especially when either or both are small. In this paper, we develop a
coupled fluid-structure model for viscous, two-dimensional channel flow of
arbitrary shape. Its flutter boundary is then compared to results of
two-dimensional direct numerical simulations to explore the model's validity.
Provided the non-dimensional channel height remains small, the analysis shows
that the model is not only able to replicate DNS results within the parametric
limits that ensure the underlying assumptions are met, but also over a wider
range of Reynolds numbers and fluid-structure mass ratios. Model predictions
also converge toward an inviscid model for the same geometry as Reynolds number
increases
The onset of instability in unsteady boundary-layer separation
The process of unsteady two-dimensional boundary-layer separation at high Reynolds number is considered. Solutions of the unsteady non-interactive boundary-layer equations are known to develop a generic separation singularity in regions where the pressure gradient is prescribed and adverse. As the boundary layer starts to separate from the surface, however, the external pressure distribution is altered through viscous-inviscid interaction just prior to the formation of the separation singularity; hitherto this has been referred to as the first interactive stage. A numerical solution of this stage is obtained here in Lagrangian coordinates. The solution is shown to exhibit a high-frequency inviscid instability resulting in an immediate finite-time breakdown of this stage. The presence of the instability is confirmed through a linear stability analysis. The implications for the theoretical description of unsteady boundary-layer separation are discussed, and it is suggested that the onset of interaction may occur much sooner than previously thought
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