755 research outputs found
Proof of uniform convergence for a cell-centered AP discretization of the hyperbolic heat equation on general meshes
International audienceWe prove the uniform AP convergence on unstructured meshes in 2D of a generalization, of the Gosse-Toscani 1D scheme for the hyperbolic heat equation. This scheme is also a nodal extension in 2D of the Jin-Levermore scheme described in [18] for the 1D case. In 2D, the proof is performed using a new diffusion scheme
Velocity and energy relaxation in two-phase flows
In the present study we investigate analytically the process of velocity and
energy relaxation in two-phase flows. We begin our exposition by considering
the so-called six equations two-phase model [Ishii1975, Rovarch2006]. This
model assumes each phase to possess its own velocity and energy variables.
Despite recent advances, the six equations model remains computationally
expensive for many practical applications. Moreover, its advection operator may
be non-hyperbolic which poses additional theoretical difficulties to construct
robust numerical schemes |Ghidaglia et al, 2001]. In order to simplify this
system, we complete momentum and energy conservation equations by relaxation
terms. When relaxation characteristic time tends to zero, velocities and
energies are constrained to tend to common values for both phases. As a result,
we obtain a simple two-phase model which was recently proposed for simulation
of violent aerated flows [Dias et al, 2010]. The preservation of invariant
regions and incompressible limit of the simplified model are also discussed.
Finally, several numerical results are presented.Comment: 37 pages, 10 figures. Other authors papers can be downloaded at
http://www.lama.univ-savoie.fr/~dutykh
Finite Volume Streaming-based Lattice Boltzmann algorithm for fluid-dynamics simulations: a one-to-one accuracy and performance study
A new finite volume (FV) discretisation method for the Lattice Boltzmann (LB)
equation which combines high accuracy with limited computational cost is
presented. In order to assess the performance of the FV method we carry out a
systematic comparison, focused on accuracy and computational performances, with
the standard (ST) Lattice Boltzmann equation algorithm. To our
knowledge such a systematic comparison has never been previously reported. In
particular we aim at clarifying whether and in which conditions the proposed
algorithm, and more generally any FV algorithm, can be taken as the method of
choice in fluid-dynamics LB simulations. For this reason the comparative
analysis is further extended to the case of realistic flows, in particular
thermally driven flows in turbulent conditions. We report the first successful
simulation of high-Rayleigh number convective flow performed by a Lattice
Boltzmann FV based algorithm with wall grid refinement.Comment: 15 pages, 14 figures (discussion changes, improved figure
readability
Optimized explicit Runge-Kutta schemes for the spectral difference method applied to wave propagation problems
Explicit Runge-Kutta schemes with large stable step sizes are developed for
integration of high order spectral difference spatial discretization on
quadrilateral grids. The new schemes permit an effective time step that is
substantially larger than the maximum admissible time step of standard explicit
Runge-Kutta schemes available in literature. Furthermore, they have a small
principal error norm and admit a low-storage implementation. The advantages of
the new schemes are demonstrated through application to the Euler equations and
the linearized Euler equations.Comment: 37 pages, 3 pages of appendi
Seventh Copper Mountain Conference on Multigrid Methods
The Seventh Copper Mountain Conference on Multigrid Methods was held on 2-7 Apr. 1995 at Copper Mountain, Colorado. This book is a collection of many of the papers presented at the conference and so represents the conference proceedings. NASA Langley graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The multigrid discipline continues to expand and mature, as is evident from these proceedings. The vibrancy in this field is amply expressed in these important papers, and the collection shows its rapid trend to further diversity and depth
A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure
We propose a positivity preserving entropy decreasing finite volume scheme
for nonlinear nonlocal equations with a gradient flow structure. These
properties allow for accurate computations of stationary states and long-time
asymptotics demonstrated by suitably chosen test cases in which these features
of the scheme are essential. The proposed scheme is able to cope with
non-smooth stationary states, different time scales including metastability, as
well as concentrations and self-similar behavior induced by singular nonlocal
kernels. We use the scheme to explore properties of these equations beyond
their present theoretical knowledge
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