60,656 research outputs found
A new discrete velocity method for Navier-Stokes equations
The relation between Latttice Boltzmann Method, which has recently become
popular, and the Kinetic Schemes, which are routinely used in Computational
Fluid Dynamics, is explored. A new discrete velocity model for the numerical
solution of the Navier-Stokes equations for incompressible fluid flow is
presented by combining both the approaches. The new scheme can be interpreted
as a pseudo-compressibility method and, for a particular choice of parameters,
this interpretation carries over to the Lattice Boltzmann Method.Comment: 28 pages, 8 figure
A Compact Third-order Gas-kinetic Scheme for Compressible Euler and Navier-Stokes Equations
In this paper, a compact third-order gas-kinetic scheme is proposed for the
compressible Euler and Navier-Stokes equations. The main reason for the
feasibility to develop such a high-order scheme with compact stencil, which
involves only neighboring cells, is due to the use of a high-order gas
evolution model. Besides the evaluation of the time-dependent flux function
across a cell interface, the high-order gas evolution model also provides an
accurate time-dependent solution of the flow variables at a cell interface.
Therefore, the current scheme not only updates the cell averaged conservative
flow variables inside each control volume, but also tracks the flow variables
at the cell interface at the next time level. As a result, with both cell
averaged and cell interface values the high-order reconstruction in the current
scheme can be done compactly. Different from using a weak formulation for
high-order accuracy in the Discontinuous Galerkin (DG) method, the current
scheme is based on the strong solution, where the flow evolution starting from
a piecewise discontinuous high-order initial data is precisely followed. The
cell interface time-dependent flow variables can be used for the initial data
reconstruction at the beginning of next time step. Even with compact stencil,
the current scheme has third-order accuracy in the smooth flow regions, and has
favorable shock capturing property in the discontinuous regions. Many test
cases are used to validate the current scheme. In comparison with many other
high-order schemes, the current method avoids the use of Gaussian points for
the flux evaluation along the cell interface and the multi-stage Runge-Kutta
time stepping technique.Comment: 27 pages, 38 figure
Fluid Solver Independent Hybrid Methods for Multiscale Kinetic equations
In some recent works [G. Dimarco, L. Pareschi, Hybrid multiscale methods I.
Hyperbolic Relaxation Problems, Comm. Math. Sci., 1, (2006), pp. 155-177], [G.
Dimarco, L. Pareschi, Hybrid multiscale methods II. Kinetic equations, SIAM
Multiscale Modeling and Simulation Vol 6., No 4,pp. 1169-1197, (2008)] we
developed a general framework for the construction of hybrid algorithms which
are able to face efficiently the multiscale nature of some hyperbolic and
kinetic problems. Here, at variance with respect to the previous methods, we
construct a method form-fitting to any type of finite volume or finite
difference scheme for the reduced equilibrium system. Thanks to the coupling of
Monte Carlo techniques for the solution of the kinetic equations with
macroscopic methods for the limiting fluid equations, we show how it is
possible to solve multiscale fluid dynamic phenomena faster with respect to
traditional deterministic/stochastic methods for the full kinetic equations. In
addition, due to the hybrid nature of the schemes, the numerical solution is
affected by less fluctuations when compared to standard Monte Carlo schemes.
Applications to the Boltzmann-BGK equation are presented to show the
performance of the new methods in comparison with classical approaches used in
the simulation of kinetic equations.Comment: 31 page
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