6,721 research outputs found
Numerical simulation of conservation laws with moving grid nodes: Application to tsunami wave modelling
In the present article we describe a few simple and efficient finite volume
type schemes on moving grids in one spatial dimension combined with appropriate
predictor-corrector method to achieve higher resolution. The underlying finite
volume scheme is conservative and it is accurate up to the second order in
space. The main novelty consists in the motion of the grid. This new dynamic
aspect can be used to resolve better the areas with large solution gradients or
any other special features. No interpolation procedure is employed, thus
unnecessary solution smearing is avoided, and therefore, our method enjoys
excellent conservation properties. The resulting grid is completely
redistributed according the choice of the so-called monitor function. Several
more or less universal choices of the monitor function are provided. Finally,
the performance of the proposed algorithm is illustrated on several examples
stemming from the simple linear advection to the simulation of complex shallow
water waves. The exact well-balanced property is proven. We believe that the
techniques described in our paper can be beneficially used to model tsunami
wave propagation and run-up.Comment: 46 pages, 7 figures, 7 tables, 94 references. Accepted to
Geosciences. Other author's papers can be downloaded at
http://www.denys-dutykh.com
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
An optimal penalty method for a hyperbolic system modeling the edge plasma transport in a tokamak
The penalization method is used to take account of obstacles, such as the
limiter, in a tokamak. Because of the magnetic confinement of the plasma in a
tokamak, the transport occurs essentially in the direction parallel to the
magnetic field lines. We study a 1D nonlinear hyperbolic system as a simplified
model of the plasma transport in the area close to the wall. A penalization
which cuts the flux term of the momentum is studied. We show numerically that
this penalization creates a Dirac measure at the plasma-limiter interface which
prevents us from defining the transport term in the usual distribution sense.
Hence, a new penalty method is proposed for this hyperbolic system. For this
penalty method, an asymptotic expansion and numerical tests give an optimal
rate of convergence without spurious boundary layer. Another two-fields
penalization has also been implemented and the numerical convergence analysis
when the penalization parameter tends to reveals the presence of a boundary
layer
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