1,721,182 research outputs found
Anisotropic mesh adaption: application to Computational Fluid Dynamics
No full textZanichelli Editore S.p.A
Adaptive modeling for free-surface flows
No full textThis work represents a first step towards the simulation of the motion of water in a complex hydrodynamic configuration, such as a channel network or a river delta, by means of a suitable combination of different mathematical models. In this framework a wide spectrum of space and time scales is involved due to the presence of physical phenomena of different nature. Ideally, moving from a hierarchy of hydrodynamic models, one should solve throughout the whole domain the most complex
model (with solution u_fine) to accurately describe all the physical features of the problem at hand.
In our approach instead, for a user-defined output functional F, we aim to approximate, within a prescribed tolerance tau, the value F(u_fine) by means of the quantity F(uadapted), uadapted being the
so-called adapted solution solving the simpler models on most of the computational domain while
conning the complex ones only on a restricted region. Moving from the simplied setting where
only two hydrodynamic models, ne and coarse, are considered, we provide an ecient tool able to
automatically select the regions of the domain where the coarse model rather than the ne one are to
be solved, while guaranteeing |F(uÞne)F(uadapted)| below the tolerance . This goal is achieved via
a suitable a posteriori modeling error analysis developed in the framework of a goal-oriented theory.
We extend the dual-based approach provided in [Braack and Ern, Multiscale Model Sim. 1 (2003)
221238], for steady equations to the case of a generic time-dependent problem. Then this analysis is
specialized to the case we are interested in, i.e. the free-surface ows simulation, by emphasizing the
crucial issue of the time discretization for both the primal and the dual problems. Finally, in the last
part of the paper a widespread numerical validation is carried out
Reliability and efficiency of an anisotropic Zienkiewicz-Zhu error estimator
No full textIn this paper we study the efficiency and the reliability of an anisotropic a posteriori error estimator in the case of the Poisson problem supplied with mixed boundary conditions. The error estimator may be classified as a residual-based one, but its novelty is twofold: firstly, it employs anisotropic estimates of the interpolation error for linear triangular
finite elements and, secondly, it makes use of the Zienkiewicz–Zhu recovery procedure to approximate the gradient of the exact solution. Finally, we describe the adaptive procedure used to obtain a numerical solution satisfying a given accuracy, and we include some numerical test cases to assess the robustness of the proposed numerical algorithm
Space-time adaptation for purely diffusive problems in an anisotropic framework
No full textThe main goal of this work is the proposal of an efficient space-time
adaptive procedure for a cGdG approximation of an unsteady diffusion problem.
We derive a suitable a posteriori error estimator where the contribution of the
spatial and of the temporal discretization is kept distinct. In particular our
interest is addressed to phenomena characterized by temporal multiscale as
well as strong spatial directionalities. On the one hand we devise a sound
criterion to update the time step, able to follow the evolution of the problem
under investigation. On the other hand we exploit an anisotropic triangular
adapted grid. The reliability and the efficiency of the proposed error estimator
are assessed numerically
Output functional control for nonlinear equations driven by anisotropic mesh adaption: the navier–stokes equations
No full textThe contribution of this paper is twofold. Firstly, moving from the very well-known
dual-weighted residual (DWR) method, we set up a theoretical framework for a goal-oriented a posteriori
analysis of nonlinear partial differential equations accounting for different approximations of
the primal and dual problems; nonhomogeneous Dirichlet boundary conditions, even different on
passing from the primal to the dual problem; the error due to data approximation; and the effect
of a possible stabilization. Secondly, moving from this framework and employing anisotropic interpolation
error estimates, a sound anisotropic mesh adaption procedure is devised for the numerical
approximation of the Navier–Stokes equations by continuous piecewise linear finite elements. The
resulting adaptive procedure is thoroughly addressed and validated on some relevant test cases
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