Results 1  10
of
10
Heuristic a posteriori estimation of error due to dissipation in finite volume schemes and application to mesh adaptation
 Journal of Computational Physics
"... A heuristic method is proposed to estimate a posteriori that part of the total discretization error which is attributable to the smoothing effect of added dissipation, for finite volume discretizations of the Euler equations. This is achieved by observing variation in a functional of the solution as ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
(Show Context)
A heuristic method is proposed to estimate a posteriori that part of the total discretization error which is attributable to the smoothing effect of added dissipation, for finite volume discretizations of the Euler equations. This is achieved by observing variation in a functional of the solution as the level of dissipation is varied, and it is deduced for certain testcases that the dissipation alone accounts for the majority of the functional error. Based on this result an error estimator and mesh adaptation indicator is proposed for functionals, relying on the solution of an adjoint problem. The scheme is considerably implementationally simpler and computationally cheaper than other recently proposed a posteriori error estimators for finite volume schemes, but does not account for all sources of error. In mind of this, emphasis is placed on numerical evaluation of the performance of the indicator, and it is shown to be extremely effective in both estimating and reducing error for a range of 2d and 3d flows. Key words: a posteriori error estimation, goaloriented mesh adaptation, finite volume methods, dissipation error, adjoint problem
Goaloriented mesh adaptation using a dissipationbased error indicator
 University of Reading
, 2007
"... A method is proposed to estimate a posteriori that part of the total discretization error which is attributable to the smoothing effect of added dissipation, for finite volume discretizations of the Euler equations. This is achieved by observing variation in a functional of the solution as the leve ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
A method is proposed to estimate a posteriori that part of the total discretization error which is attributable to the smoothing effect of added dissipation, for finite volume discretizations of the Euler equations. This is achieved by observing variation in a functional of the solution as the level of dissipation is varied, and it is deduced for certain testcases that the dissipation alone accounts for the majority of the functional error. Based on this result an error estimator and mesh adaptation indicator is proposed for functionals, relying on the solution of an adjoint problem. The scheme is considerably implementationally simpler and computationally cheaper than other recently proposed a posteriori error estimators for finite volume schemes, but does not account for all sources of error. In mind of this, emphasis is placed on numerical evaluation of the performance of the indicator, and it is shown to be extremely effective in both estimating and reducing error for a range of 2d and 3d flows. I.
Review and Unification of Methods for Computing Derivatives of Multidisciplinary Computational Models
"... This is a preprint of the following article, which is available from ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
This is a preprint of the following article, which is available from
Ecole Doctorale de Sciences Fondamentales Appliquées (EDSFA) THESE
, 2014
"... Adjointbased aerostructural sensitivity analysis for wing design ..."
aan de Technische Universiteit Delft;
"... ter verkrijging van de graad van doctor ..."
(Show Context)
GT200959062 THE DISCRETE ADJOINT OF A TURBOMACHINERY RANS SOLVER
"... ABSTRACT Since ..."
(Show Context)
SUMMARY
"... Goaloriented mesh adaptation using a dissipationbased error indicator ..."
(Show Context)
Efficient A Posteriori Error Estimation for Finite Volume Methods
"... The propagation of error in numerical solutions of the compressible NavierStokes equations is examined using linearized, and adjoint linearized versions of the discrete flow solver. With the forward linearization it is possible, given a measure of the local residual error in the field, to obtain es ..."
Abstract
 Add to MetaCart
(Show Context)
The propagation of error in numerical solutions of the compressible NavierStokes equations is examined using linearized, and adjoint linearized versions of the discrete flow solver. With the forward linearization it is possible, given a measure of the local residual error in the field, to obtain estimates of global solution error. This allows for example the computation of error estimates on pressure distributions. With the backward or adjoint linearization it is possible, for any given scalar output quantity, to identify those regions of the field which contribute the most to the error in that quantity. This information may be used to refine the mesh in a way that minimizes error in this output functional. Both approaches are be used, not only to provide accurate error estimates, but also to correct the output. In the following we concentrate on the solution error due to explicitly added artificial dissipation in the spatial discretization. By comparing with the true solution error obtained using mesh refinement studies, it is seen that this can be applied as an effective total error indicator for mesh adaptation. There are many situations in numerical simulation where some measure of residual error is known or cheaply available, but the solution error is desired. A common example is in a partially converged stationary simula
Efficient Uncertainty Quantification using
"... A flexible nonintrusive approach to parametric uncertainty quantification problems is developed, aimed at problems with many uncertain parameters, and for applications with a high cost of functional evaluations. It employs a Kriging response surface in the parameter space, augmented with gradients ..."
Abstract
 Add to MetaCart
A flexible nonintrusive approach to parametric uncertainty quantification problems is developed, aimed at problems with many uncertain parameters, and for applications with a high cost of functional evaluations. It employs a Kriging response surface in the parameter space, augmented with gradients obtained from the adjoint of the deterministic equations. The Kriging correlation parameter optimization problem is solved using the Subplex algorithm, which is robust for noisy functionals, and whose effort typically increases only linearly with problem dimension. Integration over the resulting response surface to obtain statistical moments is performed using sparse grid techniques, which are designed to scale well with dimensionality. The efficiency and accuracy of the proposed method is compared with probabilistic collocation, direct application of sparse grid methods, and MonteCarlo initially for model problems, and finally for a 2d compressible NavierStokes problem with a random geometry parameterized by 4 variables. I.