Error estimation and anisotropic mesh refinement for 3d laminar aerodynamic flow simulations

Leicht, Tobias; Hartmann, Ralf

doi:10.1016/j.jcp.2010.06.019

Cited by 97 publications

(75 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On each element of the patch, the gradient of the numerical solution has the highest accuracy at the super-convergent points, thus the high-order accurate expression of the reconstructed gradient on the patch is obtained by a least square fitting of the polynomial expressions (20) to the values of the gradient at the super-convergent points of the patch. Assuming that N s i super-convergent points, x i, , = 1 .…”

Section: Super-convergent Patch Recoverymentioning

confidence: 99%

“…24 are reported the drag and lift coefficients computed with linear and quadratic elements, on three uniformly refined grids. For comparison, are reported also the reference values computed in [20] by extrapolating the results obtained with a higher order DG method. Observing the convergence of the drag coefficient in term of DOFs, it can be noted that there is no significant gain in using a higher order approximation, with respect to the second order.…”

Section: Laminar Flow Around a Delta Wingmentioning

confidence: 99%

See 1 more Smart Citation

Linear and non-linear high order accurate residual distribution schemes for the discretization of the steady compressible Navier–Stokes equations

Abgrall

Santis

2015

Journal of Computational Physics

View full text Add to dashboard Cite

A robust and high order accurate Residual Distribution (RD) scheme for the discretization of the steady Navier-Stokes equations is presented. The proposed method is very flexible: it is formulated for unstructured grids, regardless the shape of the elements and the number of spatial dimensions. A continuous approximation of the solution is adopted and standard Lagrangian shape functions are used to construct the discrete space, as in Finite Element methods. The traditional technique for designing RD schemes is adopted: evaluate, for any element, a total residual, split it into nodal residuals sent to the degrees of freedom of the element, solve the non-linear system that has been assembled and then iterate up to convergence. The main issue addressed by the paper is that the technique relies in depth on the continuity of the normal flux across the element boundaries: this is no longer true since the gradient of the state solution appears in the flux, hence continuity is lost when using standard finite element approximations. Naive solution methods lead to very poor accuracy. To cope with the fact that the normal component of the gradient of the numerical solution is discontinuous across the faces of the elements, a continuous approximation of the gradient of the numerical solution is recovered at each degree of freedom of the grid and then interpolated with the same shape functions used for the solution, preserving the optimal accuracy of the method. Linear and non-linear schemes are constructed, and their accuracy is tested with the method of the manufactured solutions. The numerical method is also used for the discretization of smooth and shocked laminar flows in two and three spatial dimensions. Abstract A robust and high order accurate Residual Distribution (RD) scheme for the discretization of the steady Navier-Stokes equations is presented. The proposed method is very flexible: it is formulated for unstructured grids, regardless the shape of the elements and the number of spatial dimensions. A continuous approximation of the solution is adopted and standard Lagrangian shape functions are used to construct the discrete space, as in Finite Element methods. The traditional technique for designing RD schemes is adopted: evaluate, for any element, a total residual, split it into nodal residuals sent to the degrees of freedom of the element, solve the non linear system that has been assembled and then iterate up to convergence. The main issue addressed by the paper is that the technique relies in depth on the continuity of the normal flux across the element boundaries: this is no longer true since the gradient of the state solution appears in the flux, hence continuity is lost when using standard finite element approximations. Naive solution methods lead to very poor accuracy. To cope with the fact that the normal component of the gradient of the numerical solution is discontinuous across the faces of the elements, a continuous approximation of the gradient of the numerical solution is recovered at each...

show abstract

Section: Super-convergent Patch Recoverymentioning

confidence: 99%

Section: Laminar Flow Around a Delta Wingmentioning

confidence: 99%

Linear and non-linear high order accurate residual distribution schemes for the discretization of the steady compressible Navier–Stokes equations

Abgrall

Santis

2015

Journal of Computational Physics

View full text Add to dashboard Cite

show abstract

“…Over the years, to overcome this contradiction and acquire optimum precision for the solution, several adaptive approaches have evolved (Harutyunyan, Izsák, van der Vegt, & Botchev, 2008;Hicken, 2012;Lee & Zhou, 2004;Leicht & Hartmann, 2010;Zhu & Zienkiewicz, 1997). The two fundamental concerns involved in the methods of mesh refinement are "error estimation" and "mesh density control through suitable scheme".…”

Section: Error Estimationsmentioning

confidence: 99%

Case Based Reasoning Support for Adaptive Finite Element Analysis: Mesh Selection for an Integrated System

Khan¹,

Chaudhry

Sarosh

2014

APR

View full text Add to dashboard Cite

An Adaptive Finite Element Analysis Integrated System supported through application of Case Based Reasoning (CBR) methodology is being proposed in this paper. The approach is fruitful for selection of an initial mesh from a library of solutions to initiate analysis process, as already tested optimal mesh will have lesser refinement iterations. The optimal mesh distribution, represented by object-oriented method, can be easily adapted to the topology of new problem in same domain. An integrated and universal structural analysis system models human reasoning by forming solutions through the retrieval and adaptation of successful strategies used in the past. Basic insight of two distinct subjects along with resolution of involved issues and integration strategy for development of an intelligent system is elaborated here. The research explains an algorithm for case retrieval and mesh generation procedures based on the principles of mapping method.

show abstract

“…If there is a boundary condition against one of the faces of the element, then that side is neglected in (23).…”

Section: 4mentioning

confidence: 99%

“…Zhu et al [45] compared a few of them and found that KXRCF provided very good results for typical one-dimensional shock problems. In addition, Leicht and Hartmann [23] used the jump between elements to determine the direction for anisotropic refinement. In this study we propose a new estimator which results from a combination of some of these detectors and has better efficiency.…”

Section: Introductionmentioning

confidence: 99%

Discontinuous Galerkin method with the spectral deferred correction time-integration scheme and a modified moment limiter for adaptive grids

Gryngarten

Smith

Menon

2012

Commun. Appl. Math. Comput. Sci.

View full text Add to dashboard Cite

The discontinuous Galerkin (DG) method is combined with the spectral deferred correction (SDC) time integration approach to solve the fluid dynamic equations. The moment limiter is generalized for nonuniform grids with hanging nodes that result from adaptive mesh refinement. The effect of characteristic, primitive, or conservative decomposition in the limiting stage is studied. In general, primitive variable decomposition is a better option, especially in two and three dimensions. The accuracy-preserving total variation diminishing (AP-TVD) marker for troubled-cell detection, which uses an averaged-derivative basis, is modified to use the Legendre polynomial basis. Given that the latest basis is generally used for DG, the new approach avoids transforming to the averaged-derivative basis, what results in a more efficient technique. Further, a new error estimator is proposed to determine where to refine or coarsen the grid. This estimator is compared against other estimator used in the literature and shows an improved performance. Canonical tests in one, two, and three dimensions are conducted to show the accuracy of the solver.

show abstract

Error estimation and anisotropic mesh refinement for 3d laminar aerodynamic flow simulations

Cited by 97 publications

References 28 publications

Linear and non-linear high order accurate residual distribution schemes for the discretization of the steady compressible Navier–Stokes equations

Linear and non-linear high order accurate residual distribution schemes for the discretization of the steady compressible Navier–Stokes equations

Case Based Reasoning Support for Adaptive Finite Element Analysis: Mesh Selection for an Integrated System

Discontinuous Galerkin method with the spectral deferred correction time-integration scheme and a modified moment limiter for adaptive grids

Contact Info

Product

Resources

About