Output‐based mesh optimization for hybridized and embedded discontinuous Galerkin methods

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/154431/1/nme6248.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/154431/2/nme6248_am.pd

Constrained pseudo‐transient continuation

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/111771/1/nme4858.pd

A Probabilistic Approach to Inverse Convection-Diffusion

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90616/1/AIAA-2011-824-287.pd

Review of Output-Based Error Estimation and Mesh Adaptation in Computational Fluid Dynamics

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90641/1/AIAA-53965-537.pd

Output-based Adaptive Meshing Using Triangular Cut Cells

This report presents a mesh adaptation method for higher-order (p > 1) discontinuous Galerkin (DG) discretizations of the two-dimensional, compressible Navier-Stokes equations. The method uses a mesh of triangular elements that are not required to conform to the boundary. This triangular, cut-cell approach permits anisotropic adaptation without the difficulty of constructing meshes that conform to potentially complex geometries. A quadrature technique is presented for accurately integrating on general cut cells. In addition, an output-based error estimator and adaptive method are presented, with emphasis on appropriately accounting for high-order solution spaces in optimizing local mesh anisotropy. Accuracy on cut-cell meshes is demonstrated by comparing solutions to those on standard boundary-conforming meshes. Adaptation results show that, for all test cases considered, p = 2 and p = 3 discretizations meet desired error tolerances using fewer degrees of freedom than p = 1. Furthermore, an initial-mesh dependence study demonstrates that, for sufficiently low error tolerances, the final adapted mesh is relatively insensitive to the starting mesh

High-Order Output-Based Adaptive Simulations of Turbulent Flow in Two Dimensions

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/140692/1/1.J054517.pd

Improving High-Order Finite Element Approximation Through Geometrical Warping

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/140695/1/1.J055071.pd

A simplex cut-cell adaptive method for high-order discretizations of the compressible Navier-Stokes equations

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2007.Includes bibliographical references (p. 169-175).While an indispensable tool in analysis and design applications, Computational Fluid Dynamics (CFD) is still plagued by insufficient automation and robustness in the geometry-to-solution process. This thesis presents two ideas for improving automation and robustness in CFD: output-based mesh adaptation for high-order discretizations and simplex, cut-cell mesh generation. First, output-based mesh adaptation consists of generating a sequence of meshes in an automated fashion with the goal of minimizing an estimate of the error in an engineering output. This technique is proposed as an alternative to current CFD practices in which error estimation and mesh generation are largely performed by experienced practitioners. Second, cut-cell mesh generation is a potentially more automated and robust technique compared to boundary-conforming mesh generation for complex, curved geometries. Cut-cell meshes are obtained by cutting a given geometry of interest out of a background mesh that need not conform to the geometry boundary. Specifically, this thesis develops the idea of simplex cut cells, in which the background mesh consists of triangles or tetrahedra that can be stretched in arbitrary directions to efficiently resolve boundary-layer and wake features.(cont.) The compressible Navier-Stokes equations in both two and three dimensions are discretized using the discontinuous Galerkin (DG) finite element method. An anisotropic h-adaptation technique is presented for high-order (p > 1) discretizations, driven by an output-error estimate obtained from the solution of an adjoint problem. In two and three dimensions, algorithms are presented for intersecting the geometry with the background mesh and for constructing the resulting cut cells. In addition, a quadrature technique is proposed for accurately integrating high-order functions on arbitrarily-shaped cut cells and cut faces. Accuracy on cut-cell meshes is demonstrated by comparing solutions to those on standard, boundary-conforming meshes. In two dimensions, robustness of the cut-cell, adaptive technique is successfully tested for highly-anisotropic boundary-layer meshes representative of practical high-Re simulations. In three dimensions, robustness of cut cells is demonstrated for various representative curved geometries. Adaptation results show that for all test cases considered, p = 2 and p = 3 discretizations meet desired error tolerances using fewer degrees of freedom than p = 1.Krzysztof Jakub Fidkowski.Ph.D

An Unsteady Entropy Adjoint Approach for Adaptive Solution of the Shallow-Water Equations

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90693/1/AIAA-2011-3694-887.pd

A high-order discontinuous Galerkin multigrid solver for aerodynamic applications

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2004.Includes bibliographical references (p. 87-90).This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Results are presented from the development of a high-order discontinuous Galerkin finite element solver using p-multigrid with line Jacobi smoothing. The line smoothing algorithm is presented for unstructured meshes, and p-multigrid is outlined for the nonlinear Euler equations of gas dynamics. Analysis of 2-D advection shows the improved performance of line implicit versus block implicit relaxation. Through a mesh refinement study, the accuracy of the discretization is determined to be the optimal O(h[superscript]P+l) for smooth problems in 2-D and 3-D. The multigrid convergence rate is found to be independent of the interpolation order but weakly dependent on the grid size. Timing studies for each problem indicate that higher order is advantageous over grid refinement when high accuracy is required. Finally, parallel versions of the 2-D and 3-D solvers demonstrate close to ideal coarse-grain scalability.by Krzysztof J. Fidkowski.S.M