Abstract not found

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

We present a new approach for the computation of shape sensitivities using the discrete adjoint and flow-sensitivity methods on Cartesian meshes with general polyhedral cells (cutcells) at the wall boundaries. By directly linearizing the cut-cell geometric constructors of the mesh generator, an efficient and robust computation of shape sensitivities is achieved. We show that the error convergence rate of the flow solution and its sensitivity, as well as the objective function and its gradient is consistent with the second-order spatial discretization of the three-dimensional Euler equations. The performance of the approach is demonstrated for an airfoil optimization problem in transonic flow, and a CAD-based shape optimization of a reentry capsule in hypersonic flow. The approach is well-suited for conceptual design studies where fast turn-around time is required. I.

We focus on the computation of objective function gradients using a discrete adjoint method for embedded-boundary Cartesian meshes. This is a significant step in our research toward using computer-aided design (CAD) directly for adjoint-based gradient computations. The approach treats the Cartesian mesh as a rigid structure. Under this assumption, accurate evaluation of mesh sensitivities depends directly on the formulation within the layer of non-uniform cells, or cut-cells, immediately adjacent to the surface. The formulation is based on the linearization of a simple geometric constructor, which decouples the computation of shape sensitivities of the surface triangulation from the cut-cell sensitivities. As a result, the method is well suited to CAD-based optimization using parametric solid models. Detailed verification studies of gradient accuracy are presented for several two- and three-dimensional shape optimization problems. I.

Error estimation and control are critical ingredients for improving the reliability of computational simulations. Adjoint-based techniques can be used to both estimate the error in chosen solution outputs and to provide local indicators for adaptive refinement. This article reviews recent work on these techniques for computational fluid dynamics applications in aerospace engineering. The definition of the adjoint as the sensitivity of an output to residual source perturbations is used to derive both the adjoint equation, in fully discrete and variational formulations, and the adjoint-weighted residual method for error estimation. Assumptions and approximations made in the calculations are discussed. Presentation of the discrete and variational formulations enables a side-byside comparison of recent work in output-error estimation using the finite volume method and the finite element method. Techniques for adapting meshes using output-error indicators are also reviewed. Recent adaptive results from a variety of laminar and Reynolds-averaged Navier–Stokes applications show the power of output-based adaptive methods for improving the robustness of computational fluid dynamics computations. However, challenges and areas of additional future research remain, including computable error bounds and robust mesh adaptation mechanics. I.

While an indispensable tool in analysis and design applications, Computational Fluid Dynamics (CFD) is still plagued by insufficient automation and robustness in the geometryto-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