Parallel High-Order Anisotropic Meshing Using Discrete Metric Tensors

This paper presents a metric-aligned meshing algorithm that relies on the Lp-Centroidal Voronoi Tesselation approach. A prototype of this algorithm was first presented at the Scitech conference of 2018 and this work is an extension to that paper. At the end of the previously presented work, a set of problems were mentioned which we are trying to address in this paper. First, we show a significant improvement in code performance since we were limited to present relatively benign (analytical) test cases. Second, we demonstrate here that we are able to rely on discrete metric data that is delivered by a Computational Fluid Dynamics (CFD) solver. Third, we demonstrate how to generate high-order curved elements that are aligned with the underlying discrete metric field

Constrained pseudo‐transient continuation

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

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

Characteristics‐based boundary conditions for the Euler adjoint problem

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/96707/1/fld3712.pd

Development of a High-Order Space-Time Matrix-Free Adjoint Solver

The growth in computational power and algorithm development in the past few decades has granted the science and engineering community the ability to simulate flows over complex geometries, thus making Computational Fluid Dynamics (CFD) tools indispensable in analysis and design. Currently, one of the pacing items limiting the utility of CFD for general problems is the prediction of unsteady turbulent ows.1{3 Reynolds-averaged Navier-Stokes (RANS) methods, which predict a time-invariant mean flowfield, struggle to provide consistent predictions when encountering even mild separation, such as the side-of-body separation at a wing-body junction. NASA's Transformative Tools and Technologies project is developing both numerical methods and physical modeling approaches to improve the prediction of separated flows. A major focus of this e ort is efficient methods for resolving the unsteady fluctuations occurring in these flows to provide valuable engineering data of the time-accurate flow field for buffet analysis, vortex shedding, etc. This approach encompasses unsteady RANS (URANS), large-eddy simulations (LES), and hybrid LES-RANS approaches such as Detached Eddy Simulations (DES). These unsteady approaches are inherently more expensive than traditional engineering RANS approaches, hence every e ort to mitigate this cost must be leveraged. Arguably, the most cost-effective approach to improve the efficiency of unsteady methods is the optimal placement of the spatial and temporal degrees of freedom (DOF) using solution-adaptive methods

A Robust hp-Adaptation Method for Discontinuous Galerkin Discretizations Applied to Aerodynamic Flows.

Quantitatively accurate results from realistic Computational Fluid Dynamics (CFD) simulations are often accompanied by high computational expense. Higher-order methods are good candidates for providing accurate solutions at reduced cost. However, these methods are still not robust for industrial applications. This thesis presents a solution advancement method that improves robustness of discontinuous Galerkin (DG) discretizations in the iteration to steady-state. The method includes physical realizability constraints in the solution path and provides the solver with the ability of circumventing non-physical regions of the solution space that can occur during the solution transient. Affordable accurate solutions for challenging problems are obtained via output-based $hp$-adaptation. The adaptation method proposed in this thesis directly targets output error by locally choosing between subdividing an element or raising the approximation order. The decision is made by finding the refinement option that maximizes a merit function that involves output sensitivity and computational cost. Results in two and three dimensions show savings of up to an order of magnitude in terms of number of degrees of freedom and at least a factor of two in terms of computational time when compared to uniform refinement.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/97795/1/mceze_1.pd

Inverse aerodynamic design using the adjoint method applied to the Euler equations.

Um desafio constante no projeto aerodinâmico de uma superfície é obter a forma geométrica que permite, baseado em uma determinada medida de mérito, o melhor desempenho possível. No contexto de projeto de aeronaves de transporte, o desempenho ótimo em cruzeiro é a principal meta do projetista. Nesse cenário, o uso da Dinâmica do Fluidos Computacional como não só uma ferramenta de análise mas também de síntese torna-se uma forma atrativa para melhorar o projeto de aeronaves que é uma atividade dispendiosa em termos de tempo e recursos financeiros. O método adotado para projeto aerodinâmico é baseado na teoria de controle ótimo. Essa abordagem para o problema de otimização aerodinâmica foi inicialmente proposta por Jameson (1997) e é chamada de método adjunto. Esse método apresenta uma grande diminuição de custo computacional se comparado com a abordagem de diferenças finitas para a otimização baseada em gradiente. Essa dissertação apresenta o método adjunto contínuo aplicado às equações de Euler. Tal método está inserido no contexto de um ciclo de projeto inverso aerodinâmico. Nesse ciclo, tanto o código computacional de solução das equações do escoamento quanto o código de solução das equações adjuntas foram desenvolvidos ao longo desse trabalho. Além disso, foi adotada uma metodologia de redução do gradiente da função de mérito em relação às variáveis de projeto. O algorítmo utilizado para a busca do mínimo da função de mérito é o steepest descent. Os binômios de Bernstein foram escolhidos para representar a geometria do aerofólio de acordo com a parametrização proposta por Kulfan e Bussoletti (2006). Apresenta-se um estudo dessa parametrização mostrando suas características relevantes para a otimização aerodinâmica. Os resultados apresentados estão divididos em dois grupos: validação do ciclo de projeto inverso e aplicações práticas. O primeiro grupo consiste em exercícios de projeto inverso nos quais são estabelecidas distribuições de pressão desejadas obtidas a partir de geometrias conhecidas, desta forma garante-se que tais distribuições são realizáveis. No segundo grupo, porém, as distribuições desejadas são propostas pelo projetista baseado em sua experiência e, portanto, não sendo garantida a realizabilidade dessas distribuições. Em ambos os grupos, incluem-se resultados nos regimes de escoamento transônico e subsônico incompressível.A constant endeavor in aerodynamic design is to find the shape that yields optimum performance, according to some context-dependent measure of merit. In particular for transport aircrafts, an optimum cruise performance is usually the designers main goal. In this scenario the use of the Computational Fluid Dynamics (CFD) technique as not only an analysis tool but as a design tool becomes an attractive aid to the time and financial resource consuming activity that is aircraft design. The method adopted for aerodynamic design is based on optimal control theory. This approach to the design problem was first proposed by Jameson (1997) and it is called adjoint method. It shows a great computational cost advantage over the finite difference approach to gradient-based optimization. This dissertation presents an Euler adjoint method implemented in context of an inverse aerodynamic design loop. In this loop both the flow solver and the adjoint solver were developed during the course of this work and their formulation are presented. Further on, a gradient reduction methodology is used to obtain the gradient of the cost function with respect to the design variables. The method chosen to drive the cost function to its minimum is the steepest descent. Bernstein binomials were chosen to represent the airfoil geometry as proposed by Kulfan and Bussoletti (2006). A study of such geometric representation method is carried on showing its relevant properties for aerodynamic optimization. Results are presented in two groups: inverse design loop validation and practical application. The first group consists of inverse design exercises in which the target pressure distribution is from a known geometry, this way such distribution is guaranteed to be realizable. On the second group however, the target distribution is proposed based on the designers knowledge and its not necessarily realizable. In both groups the results include transonic and subsonic incompressible conditions

Robust Metric-Aligned Quad-Dominant Meshing Using L(sub p) Centroidal Voronoi Tessellation

We introduce a meshing algorithm that can be used to both generate and adapt meshes for bounded domains in an anisotropic manner. This is particularly beneficial when anisotropic flow features like shock waves or contact discontinuities are present in the computational domain. The algorithm presented in this paper is based upon meshing under the imposed Riemannian metric tensor, which controls the orientation and size of the mesh elements. In this way there is no need for user intervention to recognize these features. We demonstrate that the method indeed aligns the elements with the underlying metric and produces right-angled simplices that can be recombined into quadrilateral elements. The aim is to eventually incorporate this meshing strategy in the monolithic high-order spectral element solver that is currently being developed at NASA Ames. This paper has two main contributions: First, we demonstrate that we can generate quad-dominant metric-aligned meshes for bounded domains using a generalized form of L(sub p)-Centroidal Voronoi Tessellation (L(sub p)-CVT). Unlike previous works, we do not rely on a background mesh and discretize the bounded domain in a hierarchical way by first discretizing the boundaries and then the volume using the underlying metric. Second, we present an alternative for clipping the Voronoi cells on the boundary, which is common practice in CVT-based meshing algorithms, by reconstructing the Voronoi cells using the defined metric field. In this way we avoid the geometrical complexity of the clipping procedure and we show that we evaluate the energy and its gradient correctly. We show that the reconstruction of the computational domain is consistent with the Lloyds algorithm that is used to compute the L(sub p)-CVT

Inverse aerodynamic design applications using the MGM hybrid formulation

The well-known modified Garabedian-Mcfadden (MGM) method is an attractive alternative for aerodynamic inverse design, for its simplicity and effectiveness (P. Garabedian and G. Mcfadden, Design of supercritical swept wings, AIAA J. 20(3) (1982), 289-291; J.B. Malone, J. Vadyak, and L.N. Sankar, Inverse aerodynamic design method for aircraft components, J. Aircraft 24(2) (1987), 8-9; Santos, A hybrid optimization method for aerodynamic design of lifting surfaces, PhD Thesis, Georgia Institute of Technology, 1993). Owing to these characteristics, the method has been the subject of several authors over the years (G.S. Dulikravich and D.P. Baker, Aerodynamic shape inverse design using a Fourier series method, in AIAA paper 99-0185, AIAA Aerospace Sciences Meeting, Reno, NV, January 1999; D.H. Silva and L.N. Sankar, An inverse method for the design of transonic wings, in 1992 Aerospace Design Conference, No. 92-1025 in proceedings, AIAA, Irvine, CA, February 1992, 1-11; W. Bartelheimer, An Improved Integral Equation Method for the Design of Transonic Airfoils and Wings, AIAA Inc., 1995). More recently, a hybrid formulation and a multi-point algorithm were developed on the basis of the original MGM. This article discusses applications of those latest developments for airfoil and wing design. The test cases focus on wing-body aerodynamic interference and shock wave removal applications. The DLR-F6 geometry is picked as the baseline for the analysis