987 research outputs found
Adjoint Sensitivity Computations for an Embedded-Boundary Cartesian Mesh Method and CAD Geometry
Cartesian-mesh methods are perhaps the most promising approach for addressing the issues of flow solution automation for aerodynamic design problems. In these methods, the discretization of the wetted surface is decoupled from that of the volume mesh. This not only enables fast and robust mesh generation for geometry of arbitrary complexity, but also facilitates access to geometry modeling and manipulation using parametric Computer-Aided Design (CAD) tools. Our goal is to combine the automation capabilities of Cartesian methods with an eficient computation of design sensitivities. We address this issue using the adjoint method, where the computational cost of the design sensitivities, or objective function gradients, is esseutially indepeudent of the number of design variables. In previous work, we presented an accurate and efficient algorithm for the solution of the adjoint Euler equations discretized on Cartesian meshes with embedded, cut-cell boundaries. Novel aspects of the algorithm included the computation of surface shape sensitivities for triangulations based on parametric-CAD models and the linearization of the coupling between the surface triangulation and the cut-cells. The objective of the present work is to extend our adjoint formulation to problems involving general shape changes. Central to this development is the computation of volume-mesh sensitivities to obtain a reliable approximation of the objective finction gradient. Motivated by the success of mesh-perturbation schemes commonly used in body-fitted unstructured formulations, we propose an approach based on a local linearization of a mesh-perturbation scheme similar to the spring analogy. This approach circumvents most of the difficulties that arise due to non-smooth changes in the cut-cell layer as the boundary shape evolves and provides a consistent approximation tot he exact gradient of the discretized abjective function. A detailed gradient accurace study is presented to verify our approach. Thereafter, we focus on a shape optimization problem for an Apollo-like reentry capsule. The optimization seeks to enhance the lift-to-drag ratio of the capsule by modifyjing the shape of its heat-shield in conjunction with a center-of-gravity (c.g.) offset. This multipoint and multi-objective optimization problem is used to demonstrate the overall effectiveness of the Cartesian adjoint method for addressing the issues of complex aerodynamic design. This abstract presents only a brief outline of the numerical method and results; full details will be given in the final paper
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
Turbulent Output-Based Anisotropic Adaptation
Controlling discretization error is a remaining challenge for computational fluid dynamics simulation. Grid adaptation is applied to reduce estimated discretization error in drag or pressure integral output functions. To enable application to high O(10(exp 7)) Reynolds number turbulent flows, a hybrid approach is utilized that freezes the near-wall boundary layer grids and adapts the grid away from the no slip boundaries. The hybrid approach is not applicable to problems with under resolved initial boundary layer grids, but is a powerful technique for problems with important off-body anisotropic features. Supersonic nozzle plume, turbulent flat plate, and shock-boundary layer interaction examples are presented with comparisons to experimental measurements of pressure and velocity. Adapted grids are produced that resolve off-body features in locations that are not known a priori
Adjoint Algorithm for CAD-Based Shape Optimization Using a Cartesian Method
Adjoint solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape optimization. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (geometric parameters that control the shape). More recently, emerging adjoint applications focus on the analysis problem, where the adjoint solution is used to drive mesh adaptation, as well as to provide estimates of functional error bounds and corrections. The attractive feature of this approach is that the mesh-adaptation procedure targets a specific functional, thereby localizing the mesh refinement and reducing computational cost. Our focus is on the development of adjoint-based optimization techniques for a Cartesian method with embedded boundaries.12 In contrast t o implementations on structured and unstructured grids, Cartesian methods decouple the surface discretization from the volume mesh. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin et developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the Euler equations. In both approaches, a boundary condition is introduced to approximate the effects of the evolving surface shape that results in accurate gradient computation. Central to automated shape optimization algorithms is the issue of geometry modeling and control. The need to optimize complex, "real-life" geometry provides a strong incentive for the use of parametric-CAD systems within the optimization procedure. In previous work, we presented an effective optimization framework that incorporates a direct-CAD interface. In this work, we enhance the capabilities of this framework with efficient gradient computations using the discrete adjoint method. We present details of the adjoint numerical implementation, which reuses the domain decomposition, multigrid, and time-marching schemes of the flow solver. Furthermore, we explain and demonstrate the use of CAD in conjunction with the Cartesian adjoint approach. The final paper will contain a number of complex geometry, industrially relevant examples with many design variables to demonstrate the effectiveness of the adjoint method on Cartesian meshes
Optimal wavy surface to suppress vortex shedding using second-order sensitivity to shape changes
A method to find optimal 2nd-order perturbations is presented, and applied to
find the optimal spanwise-wavy surface for suppression of cylinder wake
instability. Second-order perturbations are required to capture the stabilizing
effect of spanwise waviness, which is ignored by standard adjoint-based
sensitivity analyses. Here, previous methods are extended so that (i) 2nd-order
sensitivity is formulated for base flow changes satisfying linearised
Navier-Stokes, and (ii) the resulting method is applicable to a 2D global
instability problem. This makes it possible to formulate 2nd-order sensitivity
to shape modifications. Using this formulation, we find the optimal shape to
suppress the a cylinder wake instability. The optimal shape is then perturbed
by random distributions in full 3D stability analysis to confirm that it is a
local optimal at the given amplitude and wavelength. Furthermore, it is shown
that none of the 10 random wavy shapes alone stabilize the wake flow at Re=50,
while the optimal shape does. At Re=100, surface waviness of maximum height 1%
of the cylinder diameter is sufficient to stabilize the flow. The optimal
surface creates streaks by passively extracting energy from the base flow
derivatives and effectively altering the tangential velocity component at the
wall, as opposed to spanwise-wavy suction which inputs energy to the normal
velocity component at the wall. This paper presents a fully two-dimensional and
computationally affordable method to find optimal 2nd-order perturbations of
generic flow instability problems and any boundary control (such as boundary
forcing, shape modulation or suction).Comment: 19 pages, 6 figure
Cart3D Simulations for the First AIAA Sonic Boom Prediction Workshop
Simulation results for the First AIAA Sonic Boom Prediction Workshop (LBW1) are presented using an inviscid, embedded-boundary Cartesian mesh method. The method employs adjoint-based error estimation and adaptive meshing to automatically determine resolution requirements of the computational domain. Results are presented for both mandatory and optional test cases. These include an axisymmetric body of revolution, a 69deg delta wing model and a complete model of the Lockheed N+2 supersonic tri-jet with V-tail and flow through nacelles. In addition to formal mesh refinement studies and examination of the adjoint-based error estimates, mesh convergence is assessed by presenting simulation results for meshes at several resolutions which are comparable in size to the unstructured grids distributed by the workshop organizers. Data provided includes both the pressure signals required by the workshop and information on code performance in both memory and processing time. Various enhanced techniques offering improved simulation efficiency will be demonstrated and discussed
Numerical Predictions of Sonic Boom Signatures for a Straight Line Segmented Leading Edge Model
A sonic boom wind tunnel test was conducted on a straight-line segmented leading edge (SLSLE) model in the NASA Langley 4- by 4- Foot Unitary Plan Wind Tunnel (UPWT). The purpose of the test was to determine whether accurate sonic boom measurements could be obtained while continuously moving the SLSLE model past a conical pressure probe. Sonic boom signatures were also obtained using the conventional move-pause data acquisition method for comparison. The continuous data acquisition approach allows for accurate signatures approximately 15 times faster than a move-pause technique. These successful results provide an incentive for future testing with greatly increased efficiency using the continuous model translation technique with the single probe to measure sonic boom signatures. Two widely used NASA codes, USM3D (Navier-Stokes) and CART3D-AERO (Euler, adjoint-based adaptive mesh), were used to compute off-body sonic boom pressure signatures of the SLSLE model at several different altitudes below the model at Mach 2.0. The computed pressure signatures compared well with wind tunnel data. The effect of the different altitude for signature extraction was evaluated by extrapolating the near field signatures to the ground and comparing pressure signatures and sonic boom loudness levels
Shape optimisation with multiresolution subdivision surfaces and immersed finite elements
We develop a new optimisation technique that combines multiresolution
subdivision surfaces for boundary description with immersed finite elements for
the discretisation of the primal and adjoint problems of optimisation. Similar
to wavelets multiresolution surfaces represent the domain boundary using a
coarse control mesh and a sequence of detail vectors. Based on the
multiresolution decomposition efficient and fast algorithms are available for
reconstructing control meshes of varying fineness. During shape optimisation
the vertex coordinates of control meshes are updated using the computed shape
gradient information. By virtue of the multiresolution editing semantics,
updating the coarse control mesh vertex coordinates leads to large-scale
geometry changes and, conversely, updating the fine control mesh coordinates
leads to small-scale geometry changes. In our computations we start by
optimising the coarsest control mesh and refine it each time the cost function
reaches a minimum. This approach effectively prevents the appearance of
non-physical boundary geometry oscillations and control mesh pathologies, like
inverted elements. Independent of the fineness of the control mesh used for
optimisation, on the immersed finite element grid the domain boundary is always
represented with a relatively fine control mesh of fixed resolution. With the
immersed finite element method there is no need to maintain an analysis
suitable domain mesh. In some of the presented two- and three-dimensional
elasticity examples the topology derivative is used for creating new holes
inside the domain.The partial support of the EPSRC through grant # EP/G008531/1 and EC through Marie Curie Actions (IAPP) program CASOPT project are gratefully acknowledged.This is the final version of the article. It was first available from Elsevier via http://dx.doi.org/10.1016/j.cma.2015.11.01
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
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