Unsteady adjoint analysis for output sensitivity and mesh adaptation

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2012.Cataloged from department-submitted PDF version of thesis. This electronic version was submitted and approved by the author's academic department as part of an electronic thesis pilot project. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 123-135).Adjoint analysis in computational fluid dynamics (CFD) has been applied to design optimization and mesh adaptation, but due to the relative expense of unsteady analysis these applications have predominantly been for steady problems. As the use of adjoint methods continues to becomes more prevalent, more problems are encountered for which steady analysis may not be appropriate. This thesis examines three aspects of unsteady adjoint analysis. First, this work investigates problems exhibiting small-scale output unsteadiness when solved with time-inaccurate iterative solvers. It is demonstrated that unconverged steady flow calculations, even with small output unsteadiness, can lead to significant variability in the estimated output sensitivity due to the arbitrary choice of unconverged state upon which the linearization is performed. Further, time-inaccurate "unsteady" iterative solutions depend on the iterative method used and may exhibit different output and output sensitivity compared to the steady flow or time-accurate unsteady flow. With the motivation for unsteady simulation established, output and output parameter sensitivities of periodic unsteady problems are sought using finite-time averaging. Periodic outputs computed over a finite time span are found to converge slowly and output sensitivities may be nonconvergent when the period of oscillation is a function of the parameter of interest. A theoretical basis for this lack of convergence is identified and output windowing is proposed to alleviate its effect. Output windowing is shown to enable the accurate computation of periodic output sensitivities and to decrease simulation time to compute periodic outputs and sensitivities. Finally, a spatial mesh adaptation approach is developed for unsteady wake problems and other problems with smooth and persistent regions of unsteadiness. For this class of problems, a higher-order discretization coupled with a single spatial mesh approach is appropriate to capture both steady and unsteady regions. The method proposed herein extends the anisotropic, output-based Mesh Optimization via Error Sampling and Synthesis (MOESS) algorithm of Yano and Darmofal to optimize the spatial mesh driven by an unsteady flow field.by Joshua Ambre Krakos.Ph.D

Comparing Anisotropic Output-Based Grid Adaptation Methods by Decomposition

Anisotropic grid adaptation is examined by decomposing the steps of flow solution, ad- joint solution, error estimation, metric construction, and simplex grid adaptation. Multiple implementations of each of these steps are evaluated by comparison to each other and expected analytic results when available. For example, grids are adapted to analytic metric fields and grid measures are computed to illustrate the properties of multiple independent implementations of grid adaptation mechanics. Different implementations of each step in the adaptation process can be evaluated in a system where the other components of the adaptive cycle are fixed. Detailed examination of these properties allows comparison of different methods to identify the current state of the art and where further development should be targeted

First benchmark of the Unstructured Grid Adaptation Working Group

Unstructured grid adaptation is a technology that holds the potential to improve the automation and accuracy of computational fluid dynamics and other computational disciplines. Difficulty producing the highly anisotropic elements necessary for simulation on complex curved geometries that satisfies a resolution request has limited this technology's widespread adoption. The Unstructured Grid Adaptation Working Group is an open gathering of researchers working on adapting simplicial meshes to conform to a metric field. Current members span a wide range of institutions including academia, industry, and national laboratories. The purpose of this group is to create a common basis for understanding and improving mesh adaptation. We present our first major contribution: a common set of benchmark cases, including input meshes and analytic metric specifications, that are publicly available to be used for evaluating any mesh adaptation code. We also present the results of several existing codes on these benchmark cases, to illustrate their utility in identifying key challenges common to all codes and important differences between available codes. Future directions are defined to expand this benchmark to mature the technology necessary to impact practical simulation workflows

Geometry Modeling for Unstructured Mesh Adaptation

The quantification and control of discretization error is critical to obtaining reliable simulation results. Adaptive mesh techniques have the potential to automate discretization error control, but have made limited impact on production analysis workflow. Recent progress has matured a number of independent implementations of flow solvers, error estimation methods, and anisotropic mesh adaptation mechanics. However, the poor integration of initial mesh generation and adaptive mesh mechanics to typical sources of geometry has hindered adoption of adaptive mesh techniques, where these geometries are often created in Mechanical Computer- Aided Design (MCAD) systems. The difficulty of this coupling is compounded by two factors: the inherent complexity of the model (e.g., large range of scales, bodies in proximity, details not required for analysis) and unintended geometry construction artifacts (e.g., translation, uneven parameterization, degeneracy, self-intersection, sliver faces, gaps, large tolerances be- tween topological elements, local high curvature to enforce continuity). Manual preparation of geometry is commonly employed to enable fixed-grid and adaptive-grid workflows by reducing the severity and negative impacts of these construction artifacts, but manual process interaction inhibits workflow automation. Techniques to permit the use of complex geometry models and reduce the impact of geometry construction artifacts on unstructured grid workflows are models from the AIAA Sonic Boom and High Lift Prediction are shown to demonstrate the utility of the current approach

Unstructured Grid Adaptation: Status, Potential Impacts, and Recommended Investments Towards CFD 2030

International audienceUnstructured grid adaptation is a powerful tool to control Computational Fluid Dynamics (CFD) discretization error. It has enabled key increases in the accuracy, automation, and capacity of some fluid simulation applications. Slotnick et al. provide a number of case studies in the CFD Vision 2030 Study: A Path to Revolutionary Computational Aerosciences to illustrate the current state of CFD capability and capacity. The study authors forecast the potential impact of emerging High Performance Computing (HPC) environments forecast in the year 2030 and identify that mesh generation and adaptivity will continue to be significant bottlenecks in the CFD workflow. These bottlenecks may persist because very little government investment has been targeted in these areas. To motivate investment, the impacts of improved grid adaptation technologies are identified. The CFD Vision 2030 Study roadmap and anticipated capabilities in complementary disciplines are quoted to provide context for the progress made in grid adaptation in the past fifteen years, current status, and a forecast for the next fifteen years with recommended investments. These investments are specific to mesh adaptation and impact other aspects of the CFD process. Finally, a strategy is identified to di↵use grid adaptation technology into production CFD work flows

Unstructured Grid Adaptation and Solver Technology for Turbulent Flows

Unstructured grid adaptation is a tool to control Computational Fluid Dynamics (CFD) discretization error. However, adaptive grid techniques have made limited impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Issues that prevent the use of adaptive grid methods are identified by applying unstructured grid adaptation methods to a series of benchmark cases. Once identified, these challenges to existing adaptive workflows can be addressed. Unstructured grid adaptation is evaluated for test cases described on the Turbulence Modeling Resource (TMR) web site, which documents uniform grid refinement of multiple schemes. The cases are turbulent flow over a Hemisphere Cylinder and an ONERA M6Wing. Adaptive grid force and moment trajectories are shown for three integrated grid adaptation processes with Mach interpolation control and output error based metrics. The integrated grid adaptation process with a finite element (FE) discretization produced results consistent with uniform grid refinement of fixed grids. The integrated grid adaptation processes with finite volume schemes were slower to converge to the reference solution than the FE method. Metric conformity is documented on grid/metric snapshots for five grid adaptation mechanics implementations. These tools produce anisotropic boundary conforming grids requested by the adaptation process

Verification of Unstructured Grid Adaptation Components

Adaptive unstructured grid techniques have made limited impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Recent progress has matured a number of independent implementations of flow solvers, error estimation methods, and anisotropic grid adaptation mechanics. Known differences and previously unknown differences in grid adaptation components and their integrated processes are identified here for study. Unstructured grid adaptation tools are verified using analytic functions and the Code Comparison Principle. Three analytic functions with different smoothness properties are adapted to show the impact of smoothness on implementation differences. A scalar advection-diffusion problem with an analytic solution that models a boundary layer is adapted to test individual grid adaptation components. Laminar flow over a delta wing and turbulent flow over an ONERA M6 wing are verified with multiple, independent grid adaptation procedures to show consistent convergence to fine-grid forces and a moment. The scalar problems illustrate known differences in a grid adaptation component implementation and a previously unknown interaction between components. The wing adaptation cases in the current study document a clear improvement to existing grid adaptation procedures. The stage is set for the infusion of verified grid adaptation into production fluid flow simulations

Checkpointing with Time Gaps for Unsteady Adjoint CFD

© Springer International Publishing AG 2019. Gradient-based optimisation using adjoints is an increasingly common approach for industrial flow applications. For cases where the flow is largely unsteady however, the adjoint method is still not widely used, in particular because of its prohibitive computational cost and memory footprint. Several methods have been proposed to reduce the peak memory usage, such as checkpointing schemes or checkpoint compression, at the price of increasing the computational cost even further. We investigate incomplete checkpointing as an alternative, which reduces memory usage at almost no extra computational cost, but instead offers a trade-off between memory footprint and the fidelity of the model. The method works by storing only selected physical time steps and using interpolation to reconstruct time steps that have not been stored. We show that this is enough to compute sufficiently accurate adjoint sensitivities for many relevant cases, and does not add significantly to the computational cost. The method works for general cases and does not require to identify periodic cycles in the flow

Verification of Unstructured Grid Adaptation Components

Adaptive unstructured grid techniques have made limited impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Recent progress has matured a number of independent implementations of flow solvers, error estimation methods, and anisotropic grid adaptation mechanics. Known differences and previously unknown differences in grid adaptation components and their integrated processes are identified here for study. Unstructured grid adaptation tools are verified using analytic functions and the Code Comparison Principle. Three analytic functions with different smoothness properties are adapted to show the impact of smoothness on implementation differences. A scalar advection-diffusion problem with an analytic solution that models a boundary layer is adapted to test individual grid adaptation components. The scalar problems illustrate known differences in a grid adaptation component implementation and a previously unknown interaction between components. Laminar flow over a delta wing is verified with multiple, independent grid adaptation procedures to show consistent convergence to fine-grid forces and pitching moment