Author : Emmett M. Padway
Publisher :
ISBN 13 :
Total Pages : 154 pages
Book Rating : 4.5/5 (57 download)
Book Synopsis Tangent and Adjoint Problems in Partially Converged Flows by : Emmett M. Padway
Download or read book Tangent and Adjoint Problems in Partially Converged Flows written by Emmett M. Padway and published by . This book was released on 2020 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: Adjoint methods see widespread use in computational fluid dynamics (CFD) in two important domains of the field: shape optimization and output-based refinement.CFD has become more widespread as computing power has become more available and algorithms have become both more advanced and efficient. This allows for the use of cheap, low-fidelity methods in the conceptual design stage, and more accurate high-fidelity methods later in the detailed design stage. The high fidelity methods coupled with optimization toolboxes for automated design have a significant place in the detailed design process, mainly to better inform the use of expensive wind tunnel testing. Furthermore, the use of adjoint methods in shape optimization allows for cheaper sensitivity evaluation for gradient-based design approaches, allowing for scaling independent of the number of design variables. As a result highly refined/parameterized design optimizations are possible with negligible cost increases. Adjoint methods are also utilized in the context of adaptive mesh refinement as they can be used to create output-based error estimates. Adjoint-based methods form an error estimate that calculates error in the output-of-interest, and are desirable for their efficacy in tailoring/adapting meshes for maximum accuracy in the engineering quantity of interest. This can allow for coarsening meshes in areas of little engineering interest and refining in areas of high interest,thus resulting in a maximally useful mesh for engineering quantities with a given number of degrees of freedom. The adjoint systems used in these analyses require that the nonlinear problem be solved to machine precision --that the discretized form of the governing equations be satisfied. However, as the field has attempted more difficult simulations either due to the accuracy of spatial discretization of the simulation, the geometry of the model, or the increasing push to unsteady flow, it has become increasingly difficult to satisfy this constraint. Some members of thefield have demonstrated that this can lead to difficult to converge adjointproblems that provide sensitivities highly dependent on the state atwhich the simulation is terminated. Additionally, this can lead to issues with theerror estimation process by returning inaccurate error estimates and poor refinement patterns. This work develops a novel methodology for adjoint based optimization and errorestimation for unconverged simulations through linearization of the nonlinearsolution process. It contains results for various different nonlinear solversand applications of the adjoint system to design optimization and errorestimation. As CFD has been used for more complex simulations (unsteady,high-order, complex geometry) the ability to get a useful adjoint solution thatis guaranteed to not diverge is tremendously desirable. The goal of this work isto show a hierarchy of different linearizations with different approximationsand apply them to these partially converged problems. This work presents tangentand adjoint formulations for each of the various nonlinear solution strategiesused in the test cases, including the solution strategies required to avoid flowdivergence for problems with strong shocks. It also shows the varying linearsolver technologies, used in the nonlinear process, the mesh deformationprocess, and the tangent and adjoint processes. Included also are threedifferent error estimation techniques for the steady state adjoint and theiranalogues for the pseudo-time accurate adjoint. These error estimationtechniques are used to drive mesh adaptation and the algorithms for the adaptivemesh refinement package are included as well. A detailed error analysis ofapproximate linearization of the nonlinear solution process for both the tangentand adjoint modes is shown as well. The end result is a series of methods andalgorithms guaranteed to provide either adjoint based sensitivities or adjointbased error estimates that are insensitive to the specific state of terminationof the solution process and can be useful for simulations which do not fullyconverge, where the calculation of accurate sensitivities has been a majorstumbling block to date.