Presented By: Aerospace Engineering
AE Defense: Mesh-Refinement, Solution Order-Increment and Mesh-Movement Adaptation Models for Computational Fluid Dynamics
Aerospace Engineering PhD Candidate: Kaihua Ding, Dissertation Chair: Assoc. Prof. Krzysztof J. Fidkowski
Aerospace Engineering PhD Candidate: Kaihua Ding
Dissertation Chair: Assoc. Prof. Krzysztof J. Fidkowski
As numerical simulations are applied to more complex and large-scale problems, solution verification becomes increasingly important in ensuring the accuracy of the computed results. Although improvements in computer hardware have brought expensive simulations within reach, efficiency is still paramount, especially in the context of design optimization and uncertainty quantification. This thesis addresses both of these needs through contributions to solution-based adaptive algorithms, in which the discretization is modified through a feedback of solution error estimates so as to improve the accuracy. In particular, new methods are developed for two discretizations relevant to Computational Fluid Dynamics: the Active Flux method and the discontinuous Galerkin method. For the Active Flux method, which is a fully-discrete third-order discretization, both the discrete and continuous adjoint methods are derived and used to drive mesh (h) refinement and dynamic node movement, also known as “r” adaptation. For the discontinuous Galerkin method, which is an arbitrary-order finite-element discretization, efficiency improvements are presented for computing and using error estimates derived from the discrete adjoint, and a new “r” adaptation strategy is presented for unsteady problems. For both discretizations, error estimate efficacy and adaptive efficiency improvements are shown relative to other strategies.
Publications
Kaihua Ding, Krzysztof J. Fidkowski, and Philip L. Roe. Output-based Adaptation for the Active Flux Method. Journal of Computer \& Fluids, 2017 (submitting).
Kaihua Ding and Krzysztof J. Fidkowski. Output error control using $r$-adaptation. AIAA Paper, 2017-4111, 2017.
Kaihua Ding, Krzysztof J. Fidkowski, and Philip L. Roe. Continuous adjoint based error estimation and r-refinement for the active flux method. AIAA Paper 2016-0832, 2016.
Kaihua Ding, Krzysztof J. Fidkowski, and Philip L. Roe. Acceleration techniques for adjoint-based error estimation and mesh adaptation. Eighth International Conference on Computational Fluid Dynamics, ICCFD8-0249, 2014.
Kaihua Ding, Krzysztof J. Fidkowski, and Philip L. Roe. Adjoint-based error estimation and mesh adaptation for the active flux method. AIAA Paper 2013-2942, 2013.
Dissertation Chair: Assoc. Prof. Krzysztof J. Fidkowski
As numerical simulations are applied to more complex and large-scale problems, solution verification becomes increasingly important in ensuring the accuracy of the computed results. Although improvements in computer hardware have brought expensive simulations within reach, efficiency is still paramount, especially in the context of design optimization and uncertainty quantification. This thesis addresses both of these needs through contributions to solution-based adaptive algorithms, in which the discretization is modified through a feedback of solution error estimates so as to improve the accuracy. In particular, new methods are developed for two discretizations relevant to Computational Fluid Dynamics: the Active Flux method and the discontinuous Galerkin method. For the Active Flux method, which is a fully-discrete third-order discretization, both the discrete and continuous adjoint methods are derived and used to drive mesh (h) refinement and dynamic node movement, also known as “r” adaptation. For the discontinuous Galerkin method, which is an arbitrary-order finite-element discretization, efficiency improvements are presented for computing and using error estimates derived from the discrete adjoint, and a new “r” adaptation strategy is presented for unsteady problems. For both discretizations, error estimate efficacy and adaptive efficiency improvements are shown relative to other strategies.
Publications
Kaihua Ding, Krzysztof J. Fidkowski, and Philip L. Roe. Output-based Adaptation for the Active Flux Method. Journal of Computer \& Fluids, 2017 (submitting).
Kaihua Ding and Krzysztof J. Fidkowski. Output error control using $r$-adaptation. AIAA Paper, 2017-4111, 2017.
Kaihua Ding, Krzysztof J. Fidkowski, and Philip L. Roe. Continuous adjoint based error estimation and r-refinement for the active flux method. AIAA Paper 2016-0832, 2016.
Kaihua Ding, Krzysztof J. Fidkowski, and Philip L. Roe. Acceleration techniques for adjoint-based error estimation and mesh adaptation. Eighth International Conference on Computational Fluid Dynamics, ICCFD8-0249, 2014.
Kaihua Ding, Krzysztof J. Fidkowski, and Philip L. Roe. Adjoint-based error estimation and mesh adaptation for the active flux method. AIAA Paper 2013-2942, 2013.
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