Presented By: Aerospace Engineering
AE Defense: Variational Multiscale Modeling and Memory Effects in Turbulent Flow Simulations
Aerospace Engineering PhD Candidate: Eric Parish, Dissertation Chair: Associate Professor Karthik Durasaimy
Aerospace Engineering PhD Candidate: Eric Parish
Dissertation Chair: Associate Professor Karthik Durasaimy
Effective models of multiscale problems such as turbulent flows have to account for the impact of unresolved physics on the resolved scales. This dissertation advances our understanding of multiscale models and develops a mathematically rigorous closure modeling framework by combining the Mori-Zwanzig formalism of Statistical Mechanics with the Variational Multiscale method (MZ-VMS). This approach leverages scale-separation and phase-space projectors to provide a systematic modeling approach that is applicable to complex non-linear partial differential equations. Spectral as well as finite element methods are considered.
The MZ-VMS framework leads to a closure term that is non-local in time and appears as a memory integral. The resulting non-Markovian system is used as a starting point for model development. Several new insights are discovered: We show that unresolved scales lead to memory effects that are driven by the coarse-scale residual and, in the case of finite elements, inter-element jumps. Connections between MZ-based methods, artificial viscosity, and VMS models are explored.
Large eddy simulations of Burgers’ equation, turbulent flows, and magnetohydrodynamic turbulence using spectral and discontinuous Galerkin methods are explored. We show that MZ-VMS models lead to substantial improvements in the prediction of quantities of interest. Applications to discontinuous Galerkin methods show that modern flux schemes can inherently capture memory effects. We conclude by demonstrating how ideas from MZ-VMS can be adapted for shock-capturing and filtering methods.
Dissertation Committee
Chair: Associate Professor Karthik Duraisamy
Cognate: Associate Professor Eric Johnsen
Members: Associate Professor Krzysztof Fidkowski, Professor Venkat Raman, Professor Philip Roe
Publications List
Parish, E.J. and Duraisamy, K., "Mori-Zwanzig and the Variational Multiscale Method: A Unified Framework for Multiscale Modeling" CMAME, Submitted, 2017.
Parish, E.J. and Duraisamy, K., "A Dynamic Subgrid Model for Large Eddy Simulations Based on the Mori-Zwanzig Formalism," Journal of Computational Physics, Vol. 349, pp. 154-175, 2017.
Gouasmi, A., Parish, E.J., and Duraisamy, K., "A priori estimation of memory effects in reduced-order models of nonlinear systems using the Mori-Zwanzig formalism," Proc. Roy. Soc. A, Vol 473, 2017.
Parish, E.J. and Duraisamy, K., "Non-Markovian closure models for Large Eddy Simulations based on the Mori-Zwanzig formalism," Phy. Rev. Fluids, Vol. 2, No. 1, 2017.
Parish, E.J., Duraisamy, K., and Chandrashekar, P. "Generalized Riemann problem-based upwind scheme for the vorticity transport equations," Computers and Fluids, Vol. 132, No. 25, pg. 10-18, 2016.
Parish, E.J. and Duraisamy, K.. ”A Paradigm for data-driven predictive modeling using field inversion and machine learning," Journal of Computational Physics, Vol. 305, No. 15, 2015.
Dissertation Chair: Associate Professor Karthik Durasaimy
Effective models of multiscale problems such as turbulent flows have to account for the impact of unresolved physics on the resolved scales. This dissertation advances our understanding of multiscale models and develops a mathematically rigorous closure modeling framework by combining the Mori-Zwanzig formalism of Statistical Mechanics with the Variational Multiscale method (MZ-VMS). This approach leverages scale-separation and phase-space projectors to provide a systematic modeling approach that is applicable to complex non-linear partial differential equations. Spectral as well as finite element methods are considered.
The MZ-VMS framework leads to a closure term that is non-local in time and appears as a memory integral. The resulting non-Markovian system is used as a starting point for model development. Several new insights are discovered: We show that unresolved scales lead to memory effects that are driven by the coarse-scale residual and, in the case of finite elements, inter-element jumps. Connections between MZ-based methods, artificial viscosity, and VMS models are explored.
Large eddy simulations of Burgers’ equation, turbulent flows, and magnetohydrodynamic turbulence using spectral and discontinuous Galerkin methods are explored. We show that MZ-VMS models lead to substantial improvements in the prediction of quantities of interest. Applications to discontinuous Galerkin methods show that modern flux schemes can inherently capture memory effects. We conclude by demonstrating how ideas from MZ-VMS can be adapted for shock-capturing and filtering methods.
Dissertation Committee
Chair: Associate Professor Karthik Duraisamy
Cognate: Associate Professor Eric Johnsen
Members: Associate Professor Krzysztof Fidkowski, Professor Venkat Raman, Professor Philip Roe
Publications List
Parish, E.J. and Duraisamy, K., "Mori-Zwanzig and the Variational Multiscale Method: A Unified Framework for Multiscale Modeling" CMAME, Submitted, 2017.
Parish, E.J. and Duraisamy, K., "A Dynamic Subgrid Model for Large Eddy Simulations Based on the Mori-Zwanzig Formalism," Journal of Computational Physics, Vol. 349, pp. 154-175, 2017.
Gouasmi, A., Parish, E.J., and Duraisamy, K., "A priori estimation of memory effects in reduced-order models of nonlinear systems using the Mori-Zwanzig formalism," Proc. Roy. Soc. A, Vol 473, 2017.
Parish, E.J. and Duraisamy, K., "Non-Markovian closure models for Large Eddy Simulations based on the Mori-Zwanzig formalism," Phy. Rev. Fluids, Vol. 2, No. 1, 2017.
Parish, E.J., Duraisamy, K., and Chandrashekar, P. "Generalized Riemann problem-based upwind scheme for the vorticity transport equations," Computers and Fluids, Vol. 132, No. 25, pg. 10-18, 2016.
Parish, E.J. and Duraisamy, K.. ”A Paradigm for data-driven predictive modeling using field inversion and machine learning," Journal of Computational Physics, Vol. 305, No. 15, 2015.
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