Output-Based Error Estimation and Model Reduction for Chaotic Flows

Turbulent flows are characterized by chaotic variations in state variables and are commonly found in many applications such as jet engine mixing and flow over bluff bodies. Large Eddy Simulations (LES) of these chaotic flows have already proven to be useful to the design process. However, LES is resource and time-intensive. Application of output-based methods for error estimation and mesh adaptation would decrease the cost of these chaotic simulations while still retaining their overall accuracy. However, a direct application of unsteady adjoint-based methods is not possible due to the flows’ inherent sensitivity to the initial conditions and the exponential growth of the corresponding adjoint solutions. This dissertation proposes the Hyper-Reduced Order Modeling-Least Squares Shadowing (HROM-LSS) method, which combines model reduction principles with adjoint sensitivity techniques for chaotic flows to calculate accurate adjoints that are cheaper to solve for than the Least Squares Shadowing (LSS) method on its own. All primal solutions are solved using the discontinuous Galerkin finite element method. Results of the HROM-LSS method for the Kuramoto-Sivashinsky equation and the NACA 0012 airfoil at high Reynolds numbers show promise for this combined method and have been shown to outperform the LSS method when calculating the effect of the discretization errors on the output. In particular, the average CPU times for the HROM-LSS method are reduced by as much as 97.44% for short time simulations and as much as 64% for longer simulations, making the HROM-LSS method a more practical option to calculate adjoint for chaotic flows in order to perform output-based error estimation for turbulent flows.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/149954/1/ykmizu_1.pd

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Software for Exascale Computing - SPPEXA 2016-2019

This open access book summarizes the research done and results obtained in the second funding phase of the Priority Program 1648 "Software for Exascale Computing" (SPPEXA) of the German Research Foundation (DFG) presented at the SPPEXA Symposium in Dresden during October 21-23, 2019. In that respect, it both represents a continuation of Vol. 113 in Springer’s series Lecture Notes in Computational Science and Engineering, the corresponding report of SPPEXA’s first funding phase, and provides an overview of SPPEXA’s contributions towards exascale computing in today's sumpercomputer technology. The individual chapters address one or more of the research directions (1) computational algorithms, (2) system software, (3) application software, (4) data management and exploration, (5) programming, and (6) software tools. The book has an interdisciplinary appeal: scholars from computational sub-fields in computer science, mathematics, physics, or engineering will find it of particular interest