Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018

This open access book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions

On the well-posedness of the multi-dimensional Roe-Liu-Vinokur linearization for residual distribution schemes

In reference, Liu and Vinokur proposed an strategy to derive a Roe-like linearization for flows in thermo-chemical non-equilibrium (TCNEQ). In the context of approximated Riemann solvers, being able to determine a Roe-like averaged state Z→avg respecting property U guarantees that a discrete linearized description of the Riemann problem provides a solution consistent with that of the original non-linear problem, i.e., the numerical algorithm can - in the words of Roe - "recognize a shock wave"

Enabling Automated, Reliable and Efficient Aerodynamic Shape Optimization With Output-Based Adapted Meshes

Simulation-based aerodynamic shape optimization has been greatly pushed forward during the past several decades, largely due to the developments of computational fluid dynamics (CFD), geometry parameterization methods, mesh deformation techniques, sensitivity computation, and numerical optimization algorithms. Effective integration of these components has made aerodynamic shape optimization a highly automated process, requiring less and less human interference. Mesh generation, on the other hand, has become the main overhead of setting up the optimization problem. Obtaining a good computational mesh is essential in CFD simulations for accurate output predictions, which as a result significantly affects the reliability of optimization results. However, this is in general a nontrivial task, heavily relying on the user’s experience, and it can be worse with the emerging high-fidelity requirements or in the design of novel configurations. On the other hand, mesh quality and the associated numerical errors are typically only studied before and after the optimization, leaving the design search path unveiled to numerical errors. This work tackles these issues by integrating an additional component, output-based mesh adaptation, within traditional aerodynamic shape optimizations. First, we develop a more suitable error estimator for optimization problems by taking into account errors in both the objective and constraint outputs. The localized output errors are then used to drive mesh adaptation to achieve the desired accuracy on both the objective and constraint outputs. With the variable fidelity offered by the adaptive meshes, multi-fidelity optimization frameworks are developed to tightly couple mesh adaptation and shape optimization. The objective functional and its sensitivity are first evaluated on an initial coarse mesh, which is then subsequently adapted as the shape optimization proceeds. The effort to set up the optimization is minimal since the initial mesh can be fairly coarse and easy to generate. Meanwhile, the proposed framework saves computational costs by reducing the mesh size at the early stages of the optimization, when the design is far from optimal, and avoiding exhaustive search on low-fidelity meshes when the outputs are inaccurate. To further improve the computational efficiency, we also introduce new methods to accelerate the error estimation and mesh adaptation using machine learning techniques. Surrogate models are developed to predict the localized output error and optimal mesh anisotropy to guide the adaptation. The proposed machine learning approaches demonstrate good performance in two-dimensional test problems, encouraging more study and developments to incorporate them within aerodynamic optimization techniques. Although CFD has been extensively used in aircraft design and optimization, the design automation, reliability, and efficiency are largely limited by the mesh generation process and the fixed-mesh optimization paradigm. With the emerging high-fidelity requirements and the further developments of unconventional configurations, CFD-based optimization has to be made more accurate and more efficient to achieve higher design reliability and lower computational cost. Furthermore, future aerodynamic optimization needs to avoid unnecessary overhead in mesh generation and optimization setup to further automate the design process. The author expects the methods developed in this work to be the keys to enable more automated, reliable, and efficient aerodynamic shape optimization, making CFD-based optimization a more powerful tool in aircraft design.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163034/1/cgderic_1.pd