WENO Schemes and Application to Steady-State Hypersonic Flow Solutions
Speaker: Rômulo Bessi Freitas, Professor, Celso Suckow da Fonseca Federal Center for Technological Education – CEFET/RJ, Brazil
Date: Thursday, December 15, 2022
Time: 3:00pm
Location: NIA, Room 101C
POC: Pedro Paredes, NIA, Pedro.paredes@nianet.org
Abstract
Non-essential oscillation (ENO) schemes allow for the high-order solution of hypersonic numerical flow configurations. However, the classical group of weighted ENO (WENO) schemes may introduce the phenomenon of post-shock oscillations. This type of numerical error is the main reason for the prevent numerical convergence of the solution, i.e., the time evolution of the residual to reach machine zero values. A novel WENO scheme was recently proposed to solve this problem. The present work provides a brief review of a set of WENO schemes (namely, WENOZS, WENOZM, WENOZ, WENOZ+, WENOS, WENOQZ) and some details about the best practices to reach a converged and accurate steady-state solution for hypersonic flow conditions.
Bio
Rômulo graduated in mathematics from the Federal Rural University of Rio de Janeiro – UFRRJ. He has a master’s degree in Aerospace and Mechanical Engineering from the Technological Institute of Aeronautics – ITA and Ph.D. in Mechanical Engineering from Fluminense Federal University. Currently, He is a professor at Celso Suckow da Fonseca Federal Center for Technological Education – CEFET/RJ, Brazil. He has experience in computationalmethods to solve problems related to fluid mechanics and transport phenomena with an emphasis on stability analysis.
WENO Scheme Implementation for Eigenvalue Problems in Linear Stability Analysis
Speaker: Kamil Dylewicz, PhD Candidate, University of Liverpool
Time: 3:30pm
Abstract
Numerical approximations of flow derivatives using finite-difference schemes in presence of discontinuities, e.g., shock waves, result in spurious numerical oscillations being introduced to the solution. Such numerical artefacts can corrupt the solution or prevent numerical convergence. Shock capturing is one of the approaches used to prevent such numerical oscillations in DNS and LES. A shock capturing approach selects an upwind scheme among several candidate stencils, as in essentially non-oscillatory (ENO) schemes, or uses a convex combination of all the candidate stencils, as in the weighted ENO (WENO) schemes. In this work, fifth order WENO scheme has been implemented to the eigenvalue problem arising from one-dimensional local stability analysis. The results show that it can correctly recover convective instabilities with strong discontinuities. The WENO5 implementation is also shown to significantly reduce the amplitudes of spurious oscillations introduced to eigenfunctions near strong discontinuities. Ongoing work is being performed to implement alternative WENO and flux splitting formulations and to apply these schemes multidimensional stability analysis problems.
Bio
Kamil holds a Master of Aerospace Engineering and graduated from the University of Liverpool (England, United Kingdom) in June 2021 with a First Class Honours Degree. He was awarded institution best research project prize for meritorious performance on the course by the Institution of Mechanical Engineers (London, United Kingdom). Currently a PhD student under supervision of Professor Vassilios Theofilis at the University of Liverpool with research activities focused on stability analysis of super- and hypersonic flows on complex geometries.
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