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Article

Galilean-Invariant Characteristic-Based Volume Penalization Method for Supersonic Flows with Moving Boundaries

1
Sportradar, San Francisco, CA 94105, USA
2
Adaptive Wavelet Technologies LLC, Superior, CO 80027, USA
3
Engineering Department, University of Campania Luigi Vanvitelli, 81031 Aversa, Italy
4
Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, 125047 Moscow, Russia
*
Author to whom correspondence should be addressed.
Academic Editor: Laura A. Miller
Fluids 2021, 6(8), 293; https://doi.org/10.3390/fluids6080293
Received: 17 June 2021 / Revised: 15 August 2021 / Accepted: 17 August 2021 / Published: 20 August 2021
(This article belongs to the Special Issue Wavelets and Fluid Dynamics)
This work extends the characteristic-based volume penalization method, originally developed and demonstrated for compressible subsonic viscous flows in (J. Comput. Phys. 262, 2014), to a hyperbolic system of partial differential equations involving complex domains with moving boundaries. The proposed methodology is shown to be Galilean-invariant and can be used to impose either homogeneous or inhomogeneous Dirichlet, Neumann, and Robin type boundary conditions on immersed boundaries. Both integrated and non-integrated variables can be treated in a systematic manner that parallels the prescription of exact boundary conditions with the approximation error rigorously controlled through an a priori penalization parameter. The proposed approach is well suited for use with adaptive mesh refinement, which allows adequate resolution of the geometry without over-resolving flow structures and minimizing the number of grid points inside the solid obstacle. The extended Galilean-invariant characteristic-based volume penalization method, while being generally applicable to both compressible Navier–Stokes and Euler equations across all speed regimes, is demonstrated for a number of supersonic benchmark flows around both stationary and moving obstacles of arbitrary shape. View Full-Text
Keywords: immersed boundary; volume penalization; moving obstacles; Galilean invariance; hyperbolic system; adaptive mesh refinement; wavelets; Euler equations; Navier–Stokes equations immersed boundary; volume penalization; moving obstacles; Galilean invariance; hyperbolic system; adaptive mesh refinement; wavelets; Euler equations; Navier–Stokes equations
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MDPI and ACS Style

Kasimov, N.; Dymkoski, E.; De Stefano, G.; Vasilyev, O.V. Galilean-Invariant Characteristic-Based Volume Penalization Method for Supersonic Flows with Moving Boundaries. Fluids 2021, 6, 293. https://doi.org/10.3390/fluids6080293

AMA Style

Kasimov N, Dymkoski E, De Stefano G, Vasilyev OV. Galilean-Invariant Characteristic-Based Volume Penalization Method for Supersonic Flows with Moving Boundaries. Fluids. 2021; 6(8):293. https://doi.org/10.3390/fluids6080293

Chicago/Turabian Style

Kasimov, Nurlybek, Eric Dymkoski, Giuliano De Stefano, and Oleg V. Vasilyev. 2021. "Galilean-Invariant Characteristic-Based Volume Penalization Method for Supersonic Flows with Moving Boundaries" Fluids 6, no. 8: 293. https://doi.org/10.3390/fluids6080293

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