An improved ghost‐cell immersed boundary method for compressible flow simulations. (17th June 2016)

• Record Type: Journal Article
• Authors: Chi, Cheng; Lee, Bok Jik; Im, Hong G.
• Is Part Of: International journal for numerical methods in fluids. Volume 83:Number 2(2017)
• Page Start: 132
• Page End: 148
• Publication Date: 2016-06-17
• Subjects: compressible flow -- Cartesian grid -- immersed boundary -- ghost‐cell method -- level‐set method -- cut‐cell method; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4262
• Languages: English
• ISSNs: 0271-2091

Abstract

Summary: This study presents an improved ghost‐cell immersed boundary approach to represent a solid body in compressible flow simulations. In contrast to the commonly used approaches, in the present work, ghost cells are mirrored through the boundary described using a level‐set method to farther image points, incorporating a higher‐order extra/interpolation scheme for the ghost‐cell values. A sensor is introduced to deal with image points near the discontinuities in the flow field. Adaptive mesh refinement is used to improve the representation of the geometry efficiently in the Cartesian grid system. The improved ghost‐cell method is validated against four test cases: (a) double Mach reflections on a ramp, (b) smooth Prandtl–Meyer expansion flows, (c) supersonic flows in a wind tunnel with a forward‐facing step, and (d) supersonic flows over a circular cylinder. It is demonstrated that the improved ghost‐cell method can reach the accuracy of second order in L 1 norm and higher than first order in L ∞ norm. Direct comparisons against the cut‐cell method demonstrate that the improved ghost‐cell method is almost equally accurate with better efficiency for boundary representation in high‐fidelity compressible flow simulations. Copyright © 2016 John Wiley & Sons, Ltd. Abstract : We present an improved ghost‐cell immersed boundary approach to represent a solid body in compressible flow simulations. In contrast to the commonly used approaches, in the present work, ghost cells are mirrored through the boundary described using a level‐set method to farther image points, incorporating a higher‐order extrapolation/interpolation scheme for the ghost‐cell values. Direct comparisons against the cut‐cell method demonstrate that the present method is almost equally accurate with better efficiency for boundary representation in high‐fidelity compressible flow simulations.