Development and validation of a sharp interface immersed boundary method for high-speed flows

TL;DR

This paper introduces a novel sharp-interface immersed boundary method integrated with OpenFOAM for high-speed compressible flows, effectively capturing shock waves and complex geometries without body-fitted meshes.

Contribution

It extends IBM techniques to compressible regimes with a slip boundary condition and multiple flux schemes, validated through extensive high-speed flow simulations.

Findings

Accurate shock capturing with minimal oscillations

Excellent agreement with analytical solutions

Effective for dynamic and complex geometries

Abstract

This study presents an advanced sharp-interface immersed boundary method (IBM) integrated with the blastFOAM library on the OpenFOAM platform for high-speed compressible flow simulations. The developed solver extends the existing IBM techniques available in OpenFOAM to compressible regimes, tackling challenges such as shock waves, expansions, and dynamic geometries without needing body-fitted meshes. A novel contribution of this work is the implementation of a slip boundary condition for velocity at immersed surfaces, specifically designed to handle inviscid highspeed flows. The method also combines the second-order polynomial IBM reconstruction with multiple flux schemes such as Kurganov, Tadmor, HLL (Harten-Lax-van Leer), and AUSM+up (Advection Upstream Splitting Method Plus Upwind). The technique achieves significant accuracy across diverse high-speed flow conditions. Extensive validation is performed through supersonic flow cases over a wedge, a cylinder, an aerofoil, a sphere, and a moving piston. Results show excellent agreement with analytical and body-fitted solutions, with sharp resolution of shocks, minimal numerical oscillations, and shock reflections. A grid convergence study confirms the solver's reliability across varying mesh resolutions, while three-dimensional simulations highlight its capability for scaled-up applications. This solver provides a flexible, efficient, and accurate tool for capturing high-speed flow phenomena across various Mach numbers and geometries. It offers significant advantages in mesh handling, particularly for dynamic or intricate configurations, making it ideal for aerospace and engineering applications involving compressible flows.