Immersed boundary method for viscous compressible flows around moving bodies

Abstract

A ghost-point immersed boundary method for the compressible Navier–Stokes equations with moving boundaries on fixed Cartesian grids is devised by employing high order summation-by-parts (SBP) difference operators. The immersed boundaries are treated as sharp interfaces by enforcing the solid wall boundary conditions via flow variables at ghost points using bilinearly interpolated flow variables at mirror points. Simulations for compressible viscous flows induced by a transversely oscillating cylinder in a free-stream and a harmonic in-line oscillating cylinder in an initially quiescent fluid are presented and compared with experiments and incompressible fluid flow simulations obtained with body-conforming grid methods.