Numerical simulation of external compressible flows using the immersed boundary method with virtual physical model

Abstract

The objective of this study was to apply the Immersed Boundary Method with the Virtual Physical Model to study external compressible flows. The Immersed Boundary methods have been increasingly used to model flows with submerged objects, particularly when they are in movement or deformation. These methods use independent grids to represent the domain and the immersed bodies. The domain is represented by an Eulerian mesh, whereas the 2D immersed body is represented by a set of points, which is called Lagrangian mesh. The no-slip condition is enforced by the force field introduced into the momentum equation. Another advantage of this approach is that the drag and lift forces can be calculated directly by using the Lagrangian force field. In the Virtual Physical Model, the force is first obtained in the Lagrangian grid by using the conservation laws and then is distributed to the Eulerian grid. In the present work, a nonuniform Cartesian grid and a central finite volume scheme with second order accuracy were used in the spatial discretization of the Navier-Stokes equations. The Euler method was applied for time discretization. Subsonic flows were simulated over a circular profile with adiabatic walls for different Reynolds numbers. Supersonic shock wave reflection problems were also simulated. Relevant parameters such as drag and lift forces, Strouhal number and pressure distribution were compared with numerical and experimental results from literature. In addition, this study was carried out using OpenFOAM program, seeking to validate the methodology and the in-house CFD code developed in this work.