A ghost-cell immersed boundary method for inviscid compressible flows

An immersed boundary method (IBM) is presented, that can be applied to inviscid compressible flows, described by the full-potential or Euler equations, to start with. Possible applications that we envisage are preliminary aircraft design and rotor-flow computations. Although Navier-Stokes methods have improved significantly in the last three decades, and although computations with the latter equations are nowadays performed on complete aircraft configurations, the large computational effort required and the (re)meshing of grids still inhibit easy routine use. Especially when considering (multidisciplinary) optimization studies, an aerodynamic analysis must be quick, and therefore panel methods or vortex lattice methods are still widely used. With the latter methods, the creation of a volume grid is circumvented and complex 3D configurations can be handled in a relatively easy way. When including compressibility or viscosity, it is necessary to introduce a volume grid. With the use of an IBM such a grid can be extremely simple, and fast solvers can be applied. To get a proof of concept, here we consider the 2D full potential equation and the 2D Euler equations. Immersed boundary methods for compressible flows are relatively new. The work of de Tullio et al. [2] uses a similar approach as ours, but the distinction between interface and fluid cells, and the boundarycondition treatment are different. Ghias et al. [3] employ a hybrid method, combining curvilinear meshes with an immersed boundary strategy. This method has a number of advantages, especially for viscous flow, but we believe that the strength of IBMs lies in handling arbitrary geometries by using Cartesian grids only, in order to minimize the amount of user interaction. Increased mesh resolution near boundaries can be achieved with (automatic) mesh refinement.