A sharp interface immersed boundary method for compressible viscous flows

A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries

“…This Poisson equation is solved with a highly efficient geometric multigrid method [3] which employs a Gauss-Siedel line-SOR smoother [38]. Once the pressure correction is obtained, the pressure and velocity are updated as (11) (12) (13) These separately updated face-velocities satisfy discrete mass-conservation to machine accuracy and use of these velocities in estimating the non-linear convective flux in equation (3) leads to a more accurate and robust solution procedure. The advantage of separately computing the face-center velocities was initially proposed by Zang et al [53] and discussed in the context of the Cartesian grid methods in Ye et al [51].…”

“…The current immersed boundary method employs a multi-dimensional ghost-cell methodology to impose the boundary conditions on the immersed boundary and is similar in spirit to the methodology proposed by Majumdar et al [21] and employed by Ghias et al [10,11] among others. However, unlike these previous efforts, the current solver is designed from the start for fast, efficient and accurate solution of flows with complex three-dimensional, moving boundaries.…”

“…However, unlike these previous efforts, the current solver is designed from the start for fast, efficient and accurate solution of flows with complex three-dimensional, moving boundaries. In Ghias et al [11] in particular, similar ideas have been used for simulating compressible flows with 2D stationary immersed boundaries. As discussed in detail in that paper, the methodology used here has a general similarity to the ghost-fluid method of Gibou et al [12] which also employs ghost-cells for imposing the boundary conditions on the immersed boundary.…”

“…As described in Ghias et al [11], the current ghost-cell methodology has some general similarities with the ghost-fluid method (GFM) of Gibou et al [12] which also employs ghostnodes to impose the boundary conditions on the immersed boundary. There are however some key differences between the two methods that have an impact on the accuracy, robustness and efficiency of the two methods.…”

“…These include methods of Udaykumar et al [44], Ye et al [51], Fadlun et al [9], Kim et al [16], Gibou et al [12], You et al [52], Balaras [2], Marella et al [22], Ghias et al [11] and others. The key advantage of the first category of methods is that they are formulated relatively independent of the spatial discretization and therefore can be implemented into an existing Navier-Stokes solver with relative ease.…”