Christoph Hader

A locally stabilized immersed boundary method for the compressible Navier-Stokes equations

A higher-order immersed boundary method for solving the compressible Navier-Stokes equations is presented. The distinguishing feature of this new immersed boundary method is that the coefficients of the irregular finite-difference stencils in the vicinity of the immersed boundary are optimized to obtain improved numerical stability. This basic idea was introduced in a previous publication by the authors for the advection step in the projection method used to solve the incompressible Navier-Stokes equations. This paper extends the original approach to the compressible Navier-Stokes equations considering flux vector splitting schemes and viscous wall boundary conditions at the immersed geometry. In addition to the stencil optimization procedure for the convective terms, this paper discusses other key aspects of the method, such as imposing flux boundary conditions at the immersed boundary and the discretization of the viscous flux in the vicinity of the boundary. Extensive linear stability investigations of the immersed scheme confirm that a linearly stable method is obtained. The method of manufactured solutions is used to validate the expected higher-order accuracy and to study the error convergence properties of this new method. Steady and unsteady, 2D and 3D canonical test cases are used for validation of the immersed boundary approach. Finally, the method is employed to simulate the laminar to turbulent transition process of a hypersonic Mach 6 boundary layer flow over a porous wall and subsonic boundary layer flow over a three-dimensional spherical roughness element.

Numerical investigation of porous walls for a Mach 6.0 boundary layer using an immersed boundary method

Temporal direct numerical simulations (TDNS) were carried out for a Mach 6.0 boundary layer on a 2-D porous wall. The porous wall was implemented with an immersed boundary scheme. For validation purposes results were compared with results obtained with an analytical porous wall model. A grid convergence study was conducted to conrm that the grid resolution was adequate. A parameter study revealed that the geometric dimensions for which the porous coating most eectively attenuates the growth of disturbances in the boundary layers. For the optimal parameter setting signicant stabilization of the temporal growth of the instability waves is observed. The optimal cavity depth for dierent numbers of pores per disturbance wavelength was found to remain approximately the same. The present study showed that porous coatings can be modeled with an immersed boundary scheme.

Novel immersed boundary/interface method for the compressible navier-stokes equations

An extension of the immersed interface method developed by Brehm and Fasel 1‐3 to the compressible Navier-Stokes equations is presented. The extension of the immersed interface/boundary method 1,2 contains some modifications to the original approach in order to incorporate characteristics of the compressible Navier-Stokes equations. The van Leer flux splitting approach utilized in the compressible Navier-Stokes solver was considered in the design of the finite dierence stencils in the vicinity of the immersed boundary. The extensive stability investigations of the immersed scheme confirm that a stable immersed boundary treatment is achieved. The simulation results for a Mach 6 boundary layer flow over a flat plate and a porous wall validate the proposed immersed boundary method for the compressible Navier-Stokes equations.

Numerical investigation of transition delay for various controlled breakdown scenarios in a Mach 6 Boundary Layer using porous walls

The influence of porous walls on the transition process of a Mach 6 Boundary Layer for different controlled breakdown scenarios is investigated using temporal direct numerical simulations. This study focusses on the non-linear regime where prior studies have mainle focussed on the linear stage. The fundamental and subharmonic resonance scenario are compared for a smooth wall case and a porous wall geometry. The porous walls showed potential to delay transition for the fundamental resonance scenario. The goal in this paper is to show that for other breakdown scenarios the porous walls still remain effective in delaying transition.