A Higher-Order Immersed Boundary Method for Solving the Compressible Navier-Stokes Equations

Speaker: Christoph Brehm, STC / Applied Modeling & Simulation Branch, NASA Ames Research Center
September 18, 2014

Presentation

Abstract

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 locally stabilized by solving a local optimization problem. This basic idea was introduced in a previous publication by the presenter for the advection step in the projection method used to solve the incompressible Navier-Stokes equations. This paper extends the original idea to the compressible Navier-Stokes equations considering flux vector splitting schemes and viscous wall boundary conditions at the immersed geometry. Important key aspects, such as imposing flux boundary conditions at the immersed boundary and the discretization of the viscous flux in the vicinity of the boundary, are discussed and analyzed. Extensive linear stability investigations of the immersed scheme confirm that a linearly stable method is obtained. The method of manufactured solutions is used to confirm 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 used 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.

Biography

Christoph Brehm joined the Science & Technology Corporation (STC) / Applied Modeling and Simulation branch at NASA Ames in 2012. He has been working in the LAVA group with special emphasis on unsteady flows, e.g., launch environment flows, buffeting and acoustics. Recently, he started an effort in developing higher-order shock capturing schemes for ILES/LES with the LAVA framework. He received a B.S./M.S. equivalent degree at the University of Stuttgart (Germany) and a Ph.D. at the University of Arizona under the supervision of Professor H.F. Fasel working on active flow control, immersed boundary methods and transition research.

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