TITLE:  A Locally Stabilized Higher-Order Immersed Boundary Method and its Application to NASA Relevant Flow Problems

 

ABSTRACT: A higher-order immersed boundary method for solving the compressible Navier-Stokes equations will be presented. The distinguishing feature of this new immersed boundary method is that the coecients of the irregular nite dierence stencils in the vicinity of the immersed boundary are locally stabilized by solv- ing a local optimization problem. The concept was rst 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 presentation extends the original idea to the compressible Navier-Stokes equations considering ux vector splitting schemes and viscous wall boundary conditions at the immersed geometry. Key aspects, such as imposing higher-order accurate 

ux boundary conditions at the immersed boundary and the higher-order discretization of the viscous uxes in the vicinity of the boundary, will be presented.  Extensive linear stability investigations conrm that the immersed boundary method is linearly stable. The method of manufactured solutions is used to conrm the expected higher-order accuracy and to study the error convergence properties of this new method. The second part of this presentation focuses on the application of the higher-order immersed boundary method to NASA relevant ow problems, such as launch environment ows, a rocket plume jet impingement problem, and the ow past a contra-rotating open rotor.

 

For more information on the Analysis and PDE Seminars, please visit http://ms.uky.edu/~mhto224/seminar/PDEseminarF2016.html