High Order Cut-Cell Method for Direct Numerical Simulations*

 Cut-cell methods for unsteady flow problems can greatly simplify the

  grid generation process and allow for high-fidelity simulations on

  complex geometries.  Recently, our novel approach to the design of finite-difference

  cut-cell stencils allowed for stable discretizations of elliptic, parabolic and hyperbolic,

  systems using non-dissipative schemes in the interior of the domain.

  This was accomplished without the need for any ad-hoc stabilization by

  constructing the discrete operators based on two simple and intuitive design principles.

  These principles, and an a-priori optimization process, allowed for

  the construction of stable 8th order approximations to elliptic and

  parabolic problems and stable and conservative 4th order

  approximations to hyperbolic problems.  In this work, the extension of 

  the method to more general boundary conditions will be presented.