Grid generation for fluid-flow simulations over complex geometries can be highly simplified by cut-cell methods. Construction of provably stable high-order boundary implementation for cut-cell discretizations, however, remains a challenge, especially for inviscid problems using strong (or exact) boundary conditions. Existing energy-stability proofs of difference methods require imposing the boundary conditions weakly or by a projection approach, where the computed boundary values may not be exact, which can adversely influence turbulence/mixing statistics in a direct numerical simulation. A framework to prove energy-stability with strong boundary treatment is developed and used to obtain boundary implementation for a Cartesian cut-cell discretization. Linear and non-linear numerical tests to verify the accuracy, stability and conservation properties of the developed method will be presented.
