Higher-order EB method for the Incompressible Navier-Stokes Equations.*

We present a higher-order embedded boundary (EB) method to solve partial  differential equations in the presence of complex geometries for structured meshes. 

We focus on the development and analysis of a new EB method that creates a water-tight grid via the divergence theorem, and uses cell/faces averages to achieve high order accuracy and stability for finite volume operators in the incompressible Navier-Stokes equations. 

The method uses a novel weighted least squares approach to find the appropriate stencil coefficients for several operators to ensure conservation, accuracy, and stability in the presence of smooth and non-smooth geometries. We present results that verify the accuracy of the method, and use an eigenvalue analysis to demonstrate linear operator stability even with arbitrarily-small cut cells. Finally, we show the difference in accuracy between low-order and high-order results for simple and complex flow fields.