Cartesian Grid Embedded Boundary Methods for Partial Differential Equations

P. Colella, D. T. Graves, B. van Straalen, T. J. Ligocki

We present our approach to solving partial differential equations in complex geometries using embedded boundary methods. We present the fundamentals of discretizing elliptic and hyperbolic equations. We present our approach to grid generation. With an implicit function description, our method can be generalized to arbitrarily high order accuracy and any number of dimensions. We present the numerical analysis that supports this approach as well as a number of examples of existing embedded boundary applications.