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A Fourth-Order Accurate Embedded Boundary Method for the Wave Equation

A fourth-order accurate embedded boundary method for the scalar wave equation with Dirichlet or Neumann boundary conditions is described. The method is based on a compact Pade-type discretization of spatial derivatives together with a Taylor series method (modified equation) in time. A novel approach for enforcing boundary conditions is introduced which uses interior boundary points instead of exterior ghost points. This technique removes the small-cell stiffness problem for both Dirichlet and Neumann boundary conditions, is more accurate and robust than previous methods based on exterior ghost points, and guarantees that the solution is single-valued when slender bodies are treated. Numerical experiments are presented to illustrate the stability and accuracy of the method as well as its application to problems with complex geometries.