A spectral multidomain method for the solution of hyperbolic systems (Q1081473)

A multidomain Chebyshev spectral collocation method for solving hyperbolic partial differential equations has been developed. Though spectral methods are global methods, an attractive idea is to break a computational domain into several subdomains, and a way to handle the interfaces is described. The multidomain approach offers advantages over the use of a single Chebyshev grid. It allows complex geometries to be covered, and local refinement can be used to resolve important features. For steady-state problems it reduces the stiffness associated with the use of explicit time integration as a relaxation scheme. Furthermore, the proposed method remains spectrally accurate. Results showing performance of the method on one-dimensional linear models and one- and two- dimensional nonlinear gas-dynamics problems are presented.