An immersed interface method for the solution of the standard parabolic equation in range-dependent ocean environments

Abstract

A numerical approach for the treatment of irregular ocean bottoms within the framework of the standard parabolic equation is proposed. The present technique is based on the immersed interface method originally developed by LeVeque and Li [(1994). SIAM J. Numer. Anal. 31(4), 1019–1044]. The method conserves energy to high order accuracy and naturally handles generic range-dependent bathymetries, without requiring any additional specific numerical procedure. An illustration of its capabilities is provided by solving the well-known wedge problem.