The Discrete Non Local (DNL) Radiation Boundary Condition

Abstract

A general methodology for developing absorbing boundary conditions is presented [1,10,11]. In the plane case, it is based on a straightforward solution of the system of ODE's that arise from partial discretization in the directions transversal to the artificial boundary. This leads to an eigenvalue problem of the size of the number of degrees of freedom in the lateral discretization.
The eigenvalues are classified as in-going or right-going and the absorbing boundary condition consists in imposing a null value for the in-going modes, leaving free the right-going ones. Whereas the classification is straightforward for operators with definite sign, like the Laplace operator, a "virtual dissipative" mechanism has to be added in the mixed case, usually associated with wave propagation phenomena, like the Helmholtz equation, or potential flow with free-surface (the "wave resistance problem"). Numerical examples are presented in two companion papers at this same conference. [2,8].