The DNL absorbing boundary condition: applications to wave problems

A general methodology for developing absorbing boundary conditions is prese nted. For planar surfaces, it is based on a straightforward solution of the system of block difference equations that arise from partial discretizatio n in the directions transversal to the artificial boundary followed by disc retization on a constant step 1D grid in the direction normal to the bounda ry. This leads to an eigenvalue problem of the size of the number of degree s of freedom in the lateral discretization. The eigenvalues are classified as right- or left-going and the absorbing boundary condition consists in im posing a null value for the ingoing modes, leaving free the outgoing ones. Whereas the classification is straightforward for operators with definite s ign, like the Laplace operator, a virtual dissipative mechanism has to be a dded in the mixed case, usually associated with wave propagation phenomena, like the Helmholtz equation. The main advantage of the method is that it c an be implemented as a black-box routine, taking as input the coefficients of the linear system, obtained from standard discretization (FEM or FDM) pa ckages and giving on output the absorption matrix. We present the applicati on of the DNL methodology to typical wave problems, like Helmholtz equation s and potential how with free surface (the ship wave resistance and sea-kee ping problems). (C) 2000 Elsevier Science S.A. All rights reserved.