Direction-Adaptive Nonreflecting Boundary Conditions

Presented in this work is a nonlinear adaptive nonreflecting boundary condition (NRBC) that, when compared with classical local NRBCs, further reduces the wave reflection error at far fields in the numerical simulation of wave dominated problems. A nonlinear procedure can considerably improve the accuracy of NRBCs even if the problem itself is linear as in the case of the 2D wave equation. In fact the first- and second-order NRBCs of Engquist and Majda can be modified by adding proper weights to the coefficients of the difference equations. The weights are adaptively determined in such a way that the angle of complete absorption is locally coincident with the outgoing wave direction. The theoretical reflection coefficients and the numerical experiments show that a considerable reduction of the numerical error due to wave reflections is achieved by applying the present adaptive algorithm.