Problems of accuracy and reliability in 2-D LISA simulations

In the present paper, we discuss several problems of convergence and accuracy of numerical simulations of 2-D problems, using, for the purpose of examplification, the propagation of ultrasonic pulses in complex media. Some of the difficulties are barely an extension to 2-D of problems already studied in the 1-D case. Others are novel to the 2-D case and deserve a specific analysis. Among the latter, the approximation by which an oblique straight line must be represented as a ladder in a lattice is considered in detail.