Essentially Non-Oscillatory Methods for Numerical Wave Propagation

Abstract

In modeling applications involving wave propagation (seismic data analysis for example), one needs to obtain very accurate numerical solutions to wave equations. Standard finite difference (FD) techniques suffer serious shortcomings-numerical dispersion and spurious oscillations. The essentially non-oscillatory (ENO) method overcomes these shortcomings. It utilizes an adaptive finite difference technique and is applied to a system of first order partial differential equations that is equivalent to the acoustic wave equation. The ENO method and FD techniques are applied to an acoustic wave equation with constant wave speed in one dimension with both smooth and non-smooth initial data. These simple examples are sufficient to illustrate how spurious oscillations are introduced into the FD approximation when the initial data is not smooth, and shows that the ENO method does not suffer the same effects. A two dimensional problem is also presented with similar results.