1887

Abstract

Summary

In this work, we couple several time integration schemes to a finite-difference staggered-grid fourth-order accurate method for 1 -D wave propagation. These implementations include two conventional Runge Kutta (RK) schemes with third and fourth order accuracy, and two optimized RK methods for dissipation and dispersion reduction that also offer fourth order accuracy on linear problems. In addition, we also apply the time-staggering Leap frog integration with second and fourth order accuracy. As a nearly analytic reference, an exponentially time differencing scheme is also employed. We first carry out a eigenvalue stability analysis of all these methods to find limiting integration steps. Then, we quantify their dissipation and dispersion errors on solving a homogeneous problem at different grid resolutions and propagation distances. For all tests, accuracy of numerical results significantly increases with the discretization order, and the high precision of one member of the optimized fourth-order RK schemes is also accompanied by a large stability bound. Thus, we recommend to analyze this scheme family on heterogeneous and/or multidimensional problems.

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/content/papers/10.3997/2214-4609.201601177
2016-05-31
2020-07-11
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