High Efficient Numerical Methods for Viscous and Nonviscous Wave Problems

This paper is concerned with accurate and efficient numerical methods for solving viscous and nonviscous wave problems. The paper first introduces a new second-order PR-ADI like scheme. For an efficient simulation, the scheme is also extended to a high-order compact PRADI like method. Both of them have the advantages of unconditional stability, less impact of the perturbing terms on the accuracy, and being convenient to compute the boundary values of the intermediates. Besides this, the compact scheme has high-order accuracy and costs less in computational time. Numerical results are presented to show the accuracy and efficiency of the new algorithms.