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. Author manuscript; available in PMC: 2018 Dec 1.

Published in final edited form as: Wave Motion. 2017 Sep 11;75:36–49. doi: 10.1016/j.wavemoti.2017.08.004

(a) The distribution of the scaled pressure rp′/r₀ on the r-axis at t = 5.12 µs. The analytical (−) and numerical (◦) solutions are compared. The numerical solution with and without the geometric component in the source term, G(t)), (×) are plotted. One of every five data points are shown for the numerical solutions. (b) The magnitude of the scaled error between the same analytical and numerical solutions, $E = r ((p_{Numel}^{'} - p_{Anal}^{'}) / p_{Anal}^{'}) / r_{0}$ , on the r-axis at t = 5.12 µs. The error in terms of the numerical solution with the geometric component (◦) and without the geometric component (×) in the source term are plotted. (c)L_1,2,∞-norm of the error between the analytical solution and the numerical solution at t = 5.12 µs as a function of the grid size (2N × N). Reference slopes for the first and second order convergence are included.

(a) The distribution of the scaled pressure rp′/r₀ on the r-axis at t = 5.12 µs. The analytical (−) and numerical (◦) solutions are compared. The numerical solution with and without the geometric component in the source term, G(t)), (×) are plotted. One of every five data points are shown for the numerical solutions. (b) The magnitude of the scaled error between the same analytical and numerical solutions, $E = r ((p_{Numel}^{'} - p_{Anal}^{'}) / p_{Anal}^{'}) / r_{0}$ , on the r-axis at t = 5.12 µs. The error in terms of the numerical solution with the geometric component (◦) and without the geometric component (×) in the source term are plotted. (c)L_1,2,∞-norm of the error between the analytical solution and the numerical solution at t = 5.12 µs as a function of the grid size (2N × N). Reference slopes for the first and second order convergence are included.