National Aeronautics and Space Administration
Date of this Version
2013
Citation
Journal of Computational Physics 250 (2013) 703–712.
Abstract
This corrigendum contains a correction to some of the figures in the article ‘‘Spurious behavior of shock-capturing methods by the fractional step approach: Problems containing stiff source terms and discontinuities’’ [J. Comput. Phys. 241 (2013) 266–291]. There was a computer coding error in the computer code that generates the results. The coding error consists of failing to update the temperature from the final solution of the RK4 convection step time evolution before the reaction step using the Strang splitting in Eq. (29). In addition, if Nr > 1, the error includes no update to the temperature for each sub-iteration on the reaction step in Eq. (29). The error affects Figs. 5–12, 14–17, 19–22.
By fixing the bug in the computer code, there are minor difference in the solution behavior by the studied numerical methods with the majority of the conclusion remains the same. There is however an improvement (reduction) in the spurious behavior by WENO5/SR. The correction to the text portion are:
Page 277, line 5 from bottom should be replaced by ‘‘Fig. 8 indicates that as we increase the stiffness coefficient further, WENO5/SR still produces the correct shock speed for the 1000K0 stiffness, whereas WENO5fi/SR + split exhibit oscillatory solutions for the same grid and CFL = 0.05.’’
Page 278, second line below Section 4.1.3 should be replaced by ‘‘Fig. 9 shows the effect of the time steps for five CFL values that are under the CFL limit (left sub-figure), using 50 grid points and WENO5. The right sub-figure shows the error in terms of the number of grid points away from the reference shock location (Err) for three stiffness coefficients 100K0, 1000K0 and 10000K0’’
Page 287, the last five lines should be replaced by ‘‘Again, WENO5/SR,WENO5fi and WENO5fi + split are able to obtain the correct shock speed with similar accuracy.’’