Issue 61

N. Razali et alii, Frattura ed Integrità Strutturale, 61 (2022) 214-229; DOI: 10.3221/IGF-ESIS.61.14

The results above and the application of the von Neumann stability analysis obtain

 v t

  1 k



 

 k x

i

sin

(19)



x

  c t CFL x 

(20)

Thus,

  1   k

(21) Therefore, the solution explodes (oscillatory) and becomes unstable for ∆ t and ∆ x . The above results show that all CFL values smaller than 0.01 become the diffuser of the exact solution. For values greater than 0.01, the solution becomes unstable, as shown in the figures when CFL=1.0. Results of Lax differencing (step-wave) method 1) CFL=0.5

Figure 7: Lax differencing (step-wave) method results for CFL=0.5.

Figure 8: Lax differencing (step-wave) method mesh results for CFL=0.5

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