Solving Hyperbolic Equations with Finite Volume Methods by M. Elena Vázquez-Cendón

Author:M. Elena Vázquez-Cendón
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Fig. 5.6CFL condition applied to the transport equation. a Values employed in the parameters of the figure: , , . The CFL condition is satisfied; b Values employed in the parameters of the figure: , , . The CFL condition is not satisfied

Figure 5.6a shows a situation in which , and therefore the information travels a distance smaller than the length of the cell in each time step. In this case it makes sense to define the flux at depending only on and .

Figure 5.6b illustrates a case in which . We see how the exact solution at the cell and time depends also on , and therefore the exact flux at also depends on this value. The method suggested in (5.11) will become unstable if the numeric flux function depends only on and .

This is a consequence of the CFL condition, in which

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