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First order scheme: Rusanov scheme

The equation for Rusanov scheme is shown in eq.(64). This is a first order scheme, which means that only one step is needed to finish a round of computation. Figure 6 shows the result of shock tube problem with this scheme at time t=1.2, together with the analytical solution result of the problem at the same time. From this figure, we can see that, generally, the simulation result fits the basic configuration of theoretical result quite well. We can also see clearly that diffusive error is very obvious in some part ofs the result and all the corners are smoothed.

Figure 6: Result of Rusanov scheme for one-dimensional shock-tube simulation