Question: Euler equation for gas dynamics: CX where P 0= m E m E(Q)= mu p Eu+ pu m=pu is the momentum. The equation of state

Euler equation for gas dynamics: CX where P 0= m E m E(Q)= mu p Eu+ pu m=pu is the momentum. The equation of state is (Y=1.4): E= put P Y- 1 With Lax initial data: 0.445 Q= 0311 in (0,0.5) 8.928 P 0.5 Q= 0 in (0.5,1) 1 4275 Final time is T=0.16. Solve the equation with mesh size Ax=1/100 and compare it with a finer mesh solution. Use Upwind-flux vector splitting, R-K with artificial dissipation, and R-K with TVD schemes. Compare the different methods. Compare your results with benchmark solutions and discuss your results

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