Question #4 Consider the following 1-D Euler equation: др дри at дх 0 a²pu дри дрии + дх др + u дх at дх2 If the initial
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Question #4 Consider the following 1-D Euler equation: др дри at дх 0 a²pu дри дрии + дх др + u дх at дх2 If the initial condition is : u(x,t = 0) = 0 for 0 < x < 1, and u = 0.25 The boundary conditions are : u(0,t) = 1, u(1,t) = 0 Formulate a numerical scheme using finite volume and explicit for temporal derivative. Suggestion: Nx = 100 CFL = 0.001 and 0 <t<2 a) Write a simple MATLAB code to implement the numerical scheme. b) Compute and plot the u vs x at t = 0.5, 1.0, 1.5 and 2 c) Varies u from 0.25 to 0.1, 0.01, and 0.001 d) Discuss the results and impact of u to your solution.