We want to resolve numerically the following non-linear one dimensional advectio

Question

We want to resolve numerically the following non-linear one dimensional advection equation: . Let the domain L = 12,000 km, delta x = 50 km. Initial conditions are: F(x,0) = where i = 1000 km, x0 = 6000 km and U = 100 km/h. We consider a periodic solution with boundary conditions: F(0, t) = F(L, t) . a) Choose 2 time steps . Delta t1 that satisfies CFL condition and delta t2 that does not satisfies CFL condition b) Calculate how much time t=T we would need to have the maximum value of x within xL=L=12000km then calculate the number of time steps in both cases c) Write a scilab programm to resolve the equation with delta t1 and delta t2 using the leapfrog method. Use Euler's backward method for the first time step

Explanation / Answer

Time to be taken will be: 120 Hours.

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