Axially Symmetric Heat Transfer - Explicit FV Code

Consider the problem (from Lab 5) describing axially symmetric heat conduction in a hollow cylinder: Rin ≤ r ≤ Rout, 0 ≤ z ≤ Z, with imposed temperature boundary conditions on all boundaries, starting with a given temperature. 1. A problem with exact solution: Choose diffusivity D=1 ; Rin=1, Rout=2, Z=π ; initial condition: T(r,z,0) = LOG(r)*SIN(z) ; and boundary conditions: u(Rin, z, t) = 0 , u(Rout, z, t) = EXP(-t)*LOG(2)*SIN(z) , u( r , 0, t) = 0 , u( r , Pi, t) = 0. Verify (by hand, on paper!) that u(r,z,t) = EXP(-t)*LOG(r)*SIN(z) is the exact solution of this (weird) problem. 2. Implement the explicit scheme (Lab 5) for imposed temperature, and compare the numerical solution with the exact solution above, on MMr=MMz=32 mesh, at time 0.1 and at time 1.0 , using factor=0.9 . Calculate the max error at each of these times.NOTE:BCs are time-dependent (as in Lab3), so time should be updated before calling FLUXNOTE:π may create problems, code fluxes fornon-uniformgrid (do not use dz/2, dz).NOTE:Best way to set π to full precision is π = 4*atan(1.d0) 3. Submit only: ============================ errors at t=0.1 and at t=1.0 ============================ your code