Question 3 (Total: 10 marks) Consider a one-dimensional system of length L. The following partial differential equation describes the diffusion and convection phenomena that is taking place in the system 1

b) (1) (1) du ə at ax Where cand u are constants, and u(x = 0) = 1, u(x=L) = 0 Consider a cell center finite volume discretization as shown below: x=0 2 duy [cu+H] |=0 1-1 (1+1 Where is the flux. a) (1) Formulate a control volume and explicit time numerical scheme to discretize the governing equation, by re-write the governing equation into 1-D convective differential form, and prove that the flux is given by: du N₂-1 N q=cu +Hax (ii) Compose the discretized expression for Right-Hand Flux, qa- and qu Compose the discretized expression for Left Hand Flux (1) Design and express the numerical scheme using Explicit Scheme (iv) v) Appraise the accuracy of the numerical scheme in terms of spatial and temporal accuracy Analyze the appropriate stability criteria for the numerical method proposed Design a suitable way to model the boundary condition at x = 0 and x = L Compute the boundary condition at x = 0 and x = L