Your team leader asks you to model the transport of a chemical reactant in a pipe with varying cross section. She suggests you ignore the velocity profile and assume an average velocity that is constant for each cross section, but varies along the pipe as the cross-section varies. Consider the linear advection equation for a concentration c with flux f=ac, tc+xf=0. where a varies spatially as a=ai, which does not depend on time. Measurements at time-level n=0 at stations i produce the following data for ai in m/s and ci0 a1=0.82,a2=1.2,a3=1.43,c10=0.35,c20=0.1,c30=0.1, The stations are equally spaced at xixi1=0.6m. For all answers, work to 4 digits of accuracy. a) Use a first-order accurate upwind approximation and compute the flux either side of node i=2. Calculate the largest permissible timestep for an explicit time-discretisation at the first iteration. tmax= Score: 0/3 Unanswered Employ a finite-volume scheme with explicit time-stepping and first order upwind flux discretisation for the advection equation. The concentration of the flow upstream of the test section is c=0.35, the velocity there is a=0.75m/s. The concentration of the flow downstream of the test section is c=0.55, its velocity is a=0.9m/s. Using a timestep of t=0.31sec, compute the concentrations at n=1,n=2 and the value of c13 (You don't need to compute the other concentrations at time level 3).: c11=c21=c31=n=2c12=c22=c32=n=3c13= Your colleague complains about the accuracy of your simulation and suggests to use a central discretisation for the flux based on the averages of the fluxes either side, fi+21=21(fi+fi+1), as it is second order accurate. Using this flux, and the same data and timestep as in c), compute the concentrations at n=1,n=2 and the value of c13. Work to 4 digits of accuracy. n=1:c11=c21=c31=n=2:c12=c22=c32=n=3