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(Solved): Question 1 Consider the wave equation (del\phi )/(delt)+u(del\phi )/(delx)=0 for some passive scalar ...
Question 1
Consider the wave equation
(del\phi )/(delt)+u(del\phi )/(delx)=0
for some passive scalar \phi and with constant u>0. For the purposes of this question,
assume that equation (Q1.1) is to be discretised using a simple forward Euler scheme in
time
(del\phi )/(delt)|_(x_(m),t_(n))~~(\phi _(m)^(n+1)-\phi _(m)^(n))/(\Delta t)
a5\times 5 matrix acting on the solution vector\phi _(0).
d\phi ^(n+1)=M\phi ^(n)+c
where M is a constant matrix and c is a constant vector incorporating the boundary
conditions; state clearly the composition of M and c.
[5 marks]