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 bardiche February 9, 2011 20:58

Conservative form

Hi all, new to forum here so iam bit tip-toey :P

But i guess this is the best place to ask something like this so here goes

In the Lax-Friedrichs two-step scheme (where n is the time step and i is the spatial step of the discretization)

u(n+1/2,i+1/2) = 1/2[u(n,i+1) + u(n,i)] - (dt/2dx) [f(n,i+1)-f(n,i)]

u(n+1,i) = 1/2[u(n+1/2,i+1/2) + u(n+1/2,i-1/2)] - (dt/2dx) [f(n+1/2,i+1/2)-f(n+1/2,i-1/2)]

how would one manipulate this two step scheme to write the Lax-Friedrich scheme in Conservative form

u(n+1,i) = u(n,i) - (dt/dx) [f*(i+1/2)-f*(i-1/2)]

f* being the numerical fluxes

i have attempted combining the two steps of the scheme and trying to arrive at the conservative form but the expression seems to get quite messy and i cannot see to find the expression for f*

many thanks

B

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