Dear All

I need to code the following equation

U_{t} + F(U)_{x} = S(U)

i've read lots of books and ref. etc. but I couldn't code the methods in f90. i was able only to code the case when S(U) = 0 using upwind methods etc. so can somebody help me by giveing me a 90 code to solve any linear or nonlinear case.

many thanks

Use Strang Splitting when S(U) really is a physcial source term. In each time step you first solve

U_t + F_x=0(PDE), then solve U_t=S (ODE). Check some text books on CFD.

I'm not sure whether I have understood your question. But I have an idea... Maybe u can try it.

since F=F(U)_{x}, you can also regard S(U) as S(U,x) i.e. S(U)_{x}

then you can get:

U_{t} + F(U)_{x} - S(U)_{x} = 0 =>

U_{t} + G(U)_{x} = 0 where G = F - S

S(U) is physical sourc term. so say we solve

U_t + F_x=0(PDE) using upwind methods, what shall i use to solve U_t=S (ODE)!!!

If you are using an upwind scheme for the flux the it is necessary to incoporate source terms in the upwind formulation otherwise the results could be inaccurate depending upon the strength of the source terms. You may want to consult the following paper for the upwind procedure to incorporate source terms:

Construction of Second-Order TVD Schemes for Non- homogeneous Hyperbolic Conservation Laws, L. Gascon and J.M. Corberan, J. of Computational Physics, Vol. 172, pp. 261-297(2001).

Generally, U_t=S(U) is very stiff, so you must use a stiff ODE solver.

what do you mean by:

U_t=S(U) is very stiff

thanks