Finite difference solution for diffusion-advection-reaction (heat) in 1D

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Finite difference solution for diffusion-advection-reaction (heat) in 1D

Feb 20, 2012 compiled on — Wednesday July 06, 2016 at 08:23 AM

This Demonstration solves the diffusion-advection-reaction partial differential equation (PDE) $cuxx = dut + au+ f (x, t)$ in one dimension. The domain is discretized in space and for each time step the solution $u$ at time $tn+1$ is found by solving for $un+1$ from $n n+1 Aun+1 = Bun + f-+f2---$ .

The boundary conditions supported are periodic, Dirichlet and Neumann. The solution can be viewed in 3D as well as in 2D. You can select the source term $f(x,t)$ and the initial conditions from the menus in the main display. Selected preconfigured test cases are available from the pull down menu. In the above PDE $cuxx$ represents the diffusion, $dut$ represents the advection and $au$ the reaction.