CHEN 3201 Lecture Notes - Lecture 48: Dirichlet Boundary Condition, Backward Euler Method, Derivative

• School: UMN
• Department: Chemical Engineering
• Course: CHEN 3201
• Professor: Kevin Dorfman

Document Summary

This needs an initial condition (it"s 1st order in time, so need one of these) Need 2 boundary conditions since it"s 2nd order in position: discretize the domain n nodes. We discretized concentration 1st and made it a function of only time (b/c can"t solve anything numerially if it"s continuousso we made it discrete in space) We could also have discretized time first and then figured out concentrations as a function of position. Method of lines: discretize the spatial derivative haven"t made time discrete yet for the interior nodes: Chen3201_numericalmethods page 1 ordinary derivative (not partial derivative) ci(0) comes from the initial condition. This produces a system of 1st order ivps: integrate the eqns: rk4, implicit euler, etc. Dorfman almost always uses implicit euler b/c explicit methods can be tricky with stability. If we have dirichlet boundary conditions c(0,t) = 1 => c1(t) = 1;