How can I solve PDE with boundary condition?
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Hi All, I do have Ws dC/dz + Kc d2C/dz2 - X=0 where Ws and X are constant Z from (0 to 5 step 0.5) and I do have Kc values each 0.5 m,
How can I solve this PDE with Matlab, using B.C. (C at 0= 10) and (C at 5 =0)
Thanks in advance
Riyadh
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Kuifeng
2017년 8월 18일
Example answer, Ref to Chap 5, Part 5.2 Steady 1D Convection and diffusion of 'An introduction to computational fluid dynamics 2nd edition' by Versteeg and Malalasekera
답변 (2개)
Torsten
2017년 8월 18일
Use "bvp4c".
By the way: this is a second-order ODE, not a PDE.
Best wishes
Torsten.
Precise Simulation
2017년 8월 24일
Alternatively, if you still prefer to solve it as a PDE, you can quite easily input and solve it with the FEATool Multiphysics FEM Finite Element toolbox directly in Matlab. The small m-script below shows how this can be achieved
% FEATool FEA problem definition.
fea.sdim = {'z'}; % Space coordinate/dimension name.
fea.dvar = {'C'}; % Dependent variable name.
fea.sfun = {'sflag1'}; % 1st order P1 FEM shape function.
s_eqn = 'Ws*Cz + Kc*Cz_z - X = 0'; % String equation definition.
fea.eqn = parseeqn( s_eqn, fea.dvar, fea.sdim );
fea.grid = linegrid( 10, 0, 5 ); % Line grid/mesh.
fea.coef = { 'Ws' 1; 'Kc' '2*z'; 'X' '3' }; % Equation coefficents/expressions.
fea.bdr.d = {10 0}; % Dirichlet BCs.
fea.bdr.n = {[] []}; % (Optional) Neumann BCs.
% Check, parse, and solve FEA problem.
fea = parseprob( fea );
fea.sol.u = solvestat( fea );
% Postprocess and visualize solution.
postplot( fea, 'surfexpr', 'C' )
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