How can I solve PDE with boundary condition?

Question

Riyadh Muttaleb 2017-8-17

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https://ww2.mathworks.cn/matlabcentral/answers/353128-how-can-i-solve-pde-with-boundary-condition

评论： Riyadh Muttaleb 2017-8-30

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 2017-8-18

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

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Answer 1

Torsten 2017-8-18

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https://ww2.mathworks.cn/matlabcentral/answers/353128-how-can-i-solve-pde-with-boundary-condition#answer_278365

Use "bvp4c".

By the way: this is a second-order ODE, not a PDE.

Best wishes

Torsten.

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Riyadh Muttaleb 2017-8-19

Thank you

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Answer 2

Precise Simulation 2017-8-24

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在 MATLAB Online 中打开

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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Riyadh Muttaleb 2017-8-30

Sorry for late response, In was in small vacation, I tried to implement the m-script, but an error says that "Undefined function or variable 'parseeqn'"

Thank you,

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