Analytic Techniques for Advection-Diffusion Equationsrsmith/MA573_F09/Anal_Tech_Adv_Diff.pdf ·...
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Analytic Techniques for Advection-Diffusion Equations “Furious activity is no substitute for understanding,” H.H. Williams
Transcript of Analytic Techniques for Advection-Diffusion Equationsrsmith/MA573_F09/Anal_Tech_Adv_Diff.pdf ·...
Analytic Techniques for Advection-Diffusion Equations
“Furious activity is no substitute for understanding,” H.H. Williams
Analytic Solution Techniques: Diffusion Equation
Recall: General advection-diffusion equation
Diffusion Equation:
Simplifying Assumption:
Analytic Solution Techniques: Diffusion Equation
Separation of Variables: Consider solutions of the form
Note:
Analytic Solution Techniques: Diffusion Equation
Forced Response:
Consider solution of the form (variation of parameters)
Expand force:
where
Analytic Solution Techniques: Diffusion Equation
Assumption: Piecewise differentiation yields
Formal Solution:
Analytic Solution Techniques: Diffusion Equation
Special Case: Periodic source
Formal Solution:
Steady State Solution