Stepwise superposition approximation approach for analytical solutions withnon-zero initial concentration using existing solutions of zero initialconcentration in contaminate transport
Hongtao Wang , Rong Han , Yan Zhao , Wenjing Lu , Yaxin Zhang
DOI:
Received July 16, 2010,Revised November 19, 2010, Accepted , Available online
Volume 23,2011,Pages 923-930
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Analytical solutions for contaminant transport are widely used for both theoretical and practical purposes. However, many existing
solutions are obtained subject to an initial condition of zero concentration, which is often unrealistic in many practical cases. This
article proposed a stepwise superposition approximation approach to solve the non-zero initial concentration problem for first-type and
third-type boundary conditions by using the existing zero initial concentration solution. Theoretical examples showed that the approach
was highly efficient if a proper superposition scheme with relative concentration increments was constructed. The key parameter that
controlled the convergence speed was the time increment (Δt) multiplied by the rate constant ( ). The approach served also as an
alternative way to make a convenient concentration calculation even if the non-zero initial concentration solution of a problem was
known.
