Prabhakaran, S (2019) Weighted Average Approximation in Finite Volume Formulation for One-Dimensional Single Species Transport and the Stability Condition for Various Schemes. International Conference on Mathematical Analysis and Computing : Mathematical Analysis and Computing pp 459–479. pp. 459-479.

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Abstract

The governing equation for one-dimensional single species transport
model in a saturated porous medium with appropriate initial and boundary conditions is discretized by using finite volume formulation. A weighted average approximation is then applied to the integral terms. Twelve different schemes of explicit,
semi-implicit, and fully implicit in nature are derived. The stability and convergence
of those numerical schemes are also discussed. The numerical experiments are carried out for the single species transport problem with degradation in liquid phase.
These numerical results are compared with the analytical solution. It is shown that
semi-implicit and fully implicit type schemes are not always unconditionally stable.
A novel numerical technique is used to approximate the reaction term of partial differential equation. Taking average for reaction term at different time levels yields
a better approximation for upwind scheme. Further, it is proved that the averaging
technique gives unconditional stability for implicit nature numerical schemes.

Item Type: Article
Uncontrolled Keywords: Finite volume method · Weighted average · Contamination transport · Stability · Consistency · First-order reaction
Divisions: PSG College of Arts and Science > Department of Mathematics
Depositing User: Mr Team Mosys
Date Deposited: 17 Nov 2022 06:49
Last Modified: 17 Nov 2022 06:49
URI: http://ir.psgcas.ac.in/id/eprint/1638

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