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| Format: | Artículo científico |
| Language: | en |
| Published: |
Universidad Nacional de Colombia
2014
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| Online Access: | https://www.redalyc.org/articulo.oa?id=49630072004 |
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Table of Contents:
- A STABILITY AND SENSITIVITY ANALYSIS OF PARAMETRIC FUNCTIONS IN A SEDIMENTATION MODEL CARLOS D. ACOSTA RAIMUND BÜRGER CARLOS E. MEJIA Ingeniería sensitivity analysis parameter estimation discrete mollification Sedimentation of suspensions degenerate parabolic equation This paper deals with the reliable and efficient numerical identification of parameters defining the flux function and the diffusion coefficient of a strongly degenerate parabolic partial differential equation (PDE), which is the basis of a mathematical model for sedimentation-consolidation processes. A zero-flux initial-boundary value problem (IBVP) posed for this PDE describes the settling of a suspension in a column. The parameters for a given material are estimated by the repeated numerical solutions of the IBVP (direct problem) under systematic variation of the model parameters, with the aim of successively minimizing a cost functional that measures the distance between a space-dependent observation and the corresponding numerical solution. Two important features of this paper are the following. In the first place, the method proposed for the efficient and accurate numerical solution of the direct problem. We implement a well- known explicit, monotone three-point finite difference scheme enhanced by discrete mollification. The mollified scheme occupies a larger stencil but converges under a less restrictive CFL condition, which allows the use of a larger time step. The second feature is the thorough sensitivity and stability analysis of the parametric model functions that play the roles of initial guess and observation data, respectively. 2014 artículo científico 0012-7353 https://www.redalyc.org/articulo.oa?id=49630072004 en http://www.redalyc.org/revista.oa?id=496 Dyna application/pdf Universidad Nacional de Colombia Dyna (Colombia) Num.183 Vol.81