"On Quasi-one-dimensional Conservation Laws Modeling Sedimentation"
Julio César Careaga Solis, presenterar sin licentiatsavhandling
This Licentiate thesis contains studies on a one-dimensional initial-boundary value problem given by a weighted non-linear scalar conservation law (partial differential equation (PDE)) with non-convex flux function modeling the sedimentation process of solid particles in a fluid, which occurs in vessels with varying cross-sectional area. This problem is important in, for example, wastewater treatment and mineral processing, where accurate model calibration and reliable simulators are needed.
The first part (Paper I) is the study of existence and uniqueness of the entropy solutions of the PDE modeling the batch problem (closed vessel) for a class of cross-sectional area functions. This problem is solved by the method of characteristics in different cases.
The second part (Paper II) is an approach for the numerical simulation of continuous sedimentation in vessels with varying cross-sectional area applied to wastewater treatment or mineral processing. A numerical method has been developed, handling different types of vessel geometries, including the extreme geometry of conical vessels with a vertex at the bottom. An advantageous CFL condition is derived as an improvement over other numerical methods for the same kind of application.
In the third part (Papers III and IV), the inverse problem of flux identification (model calibration) is defined and solved in a parametric and explicit form. The starting point is the constructed solutions with the method of characteristics. The entropy solution for the case of a conical vessel, in which the sedimentation process is modeled by a PDE with a singular coefficient is also included. In the best case, almost the entire flux function can be identified from only one experiment. The identification method means a significant advantage in comparison with the classic method of identification with standard tests in cylindrical vessels. An algorithm necessary for the identification from discrete data is also presented. The method has been tested with experimental results in wastewater treatment.
Opponent: Dr. Katarina Gustavsson, Kungliga Tekniska Högskolan, Sverige
Avhandlingen finns tillgänglig under: http://www.maths.lth.se/matematiklth/personal/julio/lic.pdf