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In this contribution we consider the problem of flux identification in a scalar conservation law modelling the phenomenon of sedimentation. The experimental observation data used for the calibration consist of a solid concentration profile at a fixed time. The identification problem is formulated as an optimization one, where the distance between the profiles of the model simulation and observation data is minimized by a least squares cost function. The direct problem is approximated by a monotone finite volume scheme. The numerical solution of the calibration problem is obtained by a continuous genetic algorithm. Numerical results are presented in order to validate the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This contribution is a condensed version of an extended paper, where a contact manifold emerging in the interior of the phase space of a specific hyperbolic system of two nonlinear conservation laws is examined. The governing equations are modelling bidisperse suspensions, which consist of two types of small particles differing in size and viscosity that are dispersed in a viscous fluid. Based on the calculation of characteristic speeds, the elementary waves with the origin as left Riemann datum and a general right state in the phase space are classified. In particular, the dependence of the solution structure of this Riemann problem on the contact manifold is elaborated. [ABSTRACT FROM AUTHOR]

This paper analyses a continuum model of the sedimentation of polydisperse suspensions, where the volume concentrations of the solids species are the sought unknowns. This leads to systems of conservation laws which are non-genuinely nonlinear (“non-convex”) in the sense that they are only piecewise genuinely nonlinear. The solution of a Riemann problem is represented as a concatenation of elementary waves, where the linear degeneracy requires using the Liu entropy condition. After a general description of the composition of elementary waves, an algorithm for the computational construction is given. The solution of the Riemann problem is then utilized as a problem-adapted building block of a front tracking method. For the model of bidisperse suspensions, Riemann problems are classified by the location of the left and right state in the phase space of unknown variables. The front tracking method is applied to solve the initial value problem of a first-order hyperbolic 2 × 2 system of conservation laws describing the settling of a bidisperse suspension. The solution obtained by front tracking is compared with results obtained by an experiment and a finite difference scheme. [ABSTRACT FROM AUTHOR]