Performance of a Real Coded Genetic Algorithm for the Calibration of Scalar Conservation Laws

Abstract

This paper deals with the flux identification problem for scalar conservation laws. The problem is formulated as an optimization problem, where the objective function compares the solution of the direct problem with observed profiles at a fixed time. A finite volume scheme solves the direct problem and a continuous genetic algorithm solves the inverse problem. The numerical method is tested with synthetic experimental data. Simulation parameters are recovered approximately. The tested heuristic optimization technique turns out to be more robust than classical optimization techniques.

Entropy solutions and flux identification of a scalar conservation law modelling centrifugal sedimentation

“…In this case, r = b(t) meets r = h(t) at a time point t i < t s and b(t i ) < R(t i ; max ) holds. The time point t i can be found by solving the coupled nonlinear system composed by (20), (45), (41a), and (41b), evaluating all functions at t i and setting r i ∶= b(t i ) = h(t i ).…”

“…In this subcase, the bottom discontinuity r = b(t) and r = R(t; max ) intersect at t = t c , after which r = b(t) continues with the volume fraction − b (t) = Q −1 (t) in R 1 and b (t) = max in R 3 until t = t i = t s when r = b(t) and r = h(t) intersect and the steady state begins. The function b(t), t c < t < t s , is defined by Equation (23) with initial value b(t c ) = R(t c ; max ), and where the time point t c can be determined from this equality by using (45) with (t c ) = max , which gives the nonlinear equation…”

“…We refer to Bürger et al 40 for a short review of published methods in diverse applications with focus on sedimentation; see, eg, previous studies. 7,32,[41][42][43][44] Berres et al 45 identify a parametrized given flux function by solving an optimization problem with a continuous genetic algorithm. For the identification of both and the effective solids stress function with batch centrifugation, a method where an adjoint equation is solved was put forward by Berres et al 46 The identification method of Usher et al 47 by using centrifugal sedimentation is based on the assumption that the local concentration is constant along particle trajectories.…”