Numerical identification of constitutive functions in scalar nonlinear convection–diffusion equations with application to batch sedimentation

A fast and simple method for the identification of nonlinear constitutive functions in scalar convection–diffusion equations is presented. No a priori information is needed on the form of the constitutive functions, which are obtained as continuous piecewise affine functions. Accurate and frequent measurements in space and time are required. Synthetic data of batch sedimentation of particles in a liquid and traffic flow are chosen as examples where a convective flux function and a function modelling compression are identified. Real data should first undergo a denoising procedure, which is also presented. It consists of a sequence of convex optimization problems, whose constraints originate from fundamental physical properties. The methodology is applied on data from a batch sedimentation experiment of activated sludge in wastewater treatment.