Incremental Identification of Transport Coefficients in Convection-Diffusion Systems

Abstract

Abstract. In this paper, an incremental approach for the identification of a model for transport coefficients in convection-diffusion systems on the basis of high-resolution measurement data is presented. The transport is represented by a convection term with known convective velocity and by a diffusion term with an unknown, generally state-dependent transport coefficient. The identification of the transport model for this transport coefficient constitutes an ill-posed nonlinear inverse problem. We present a novel decomposition approach in which this inverse problem is split into a sequence of inverse subproblems. In the first identification step of this incremental approach a source is estimated by solving an affine-linear inverse problem by means of the conjugate gradient method. In the second identification step a nonlinear inverse problem has to be solved in order to reconstruct a transport coefficient. A Newton-type method using the conjugate gradient method in its inner iteration is used to solve this nonlinear inverse problem of coefficient estimation. Finally, in the third identification step a transport model structure is proposed and identified on the basis of the model-free transport coefficient reconstructed in the two previous steps. The ill-posedness of each inverse problem is examined by using artificially perturbed transient simulation data and appropriate regularization techniques. The identification methodology is illustrated for a three-dimensional convection-diffusion equation which has its origin in the modeling and simulation of energy transport in a laminar wavy film flow.

Parallel re-initialization of level set functions on distributed unstructured tetrahedral grids

“…The overall strategy to parallelize this solver without considering the re-initialization is discussed in [42,43]. Applications of DROPS can be found in [44][45][46][47]. In this software, the level set function is given by a piece-wise quadratic function.…”

Direct determination of the concentration dependence of diffusivities using combined model-based Raman and NMR experiments

“…First, the diffusion coefficients at infinite dilution are estimated using the King correlation [40] with Á j being the viscosity of the solvent, V 0 i and H i the molar volume and the latent heat at the normal boiling point and T the temperature, which is set to 20 • C. The King correlation is selected as it gives the best results for our test system ethyl acetate-cyclohexane compared to other alternatives including the well-known correlations developed by Wilke and Chang [41] and Siddiqi and Lucas [42]. In estimation step 2, the concentration dependence of the Maxwell-Stefan diffusion coefficient is predicted using the Vignes relation [43], which can be expressed in the form (16) The concentration dependence of the Fick diffusion coefficient is finally determined by (17) where the thermodynamic factor (x) is calculated by means of the NRTL equation [44]. The parameters are taken from the Aspen Plus data base (Version 2004.1(13.2.6.3657)).…”

“…1, left. It is based on the incremental approach [16], which has been successfully applied to the identification of transport coefficients in convection-diffusion systems [17], to the identification of reaction kinetics [18,19] and to the identification of heat fluxes in falling film [17,20] and pool boiling experiments [21]. The incremental approach yields the diffusion coefficient dataD 12 (x) without any a priori-assumption of a certain model structure.…”

On reduced modeling of mass transport in wavy falling films

“…Since the considered reduced model makes some assumptions (2D geometry, domain and velocity from LWE) to reduce the computational time, the results will be of course different from a DNS simulation or real measurements. To compensate for modeling errors and improve the model in future works, we may apply the incremental identification methodology, that has been already introduced in previous papers . The main idea is to replace the molecular diffusion coefficient D in Eq.…”

“…However, the DNS of the film fluid dynamics requires huge computational effort and sophisticated numerical tools which limit their use in practice, e.g., to perform comprehensive model identification . Therefore, there is a need for a reduced modeling approach, which is capable of representing the most important properties of the transport phenomena in falling films at a modest computational cost.…”