Producción de isosorbida a partir de la biomasa como sustituto del bisfenol A.

Treballs Finals de Màster d'Enginyeria Química, Facultat de Química, Universitat de Barcelona. Curs: 2021-2022. Tutors: Montserrat Iborra Urios, Javier Tejero SalvadorIn order to meet the sustainability criteria demanded by today's society and industry, it is necessary to work with eco-efficient processes, i.e. "producing more with less", in a way that promotes better management of resources and energy while minimising environmental impacts. Hence the importance of the term "biomass". Meeting the growing needs of plastic production while improving sustainability has been a major focus of academic and industrial research. Creating a new generation of sustainable biomass-derived materials as competitive alternatives to petroleum-based plastics can be challenging due to the need for these new materials to match both the performance and cost-effectiveness of commonly used petroplastics. This work aims to cover the most relevant catalytic strategies designed for the conversion of sorbitol, a biomass-derived platform molecule, to isosorbide. Thus, it is shown which is the best pretreatment to separate the lignocellulosic biomass, the subsequent hydrolysis of cellulose to glucose (or other C6 sugars), how from this sugar sorbitol is obtained and how from this sugar the isosorbide molecule is obtained. Isosorbide has been shown to be a good substitute for bisphenol A, as it is a molecule with very similar characteristics but is less toxic to human health and the environmen

Error analysis of proper orthogonal decomposition stabilized methods for incompressible flows

Proper orthogonal decomposition (POD) stabilized methods for the Navier-Stokes equations are considered and analyzed. We consider two cases, the case in which the snapshots are based on a non inf-sup stable method and the case in which the snapshots are based on an inf-sup stable method. For both cases we construct approximations to the velocity and the pressure. For the first case, we analyze a method in which the snapshots are based on a stabilized scheme with equal order polynomials for the velocity and the pressure with Local Projection Stabilization (LPS) for the gradient of the velocity and the pressure. For the POD method we add the same kind of LPS stabilization for the gradient of the velocity and the pressure than the direct method, together with grad-div stabilization. In the second case, the snapshots are based on an inf-sup stable Galerkin method with grad-div stabilization and for the POD model we apply also grad-div stabilization. In this case, since the snapshots are discretely divergence-free, the pressure can be removed from the formulation of the POD approximation to the velocity. To approximate the pressure, needed in many engineering applications, we use a supremizer pressure recovery method. Error bounds with constants independent on inverse powers of the viscosity parameter are proved for both methods. Numerical experiments show the accuracy and performance of the schemes

On (essentially) non-oscillatory discretizations of evolutionary convection-diffusion equations

Finite element and finite difference discretizations for evolutionary convection-dif\-fusion-reaction equations in two and three dimensions are studied which give solutions without or with small under- and overshoots. The studied methods include a linear and a nonlinear FEM-FCT scheme, simple upwinding, an ENO scheme of order 3, and a fifth order WENO scheme. Both finite element methods are combined with the Crank--Nicolson scheme and the finite difference discretizations are coupled with explicit total variation diminishing Runge--Kutta methods. An assessment of the methods with respect to accuracy, size of under- and overshoots, and efficiency is presented, in the situation of a domain which is a tensor product of intervals and of uniform grids in time and space. Some comments to the aspects of adaptivity and more complicated domains are given. The obtained results lead to recommendations concerning the use of the methods

Two-Grid Mixed Finite-Element Approximations to the Navier–Stokes Equations Based on a Newton-Type Step

This is post-peer-review, pre-copyedit version of an article published in Journal of Scientific Computing. The final of authenticated version is available online at: https://doi.org/10.1007/s10915-017-0447-2A two-grid scheme to approximate the evolutionary Navier–Stokes equations is introduced and analyzed. A standard mixed finite element approximation is first obtained over a coarse mesh of size H at any positive time T>0 . Then, the approximation is postprocessed by means of solving a steady problem based on one step of a Newton iteration over a finer mesh of size h<H . The method increases the rate of convergence of the standard Galerkin method in one unit in terms of H and equals the rate of convergence of the standard Galerkin method over the fine mesh h. However, the computational cost is essentially the cost of approaching the Navier–Stokes equations with the plain Galerkin method over the coarse mesh of size H since the cost of solving one single steady problem is negligible compared with the cost of computing the Galerkin approximation over the full time interval (0, T]. For the analysis we take into account the loss of regularity at initial time of the solution of the Navier–Stokes equations in the absence of nonlocal compatibility conditions. Some numerical experiments are shownJ. Novo: Research supported by Spanish MINECO under grants MTM2013-42538-P (MINECO, ES) and MTM2016-78995-P (AEI/FEDER, UE

A robust SUPG norm a posteriori error estimator for the SUPG finite element approximation of stationary convection-diffusion equations

A robust residual-based a posteriori estimator is proposed for the SUPG finite element method applied to stationary convection-diffusion-reaction equations. The error in the natural SUPG norm is estimated. The main concern of this paper is the consideration of the convection-dominated regime. A global upper bound and a local lower bound for the error are derived, where the global upper estimate relies on some hypotheses. Numerical studies demonstrate the robustness of the estimator and the fulfillment of the hypotheses. A comparison to other residual-based estimators with respect to the adaptive grid refinement is also provided.

Error analysis of the SUPG finite element disretization of evolutionary convection-diffusion-reaction equations

Conditions on the stabilization parameters are explored for different approaches in deriving error estimates for the SUPG finite element stabilization of time-dependent convection-diffusion-reaction equations that is combined with the backward Euler method. Standard energy arguments lead to estimates for stabilization parameters that depend on the length of the time step. The stabilization vanishes in the time-continuous limit. However, based on numerical experiences, this seems not to be the correct behavior. For this reason, the time-continuous case is analyzed under certain conditions on the coefficients of the equation and the finite element method. An error estimate with the standard order of convergence is derived for stabilization parameters of the same form that is optimal for the steady-state problem. Numerical studies support the analytical results

On (essentially) non-oscillatory discretizations of evolutionary convection-diffusion equations

Finite element and finite difference discretizations for evolutionary convection-diffusion-reaction equations in two and three dimensions are studied which give solutions without or with small under- and overshoots. The studied methods include a linear and a nonlinear FEM-FCT scheme, simple upwinding, an ENO scheme of order 3, and a fifth order WENO scheme. Both finite element methods are combined with the Crank--Nicolson scheme and the finite difference discretizations are coupled with explicit total variation diminishing Runge--Kutta methods. An assessment of the methods with respect to accuracy, size of under- and overshoots, and efficiency is presented, in the situation of a domain which is a tensor product of intervals and of uniform grids in time and space. Some comments to the aspects of adaptivity and more complicated domains are given. The obtained results lead to recommendations concerning the use of the methods

Analysis of the PSPG stabilization for the continuous-in-time discretization of the evolutionary Stokes equations

Optimal error estimates for the pressure stabilized Petrov--Galerkin (PSPG) method for the continuous-in-time discretization of the evolutionary Stokes equations are proved in the case of regular solutions. The main result is applicable to higher order finite elements. The error bounds for the pressure depend on the error of the pressure at the initial time. An approach is suggested for choosing the discrete initial velocity in such a way that this error is bounded. The ``instability of the discrete pressure for small time steps'', which is reported in the literature, is discussed on the basis of the analytical results. Numerical studies confirm the theoretical results, showing in particular that this instability does not occur for the proposed initial condition

A robust SUPG norm a posteriori error estimator for the SUPG finite element approximation of stationary convection-diffusion equations

A robust residual-based a posteriori estimator is proposed for the SUPG finite element method applied to stationary convection-diffusion-reaction equations. The error in the natural SUPG norm is estimated. The main concern of this paper is the consideration of the convection-dominated regime. A global upper bound and a local lower bound for the error are derived, where the global upper estimate relies on some hypotheses. Numerical studies demonstrate the robustness of the estimator and the fulfillment of the hypotheses. A comparison to other residual-based estimators with respect to the adaptive grid refinement is also provided