Mathematical models are used for simulating the electrochemical phenomena of proton-exchange-memb... more Mathematical models are used for simulating the electrochemical phenomena of proton-exchange-membrane (PEM) fuel cells. They differ in the scale, modeling variables, precision in specific features, and the required parameters. Often, the input parameters are not measurable and need to be estimated by minimizing the error between the model output and experimental data; however, the estimated parameters could differ from one model to another, hence provoking uncertainty about the correct values and the model’s suitability for simulating the real phenomenon. To address these issues, we introduced a self-validating methodology using three different mathematical models: The first set of parameters was estimated with a semi-empirical (SE) model; then, it was used for computing several points of the polarization curve (PC). The SE parameters and points were used to estimate a second set of parameters and to compute a single point of the PC with a macro-homogeneous (MH) model. The parameter...
In this work a parallel scheme to solve the dynamic Maxwell’s equations is presented, in order to... more In this work a parallel scheme to solve the dynamic Maxwell’s equations is presented, in order to simulate an electromagnetic wave in a two-dimensional domain composed of distinct dielectric materials and subject to boundary conditions. In this approach a Discontinuous Galerkin Finite Element Method (DG-FEM) is used to compute the solution over a discretized domain of non-overlapping straight-sided elements. In contrast to continuous Galerkin methods, the core of the simulation relies on a set of elementwise calculations instead of a global processing. These local calculations are computed simultaneously in a shared memory environment with the parallel framework proposed, taking advantage of the discontinuous nature of the solver implemented.
A discretization of the Convection-Diffusion equation is developed based on Discrete Exterior Cal... more A discretization of the Convection-Diffusion equation is developed based on Discrete Exterior Calculus (DEC). While DEC discretization of the diffusive term in the equation is well understood, the convective part (with non-constant convective flow) had not been DEC discretized. In this study, we develop such discretization of the convective term using geometric arguments. We can discretize the convective term for both compressible and incompressible flow. Moreover, since the Finite Element Method with linear interpolation functions (FEML) and DEC local matrix formulations are similar, this numerical scheme is well suited for parallel computing. Using this feature, numerical tests are carried out on simple domains with coarse and fine meshes to compare DEC and FEML and show numerical convergence for stationary problems.
Mathematical models are used for simulating the electrochemical phenomena of proton-exchange-memb... more Mathematical models are used for simulating the electrochemical phenomena of proton-exchange-membrane (PEM) fuel cells. They differ in the scale, modeling variables, precision in specific features, and the required parameters. Often, the input parameters are not measurable and need to be estimated by minimizing the error between the model output and experimental data; however, the estimated parameters could differ from one model to another, hence provoking uncertainty about the correct values and the model’s suitability for simulating the real phenomenon. To address these issues, we introduced a self-validating methodology using three different mathematical models: The first set of parameters was estimated with a semi-empirical (SE) model; then, it was used for computing several points of the polarization curve (PC). The SE parameters and points were used to estimate a second set of parameters and to compute a single point of the PC with a macro-homogeneous (MH) model. The parameter...
In this work a parallel scheme to solve the dynamic Maxwell’s equations is presented, in order to... more In this work a parallel scheme to solve the dynamic Maxwell’s equations is presented, in order to simulate an electromagnetic wave in a two-dimensional domain composed of distinct dielectric materials and subject to boundary conditions. In this approach a Discontinuous Galerkin Finite Element Method (DG-FEM) is used to compute the solution over a discretized domain of non-overlapping straight-sided elements. In contrast to continuous Galerkin methods, the core of the simulation relies on a set of elementwise calculations instead of a global processing. These local calculations are computed simultaneously in a shared memory environment with the parallel framework proposed, taking advantage of the discontinuous nature of the solver implemented.
A discretization of the Convection-Diffusion equation is developed based on Discrete Exterior Cal... more A discretization of the Convection-Diffusion equation is developed based on Discrete Exterior Calculus (DEC). While DEC discretization of the diffusive term in the equation is well understood, the convective part (with non-constant convective flow) had not been DEC discretized. In this study, we develop such discretization of the convective term using geometric arguments. We can discretize the convective term for both compressible and incompressible flow. Moreover, since the Finite Element Method with linear interpolation functions (FEML) and DEC local matrix formulations are similar, this numerical scheme is well suited for parallel computing. Using this feature, numerical tests are carried out on simple domains with coarse and fine meshes to compare DEC and FEML and show numerical convergence for stationary problems.
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