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Author: Ahmed, Naveed × End date: 2019 × Start date: 2010 × Type: Text × WGL Institute: WIAS ×

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Now showing 1 - 10 of 14
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    Far field imaging of a dielectric inclusion
    (Bristol : IOP Publ., 2015) Wahab, Abdul; Ahmed, Naveed; Abbas, Tasawar
    A non-iterative topological sensitivity framework for guaranteed far field detection of a dielectric inclusion is presented. The cases of single and multiple measurements of the electric far field scattering amplitude at a fixed frequency are taken into account. The performance of the algorithm is analyzed theoretically in terms of resolution, stability, and signal-to-noise ratio.
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    Analysis of a full space-time discretization of the Navier-Stokes equations by a local projection stabilization
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Ahmed, Naveed; Rebollo, Tomás Chacón; John, Volker; Rubino, Samuele
    A finite element error analysis of a local projection stabilization (LPS) method for the time-dependent Navier-Stokes equations is presented. The focus is on the highorder term-by-term stabilization method that has one level, in the sense that it is defined on a single mesh, and in which the projection-stabilized structure of standard LPS methods is replaced by an interpolation-stabilized structure. The main contribution is on proving, theoretically and numerically, the optimal convergence order of the arising fully discrete scheme. In addition, the asymptotic energy balance is obtained for slightly smooth flows. Numerical studies support the analytical results and illustrate the potential of the method for the simulation of turbulent ows. Smooth unsteady flows are simulated with optimal order of accuracy.
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    On the grad-div stabilization for the steady Oseen and Navier-Stokes equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Ahmed, Naveed
    This paper studies the parameter choice in the grad-div stabilization applied to the generalized problems of Oseen type. Stabilization parameters based on minimizing the H1 (Omega) error of the velocity are derived which do not depend on the viscosity parameter. For the proposed parameter choices, the H1 (Omega) error of the velocity is derived that shows a direct dependence on the viscosity parameter. Differences and common features to the situation for the Stokes equations are discussed. Numerical studies are presented which confirm the theoretical results. Moreover, for the Navier-Stokes equations, numerical simulations were performed on a two-dimensional flow past a circular cylinder. It turns out, for the MINI element, that the best results can be obtained without grad-div stabilization.
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    Higher order continuous Galerkin-Petrov time stepping schemes for transient convection-diffusion-reaction equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Ahmed, Naveed; Matties, Gunar
    We present the analysis for the higher order continuous Galerkin-Petrov (cGP) time discretization schemes in combination with the one-level local projection stabilization in space applied to time-dependent convection-diffusion-reaction problems. Optimal a-priori error estimates will be proved. Numerical studies support the theoretical results. Furthermore, a numerical comparison between continuous Galerkin-Petrov and discontinuous Galerkin time discretization schemes will be given.
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    On really locking-free mixed finite element methods for the transient incompressible Stokes equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Ahmed, Naveed; Linke, Alexander; Merdon, Christian
    Inf-sup stable mixed methods for the steady incompressible Stokes equations that relax the divergence constraint are often claimed to deliver locking-free discretizations. However, this relaxation leads to a pressure-dependent contribution in the velocity error, which is proportional to the inverse of the viscosity, thus giving rise to a (different) locking phenomenon. However, a recently proposed modification of the right hand side alone leads to a discretization that is really locking-free, i.e., its velocity error converges with optimal order and is independent of the pressure and the smallness of the viscosity. In this contribution, we extend this approach to the transient incompressible Stokes equations, where besides the right hand side also the velocity time derivative requires an improved space discretization. Semi-discrete and fully-discrete a-priori velocity and pressure error estimates are derived, which show beautiful robustness properties. Two numerical examples illustrate the superior accuracy of pressure-robust space discretizations in the case of small viscosities.
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    On the feasibility of using open source solvers for the simulation of a turbulent air flow in a dairy barn
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Janke, David; Caiazzo, Alfonso; Ahmed, Naveed; Alia, Najib; Knoth, Oswald; Moreau, Baptiste; Wilbrandt, Ulrich; Willink, Dilya; Amon, Thomas; John, Volker
    Two transient open source solvers, OpenFOAM and ParMooN, are assessed with respect to the simulation of the turbulent air flow inside and around a dairy barn. For this purpose, data were obtained in an experimental campaign at a 1:100 scaled wind tunnel model. Both solvers used different meshes, discretization schemes, and turbulence models. The experimental data and numerical results agree well for time-averaged stream-wise and vertical-wise velocities. In particular, the air exchange was predicted with high accuracy by both solvers with relative errors less than 5 % compared to the experimental results. With respect to the turbulent quantities, good agreements at the second (downwind) half of the barn inside and especially outside the barn could be achieved, where both codes accurately predicted the flow separation and the root-mean-square velocities. Deviations between simulations and experimental results regarding turbulent quantities could be observed in the first part of the barn, due to different inlet conditions between the experimental setup and the numerical simulations. Both solvers proved to be promising tools for the accurate prediction of time-dependent phenomena in an agricultural context, e.g., like the transport of particulate matter or pathogen-laden aerosols in and around agricultural buildings.
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    Numerical studies of higher order variational time stepping schemes for evolutionary Navier-Stokes equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Ahmed, Naveed; Matthies, Gunar
    We present in this paper numerical studies of higher order variational time stepping schemes combined with finite element methods for simulations of the evolutionary Navier-Stokes equations. In particular, conforming inf-sup stable pairs of finite element spaces for approximating velocity and pressure are used as spatial discretization while continuous GalerkinPetrov methods (cGP) and discontinuous Galerkin (dG) methods are applied as higher order variational time discretizations. Numerical results for the well-known problem of incompressible flows around a circle will be presented.
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    Higher-order discontinuous Galerkin time stepping and local projection stabilization techniques for the transient Stokes problem
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Ahmed, Naveed; Becher, Simon; Matthies, Gunar
    We introduce and analyze discontinuous Galerkin time discretizations coupled with continuous finite element methods based on equal-order interpolation in space for velocity and pressure in transient Stokes problems. Spatial stability of the pressure is ensured by adding a stabilization term based on local projection. We present error estimates for the semi-discrete problem after discretization in space only and for the fully discrete problem. The fully discrete pressure shows an instability in the limit of small time step length. Numerical tests are presented which confirm our theoretical results including the pressure instability.
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    Numerical study of SUPG and LPS methods combined with higher order variational time discretization schemes applied to time-dependent convection-diffusion-reaction equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Ahmed, Naveed; Matthies, Gunar
    This paper considers the numerical solution of time-dependent convection-diffusion-reaction equations. We shall employ combinations of streamline-upwind Petrov-Galerkin (SUPG) and local projection stabilization (LPS) methods in space with the higher order variational time discretization schemes. In particular, we consider time discretizations by discontinuous Galerkin (dG) methods and continuous Galerkin-Petrov (cGP) methods. Several numerical tests have been performed to assess the accuracy of combinations of spatial and temporal discretization schemes. Furthermore, the dependence of the results on the stabilization parameters of the spatial discretizations are discussed. Finally the long-time behavior of overshoots and undershoots is investigated.
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    A review of variational multiscale methods for the simulation of turbulent incompressible flows
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Ahmed, Naveed; Rebollo, Tomás Chacón; John, Volker; Rubino, Samuele
    Various realizations of variational multiscale (VMS) methods for simulating turbulent incompressible flows have been proposed in the past fifteen years. All of these realizations obey the basic principles of VMS methods: They are based on the variational formulation of the incompressible Navier-Stokes equations and the scale separation is defined by projections. However, apart from these common basic features, the various VMS methods look quite different. In this review, the derivation of the different VMS methods is presented in some detail and their relation among each other and also to other discretizations is discussed. Another emphasis consists in giving an overview about known results from the numerical analysis of the VMS methods. A few results are presented in detail to highlight the used mathematical tools. Furthermore, the literature presenting numerical studies with the VMS methods is surveyed and the obtained results are summarized.