39 results
Search Results
Now showing 1 - 10 of 39
- ItemVibrations of a laboratory-scale gas-stirred ladle with two eccentric nozzles and multiple sensors([Singapore] : Springer Singapore, 2019) Alia, Najib; Pylvänäinen, Mika; Visuri, Ville-Valtteri; John, Volker; Ollila, SeppoDuring ladle stirring, a gas is injected into the steel bath to generate a mixing of the liquid steel. The optimal process control requires a reliable measurement of the stirring intensity, for which the induced ladle wall vibrations have proved to be a potential indicator. An experimental cold water ladle with two eccentric nozzles and eight mono-axial accelerometers was thus investigated to measure the vibrations. The effect of the sensors’ positions with respect to the gas plugs on the vibration intensity was analyzed, and experimental data on several points of the ladle were collected for future numerical simulations. It is shown that the vibration root-mean-square values depend not only on process parameters, such as gas flow rate, water, and oil heights, but also on the radial and axial positions of the sensors. The vibration intensity is clearly higher, close to the gas plumes, than in the opposite side. If one of the nozzles is clogged, the vibration intensity close to the clogged nozzle drops drastically (−36 to −59%), while the vibrations close to the normal operating nozzle are hardly affected. Based on these results, guidelines are provided for an optimized vibration-based stirring.
- ItemAn adaptive SUPG method for evolutionary convection-diffusion equations(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) de Frutos, Javier; García-Archilla, Bosco; John, Volker; Novo, JuliaAn adaptive algorithm for the numerical simulation of time-dependent convectiondiffusion-reaction equations will be proposed and studied. The algorithm allows the use of the natural extension of any error estimator for the steady-state problem for controlling local refinement and coarsening. The main idea consists in considering the SUPG solution of the evolutionary problem as the SUPG solution of a particular steady-state convectiondiffusion problem with data depending on the computed solution. The application of the error estimator is based on a heuristic argument by considering a certain term to be of higher order. This argument is supported in the one-dimensional case by numerical analysis. In the numerical studies, particularly the residual-based error estimator from [18] will be applied, which has proved to be robust in the SUPG norm. The effectivity of this error estimator will be studied and the numerical results (accuracy of the solution, fineness of the meshes) will be compared with results obtained by utilizing the adaptive algorithm proposed in [6]
- ItemAnalysis 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, SamueleA 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.
- ItemAn assessment of discretizations for convection-dominated convection-diffusion equations(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Augustin, Matthias; Caiazzo, Alfonso; Fiebach, André; Fuhrmann, Jürgen; John, Volker; Linke, Alexander; Umla, RudolfThe performance of several numerical schemes for discretizing convection-dominated convection-diffusion equations will be investigated with respect to accuracy and efficiency. Accuracy is considered in measures which are of interest in applications. The study includes an exponentially fitted finite volume scheme, the Streamline-Upwind Petrov--Galerkin (SUPG) finite element method, a spurious oscillations at layers diminishing (SOLD) finite element method, a finite element method with continuous interior penalty (CIP) stabilization, a discontinuous Galerkin (DG) finite element method, and a total variation diminishing finite element method (FEMTVD). A detailed assessment of the schemes based on the Hemker example will be presented.
- ItemA study of isogeometric analysis for scalar convection-diffusion equations(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) John, Volker; Schumacher, LieselIsogeometric Analysis (IGA), in combination with the Streamline Upwind PetrovGalerkin (SUPG) stabilization, is studied for the discretization of steady-state convection-diffusion equations. Numerical results obtained for the Hemker problem are compared with results computed with the SUPG finite element method of the same order. Using an appropriate parameterization for IGA, the computed solutions are much more accurate than those obtained with the finite element method, both in terms of the size of spurious oscillations and of the sharpness of layers.
- ItemOn the parameter choice in grad-div stabilization for incompressible flow problems(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Jenkins, Eleanor W.; John, Volker; Linke, Alexander; Rebholz, Leo G.Grad-div stabilization has been proved to be a very useful tool in discretizations of incompressible flow problems. Standard error analysis for inf-sup stable conforming pairs of finite element spaces predicts that the stabilization parameter should be optimally chosen to be O(1). This paper revisits this choice for the Stokes equations on the basis of minimizing the H1( ) error of the velocity and the L2( ) error of the pressure. It turns out, by applying a refined error analysis, that the optimal parameter choice is more subtle than known so far in the literature. It depends on the used norm, the solution, the family of finite element spaces, and the type of mesh. Depending on the situation, the optimal stabilization parameter might range from being very small to very large. The analytic results are supported by numerical examples.
- ItemOn (essentially) non-oscillatory discretizations of evolutionary convection-diffusion equations(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) John, Volker; Novo, JuliaFinite 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.
- ItemA unified analysis of Algebraic Flux Correction schemes for convection-diffusion equations(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2018) Barrenechea, Gabriel R.; John, Volker; Knobloch, Petr; Rankin, RichardRecent results on the numerical analysis of Algebraic Flux Correction (AFC) finite element schemes for scalar convection-diffusion equations are reviewed and presented in a unified way. A general form of the method is presented using a link between AFC schemes and nonlinear edge-based diffusion scheme. Then, specific versions of the method, this is, different definitions for the flux limiters, are reviewed and their main results stated. Numerical studies compare the different versions of the scheme.
- ItemSUPG reduced order models for convection-dominated convection-diffusion-reaction equations(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Iliescu, Traian; John, Volker; Schyschlowa, Swetlana; Wells, DavidThis paper presents a Streamline-Upwind Petrov--Galerkin (SUPG) reduced order model (ROM) based on Proper Orthogonal Decomposition (POD). This ROM is investigated theoretically and numerically for convection-dominated convection-diffusion-reaction equations. The SUPG finite element method was used on realistic meshes for computing the snapshots, leading to some noise in the POD data. Numerical analysis is used to propose the scaling of the stabilization parameter for the SUPG-ROM. Two approaches are used: One based on the underlying finite element discretization and the other one based on the POD truncation. The resulting SUPG-ROMs and the standard Galerkin ROM (G-ROM) are studied numerically. For many settings, the results obtained with the SUPG-ROMs are more accurate. Finally, one of the choices for the stabilization parameter is recommended.
- ItemGrad-div stabilization for the evolutionary Oseen problem with inf-sup stable finite elements(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Frutos, Javier de; García-Archilla, Bosco; John, Volker; Novo, JuliaThe approximation of the time-dependent Oseen problem using inf-sup stable mixed finite elements in a Galerkin method with grad-div stabilization is studied. The main goal is to prove that adding a grad-div stabilization term to the Galerkin approximation has a stabilizing effect for small viscosity. Both the continuous-in-time and the fully discrete case (backward Euler method, the two-step BDF, and CrankNicolson schemes) are analyzed. In fact, error bounds are obtained that do not depend on the inverse of the viscosity in the case where the solution is sufficiently smooth. The bounds for the divergence of the velocity as well as for the pressure are optimal. The analysis is based on the use of a specific Stokes projection. Numerical studies support the analytical results