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Jeroen Witteveen Contents Contact information Current research Awards and honors Theses Journal articles Book chapters Conference papers Miscellaneous Upcoming conferences Professional memberships Abstracts Contact information Jeroen A.S. Witteveen Ph.D. Postdoctoral researcher Aerodynamics Department Faculty of Aerospace Engineering Delft University of Technology Kluyverweg 1 2629 HS Delft The Netherlands room 037 tel: +31(0)15 27 82046 fax: +31(0)15 27 87077 j.a.s.witteveen AT tudelft DOT nl www.jeroenwitteveen.com www.lr.tudelft.nl/aerodynamics Top of page Current research Uncertainty quantification The development of efficient and robust uncertainty quantification methods for computational fluid dynamics and fluid-structure interaction problems with unsteadiness and discontinuities in high-dimensional probability spaces. Mesh motion The development of efficient and robust mesh motion algorithms for deforming the flow mesh in fluid-structure interaction problems based on radial basis function interpolation. Front tracking The development of novel front tracking methods for the numerical treatment of the hyperbolic Euler equations of fluid mechanics. Top of page Awards and honors Da Vinci 2009 Ph.D. Thesis Award silver medal of the European Research Community On Flow, Turbulence And Combustion (ERCOFTAC). Best Master of Science graduate award 2003/2004 of the Faculty of Aerospace Engineering of Delft University of Technology. Graduated Ph.D. defense, Master and Bachelor of Science exams, Propedeuse, and secondary school with honor. Top of page Theses Efficient and robust uncertainty quantification methods for flow and fluid-structure interaction simulations, J.A.S. Witteveen, Ph.D. thesis, Delft University of Technology, Delft, The Netherlands (2009). The simple wave shock wave approximation and a new numerical method for hyperbolic flow problems, J.A.S. Witteveen, M.Sc. thesis, Delft University of Technology, Delft, The Netherlands (2004). Development of a one-dimensional conservative upwind residual distribution solver for a two-fluid model with tabulated equations of state, J.A.S. Witteveen, Internship thesis, Von Karman Institute for Fluid Dynamics, Sint-Genesius-Rode, Belgium (2002) VKI-SR 2003-06. Top of page Journal articles Transonic velocity fluctuations simulated using extrema diminishing uncertainty quantification based on inverse distance weighting, J.A.S. Witteveen, H. Bijl, Theor. Comp. Fluid Dyn. (2009) submitted. PDF Abstract Second order front tracking for the Euler equations, J.A.S. Witteveen, J. Comput. Phys. (2009) in press. PDF Abstract Effect of randomness on multi-frequency aeroelastic responses resolved by unsteady adaptive stochastic finite elements, J.A.S. Witteveen, H. Bijl, J. Comput. Phys. 228 (2009) 7025-7045. PDF Abstract A TVD uncertainty quantification method with bounded error applied to transonic airfoil flutter, J.A.S. Witteveen, H. Bijl, Commun. Comput. Phys. 6 (2009) 406-432. PDF Abstract An adaptive stochastic finite elements approach based on Newton-Cotes quadrature in simplex elements, J.A.S. Witteveen, G.J.A. Loeven, H. Bijl, Comput. Fluids 38 (2009) 1270-1288. PDF Abstract Higher period stochastic bifurcation of nonlinear airfoil fluid-structure interaction, J.A.S. Witteveen, H. Bijl, Math. Probl. Eng. 2009 (2009) 394387. PDF Abstract Effect of uncertainty on the bifurcation behavior of pitching airfoil stall flutter, S. Sarkar, J.A.S. Witteveen, G.J.A. Loeven, H. Bijl, J. Fluid Struct. 25 (2009) 304-320. PDF Abstract A monomial chaos approach for efficient uncertainty quantification in nonlinear problems, J.A.S. Witteveen, H. Bijl, SIAM J. Sci. Comput. 30 (2008) 1296-1317. PDF Abstract Probabilistic collocation for period-1 limit cycle oscillations, J.A.S. Witteveen, G.J.A. Loeven, S. Sarkar, H. Bijl, J. Sound Vib. 311 (2008) 421-439. PDF Abstract An unsteady adaptive stochastic finite elements formulation for rigid-body fluid-structure interaction, J.A.S. Witteveen, H. Bijl, Comput. Struct. 86 (2008) 2123-2140. PDF Abstract An alternative unsteady adaptive stochastic finite elements formulation based on interpolation at constant phase, J.A.S. Witteveen, H. Bijl, Comput. Method Appl. M. 198 (2008) 578-591. PDF Abstract Efficient quantification of the effect of uncertainties in advection-diffusion problems using polynomial chaos, J.A.S. Witteveen, H. Bijl, Numer. Heat Tr. B-Fund. 53 (2008) 437-465. PDF Abstract An improved front tracking method for the Euler equations, J.A.S. Witteveen, B. Koren, P.G. Bakker, J. Comput. Phys. 224 (2007) 712-728. PDF Abstract Modeling physical uncertainties in dynamic stall induced fluid-structure interaction of turbine blades using arbitrary polynomial chaos, J.A.S. Witteveen, S. Sarkar, H. Bijl, Comput. Struct. 85 (2007) 866-878. PDF Abstract Top of page Book chapters A second-order improved front tracking method for the numerical treatment of the hyperbolic Euler equations, J.A.S. Witteveen, in Hyperbolic Problems: Theory, Numerics, Applications; S. Benzoni-Gavage, D. Serre, Eds., Springer, Berlin (2008) 1077-1084. Top of page Conference papers A meshless front tracking method for the Euler equations of fluid dynamics, J.A.S. Witteveen, ECCOMAS Computational Methods in Applied Sciences CMAS2009, Bratislava, Slovakia (2009). Explicit mesh deformation using inverse distance weighting interpolation, J.A.S. Witteveen, H. Bijl, 19th AIAA Computational Fluid Dynamics Conference, San Antonio, Texas (2009) AIAA-2009-3996. A second order front tracking solution of the Euler equations, J.A.S. Witteveen, 19th AIAA Computational Fluid Dynamics Conference, San Antonio, Texas (2009) AIAA-2009-3989. Uncertainty quantification in fluid-structure interaction simulations using a simplex elements stochastic collocation approach, J.A.S. Witteveen, H. Bijl, 19th AIAA Computational Fluid Dynamics Conference, San Antonio, Texas (2009) AIAA-2009-3671. Efficient uncertainty quantification in unsteady aeroelastic simulations, J.A.S. Witteveen, H. Bijl, International Forum on Aeroelasticity and Structural Dynamics (IFASD), Seattle, Washington (2009) IFASD-2009-046. A robust and efficient uncertainty quantification method for coupled fluid-structure interaction problems, J.A.S. Witteveen, H. Bijl, ECCOMAS Computational Methods for Coupled Problems in Science and Engineering, Ischia, Italy (2009). Explicit inverse distance weighting mesh motion for coupled problems, J.A.S. Witteveen, H. Bijl, ECCOMAS Computational Methods for Coupled Problems in Science and Engineering, Ischia, Italy (2009). Uncertainty quantification for multi-frequency unsteady flow and fluid-structure interaction, J.A.S. Witteveen, H. Bijl, 11th AIAA Non-Deterministic Approaches Conference, Palm Springs, California (2009) AIAA-2009-2287. Unsteady adaptive stochastic finite elements for quantification of uncertainty in time-dependent problems, J.A.S. Witteveen, H. Bijl, 6th International Conference on Engineering Computational Technology ECT2008, Athens, Greece (2008). Uncertainty quantification in computational fluid dynamics and fluid-structure interaction, H. Bijl, J.A.S. Witteveen, G.J.A. Loeven, 13th International Conference on Computational and Applied Mathematics ICCAM 2008, Ghent, Belgium (2008). An unsteady adaptive stochastic finite elements uncertainty quantification method for fluid-structure interaction problems, J.A.S. Witteveen, H. Bijl, 5th European Congress on Computational Methods in Applied Sciences and Engineering ECCOMAS 2008, Venice, Italy (2008). Unsteady adaptive stochastic finite elements for aeroelastic systems with randomness, J.A.S. Witteveen, H. Bijl, 49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Schaumburg, Illinois (2008) AIAA-2008-2148. A probabilistic radial basis function approach for uncertainty quantification, G.J.A. Loeven, J.A.S. Witteveen, H. Bijl, Computational Uncertainty in Military Vehicle Design Symposium NATO RTO-MP-AVT-147, Athens, Greece (2007) P-35. Long-term stochastic behavior of aeroelastic systems, J.A.S. Witteveen, G.J.A. Loeven, H. Bijl, Computational Uncertainty in Military Vehicle Design Symposium NATO RTO-MP-AVT-147, Athens, Greece (2007) P-34. Modeling physical uncertainties in stall induced oscillation of an airfoil using polynomial chaos approach, S. Sarkar, J.A.S. Witteveen, H. Bijl, Asian Computational Fluid Dynamics Conference ACFD7, Bangalore, India (2007). Efficient uncertainty quantification in computational fluid-structure interactions: the probabilistic collocation method in a two step approach, G.J.A. Loeven, J.A.S. Witteveen, H. Bijl, International Workshop on Coupled Methods in Numerical Dynamics, Dubrovnik, Croatie (2007). Dynamic stall flutter analysis with uncertainties using multi-element probabilistic collocation, G.J.A. Loeven, S. Sarkar, J.A.S. Witteveen, H. Bijl, 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Honolulu, Hawaii (2007) AIAA-2007-1964. Quantifying the effect of physical uncertainties in unsteady fluid-structure interaction problems, J.A.S. Witteveen, G.J.A. Loeven, H. Bijl, 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Honolulu, Hawaii (2007) AIAA-2007-1942. Probabilistic collocation: an efficient non-intrusive approach for arbitrarily distributed parametric uncertainties, G.J.A. Loeven, J.A.S. Witteveen, H. Bijl, 45th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada (2007) AIAA-2007-317. A monomial chaos approach for efficient uncertainty quantification in computational fluid dynamics, J.A.S. Witteveen, H. Bijl, European Conference on Computational Fluid Dynamics ECCOMAS CFD, Egmond aan Zee, The Netherlands (2006). Reliable computational predictions by modeling uncertainties using arbitrary polynomial chaos, J.A.S. Witteveen, H. Bijl, European Conference on Computational Fluid Dynamics ECCOMAS CFD, Egmond aan Zee, The Netherlands (2006). Efficient uncertainty quantification using a two-step approach with chaos collocation, G.J.A. Loeven, J.A.S. Witteveen, H. Bijl, European Conference on Computational Fluid Dynamics ECCOMAS CFD, Egmond aan Zee, The Netherlands (2006). An efficient monomial chaos approach for uncertainty quantification in nonlinear computational models, J.A.S. Witteveen, H. Bijl, 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Newport, Rhode Island (2006) AIAA-2006-2071. Using polynomial chaos for uncertainty quantification in problems with nonlinearities, J.A.S. Witteveen, H. Bijl, 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Newport, Rhode Island (2006) AIAA-2006-2066. Efficient uncertainty quantification in computational fluid-structure interactions, G.J.A. Loeven, J.A.S. Witteveen, H. Bijl, 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Newport, Rhode Island (2006) AIAA-2006-1634. A second-order front tracking method applied to the Euler equations, J.A.S. Witteveen, 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada (2006) AIAA-2006-1277. Modeling arbitrary uncertainties using Gram-Schmidt polynomial chaos, J.A.S. Witteveen, H. Bijl, 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada (2006) AIAA-2006-896. An improved front tracking method for the Euler equations, J.A.S. Witteveen, P.G. Bakker, B. Koren, 17th AIAA Computational Fluid Dynamics Conference, Toronto, Canada (2005) AIAA-2005-5335. A residual distributive approach for one-dimensional two-fluid models and its relation with Godunov finite volume schemes, M. Ricchiuto, D.T. Rubino, J.A.S. Witteveen, H. Deconinck, ASTAR International Workshop on Advanced Numerical Methods for Multidimensional Simulation of Two-Phase Flow, Garching, Germany (2003). Feasibility study of a hot plume test facility, F.M. Bos, O. de Bruijn, N.P. van Hinsbergen, T.J.J. Lombaerts, P. Lucas, D.M. Luchtenburg, J.A.S. Witteveen, K.G. van der Zee, 4th European Symposium on Aerothermodynamics for Space Vehicles, Capua, Italy (2001). Top of page Miscellaneous Efficient and robust uncertainty quantification for computational fluid dynamics and fluid-structure interaction, J.A.S. Witteveen, ERCOFTAC Bulletin, December issue (2009). Uncertainty quantification in computational fluid dynamics, J.A.S. Witteveen, 1st Sino-UK-Netherlands Frontiers of Science Symposium, Beijing, China (2009). Top of page Upcoming conferences Workshop on quantification of CFD uncertainties, Vrije Universiteit Brussel, Brussels, Belgium, 29-30 October 2009. Top of page Professional memberships American Institute of Aeronautics and Astronautics, AIAA. Top of page Abstracts Transonic velocity fluctuations simulated using extrema diminishing uncertainty quantification based on inverse distance weighting, J.A.S. Witteveen, H. Bijl, Theor. Comp. Fluid Dyn. (2009) submitted. For reliable computational predictions of transonic flows it is important to resolve the significant effects of physical variations on the shock wave locations. The resulting discontinuities in probability space require extrema diminishing uncertainty quantification to avoid overshoots and undershoots in the response surface approximation. In this paper the extrema diminishing concept in probability space is extended to infinite parameter domains using inverse distance weighting interpolation of deterministic samples. Based on results for three analytical test functions the combination of Halton sampling and power parameter limit value c → ∞ is selected. The approach is employed to model spatial free stream velocity fluctuations in the highly sensitive transonic AGARD 445.6 wing test case in an up to ten-dimensional probability space. The 0.5% input variations are amplified to a coefficient of variation for the wave drag of cvD=9.58% in combination with an increase of the mean drag by 1.75% compared to the deterministic value. Keywords: Uncertainty quantification; Inverse distance weighting; Transonic flow; Extrema diminishing PACS: 47.11.-j; 47.40.-x; 47.40.Hg; 47.85.Gj PDF Back Second order front tracking for the Euler equations, J.A.S. Witteveen, J. Comput. Phys. (2009) in press. A second order front tracking method is developed for solving the hyperbolic system of Euler equations of inviscid fluid dynamics numerically. Meshless front tracking methods are usually limited to first order accuracy, since they are based on a piecewise constant approximation of the solution. Here second order convergence is achieved by deriving a piecewise linear reconstruction of the piecewise constant front tracking solution. The linearization is performed by decomposing the front tracking solution into its wave components and by linearizing the wave solutions separately. In order to construct a physically correct linearization, the physical phenomena of the front are taken into account in terms of the front types of the previously developed improved front interaction model. This front interaction model is also extended to include front numbers used in the wave decomposition. It is illustrated numerically for Sod's Riemann problem, the two interacting blast waves problem, and a two-dimensional supersonic airfoil flow validation study that the proposed front tracking method achieves second order convergence also in the presence of strong discontinuities and their interactions. PDF Back Effect of randomness on multi-frequency aeroelastic responses resolved by unsteady adaptive stochastic finite elements, J.A.S. Witteveen, H. Bijl, J. Comput. Phys. 228 (2009) 7025-7045. The Unsteady Adaptive Stochastic Finite Elements (UASFE) method resolves the effect of randomness in numerical simulations of single-mode aeroelastic responses with a constant accuracy in time for a constant number of samples. In this paper, the UASFE framework is extended to multi-frequency responses and continuous structures by employing a wavelet decomposition pre-processing step to decompose the sampled multi-frequency signals into single-frequency components. The effect of the randomness on the multi-frequency response is then obtained by summing the results of the UASFE interpolation at constant phase for the different frequency components. Results for multi-frequency responses and continuous structures show a 3 orders of magnitude reduction of computational costs compared to crude Monte Carlo simulations in a harmonically forced oscillator, a flutter panel problem, and the three-dimensional transonic AGARD 445.6 wing aeroelastic benchmark subject to random fields and random parameters with various probability distributions. Keywords: Stochastic finite elements; Fluid-structure interaction; Multi-frequency response; Wavelets PDF Back A TVD uncertainty quantification method with bounded error applied to transonic airfoil flutter, J.A.S. Witteveen, H. Bijl, Commun. Comput. Phys. 6 (2009) 406-432. The Unsteady Adaptive Stochastic Finite Elements (UASFE) approach is a robust and efficient uncertainty quantification method for resolving the effect of random parameters in unsteady simulations. In this paper, it is shown that the underlying Adaptive Stochastic Finite Elements (ASFE) method for steady problems based on Newton-Cotes quadrature in simplex elements is extrema diminishing (ED). It is also shown that the method is total variation diminishing (TVD) for one random parameter and for multiple random parameters for first degree Newton-Cotes quadrature. It is proven that the interpolation of oscillatory samples at constant phase in the UASFE method for unsteady problems results in a bounded error as function of the phase for periodic responses and under certain conditions also in a bounded error in time. The two methods are applied to a steady transonic airfoil flow and a transonic airfoil flutter problem. AMS subject classifications: 60H35, 65C30, 65N15, 65P99, 76M35. Keywords: Total variation diminishing; Extrema diminishing; Error bounds; Stochastic finite elements; Uncertainty quantification; Transonic flow; Transonic flutter. PDF Back An adaptive stochastic finite elements approach based on Newton-Cotes quadrature in simplex elements, J.A.S. Witteveen, G.J.A. Loeven, H. Bijl, Comput. Fluids 38 (2009) 1270-1288. In this paper an adaptive Stochastic Finite Elements approach with Newton-Cotes quadrature and simplex elements is developed for resolving the effect of random parameters in flow problems. The stochastic response is represented by a piecewise polynomial approximation by subdividing probability space into simplex elements. The quadrature approximation in the elements leads to solving uncoupled deterministic problems for varying parameter values. The elements are refined adaptively using a refinement measure based on the curvature of the approximation of the response weighted by the probability represented by the elements. Due to the Newton-Cotes quadrature the required number of deterministic solves is relatively low, since (i) the deterministic samples are reused in successive refinement steps due to the location of the quadrature points, and (ii) the samples are used in approximating the response in multiple elements, because most quadrature points are located on the boundaries of the elements. Monotonicity and extrema of the samples are preserved in the piecewise polynomial approximation of the response by subdividing elements where necessary in subelements with a linear approximation of the response. Applications to flows in a piston problem, a stall flutter model and transonic flow over a NACA0012 airfoil with uniformly and lognormally distributed random parameters demonstrate that the method is capable of resolving complex problems with singularities in probability space effectively. Resolving singularities is important since they can result in high sensitivities, and oscillatory or unphysical predictions. Keywords: Stochastic finite elements; Stochastic differential equations; Uncertainty quantification; Newton-Cotes quadrature; Adaptation PDF Back Higher period stochastic bifurcation of nonlinear airfoil fluid-structure interaction, J.A.S. Witteveen, H. Bijl, Math. Probl. Eng. 2009 (2009) 394387. The higher period stochastic bifurcation of a nonlinear airfoil fluid-structure interaction system is analyzed using an efficient and robust uncertainty quantification method for unsteady problems. The computationally efficient numerical approach achieves a constant error with a constant number of samples in time. The robustness of the method is assured by the extrema diminishing concept in probability space. The numerical results demonstrate that the system is even more sensitive to randomness at the higher period bifurcation than in the first bifurcation point. In this isolated point in parameter space the clear hierarchy of increasing importance of the random nonlinearity parameter, initial condition, and natural frequency ratio, respectively, even suddenly reverses. Disregarding seemingly less important random parameters based on a preliminary analysis can, therefore, be an unreliable approach for reducing the number of relevant random input parameters. Keywords: Uncertainty quantification; Fluid-structure interaction; Stochastic bifurcation; Higher period bifurcation PDF Back Effect of uncertainty on the bifurcation behavior of pitching airfoil stall flutter, S. Sarkar, J.A.S. Witteveen, G.J.A. Loeven, H. Bijl, J. Fluid Struct. 25 (2009) 304-320. In this paper the effect of system parametric uncertainty on the stall flutter bifurcation behavior of a pitching airfoil is studied. The aerodynamic moment on the two-dimensional rigid airfoil with nonlinear torsional stiffness is computed using the Onera dynamic stall model. The pitch natural frequency, a cubic structural nonlinearity parameter, and the structural equilibrium angle are assumed to be uncertain. The effect on the amplitude of the response, the bifurcation of the probability distribution, and the flutter boundary is considered. It is demonstrated that the system parametric uncertainty results already in 5% probability of pitching stall flutter at an 12.5% earlier position than the point where a deterministic analysis would predict unstable behavior. Probabilistic Collocation is found to be more efficient than the Galerkin Polynomial Chaos method and Monte Carlo simulation for modeling uncertainty in the post-bifurcation domain. Keywords: Stall flutter; Uncertainty quantification; Galerkin polynomial chaos; Probabilistic collocation; Flutter boundary PDF Back A monomial chaos approach for efficient uncertainty quantification in nonlinear problems, J.A.S. Witteveen, H. Bijl, SIAM J. Sci. Comput. 30 (2008) 1296-1317. A monomial chaos approach is presented for efficient uncertainty quantification in nonlinear computational problems. Propagating uncertainty through nonlinear equations can be computationally intensive for existing uncertainty quantification methods. It usually results in a set of nonlinear equations which can be coupled. The proposed monomial chaos approach employs a polynomial chaos expansion with monomials as basis functions. The expansion coefficients are solved for using differentiation of the governing equations, instead of a Galerkin projection. This results in a decoupled set of linear equations even for problems involving polynomial nonlinearities. This reduces the computational work per additional polynomial chaos order to the equivalence of a single Newton iteration. Error estimates are derived, and monomial chaos is applied to uncertainty quantification of the Burgers equation and a two-dimensional boundary layer flow problem. The results are compared with results of the Monte Carlo method, the perturbation method, the Galerkin polynomial chaos method, and a nonintrusive polynomial chaos method. Keywords: Uncertainty quantification; Polynomial chaos; Computational fluid dynamics; Nondeterministic approaches AMS subject classifications: 65C20, 65C30, 65N30 PDF Back Probabilistic collocation for period-1 limit cycle oscillations, J.A.S. Witteveen, G.J.A. Loeven, S. Sarkar, H. Bijl, J. Sound Vib. 311 (2008) 421-439. In this paper probabilistic collocation for limit cycle oscillations (PCLCO) is proposed. Probabilistic collocation (PC) is a non-intrusive approach to compute the polynomial chaos description of uncertainty numerically. Polynomial chaos can require impractical high orders to approximate long-term time integration problems, due to the fast increase of required polynomial chaos order with time. PCLCO is a PC formulation for modeling the long-term stochastic behavior of dynamical systems exhibiting a periodic response, i.e. a limit cycle oscillation (LCO). In the PC method deterministic time series are computed at collocation points in probability space. In PCLCO, PC is applied to a time-independent parametrization of the periodic response of the deterministic solves instead of to the time-dependent functions themselves. Due to the time-independent parametrization the accuracy of PCLCO is independent of time. The approach is applied to period-1 oscillations with one main frequency subject to a random parameter. Numerical results are presented for the harmonic oscillator, a two-dof airfoil flutter model and the fluid-structure interaction of an elastically mounted cylinder. PDF Back An unsteady adaptive stochastic finite elements formulation for rigid-body fluid-structure interaction, J.A.S. Witteveen, H. Bijl, Comput. Struct. 86 (2008) 2123-2140. An adaptive stochastic finite elements approach for unsteady problems is developed. Time-dependent solutions of dynamical systems are known to be sensitive to small input variations. Stochastic finite elements methods usually require a fast increasing number of elements with time to capture the effect of random input parameters in these unsteady problems. The resulting large number of samples required for resolving the asymptotic stochastic behavior, results for computationally intensive fluid-structure interaction simulations in impractically high computational costs. The unsteady adaptive stochastic finite elements (UASFE) formulation proposed in this paper maintains a constant interpolation accuracy in time with a constant number of samples. The approach is based on a time-independent parametrization of the sampled time series in terms of frequency, phase, amplitude, reference value, damping, and higher-period shape function. This parametrization is interpolated using a robust adaptive stochastic finite elements method based on Newton-Cotes quadrature in simplex elements. The effectiveness of the UASFE approach is illustrated by applications to a mass-spring-damper system, the Duffing equation, and a rigid-airfoil fluid-structure interaction problem with multiple random input parameters. The results are verified by comparison to those of Monte Carlo simulations. Keywords: Stochastic finite elements; Fluid-structure interaction; Unsteady problems; Random parameters PDF Back An alternative unsteady adaptive stochastic finite elements formulation based on interpolation at constant phase, J.A.S. Witteveen, H. Bijl, Comput. Method Appl. M. 198 (2008) 578-591. The unsteady adaptive stochastic finite elements method based on time-independent parametrization (UASFE-ti) is an efficient approach for resolving the effect of random parameters in unsteady simulations. It achieves a constant accuracy in time with a constant number of samples, in contrast with the usually fast increasing number of samples required by other methods. In this paper, an alternative unsteady adaptive stochastic finite elements formulation based on interpolation at constant phase (UASFE-cp) is developed to further improve the accuracy and extend the applicability of UASFE-ti. In addition to achieving a constant number of samples in time, interpolation at constant phase: (1) eliminates the parametrization error of the time-independent parametrization; (2) resolves time-dependent functionals, which cannot be modeled by the parametrization; and (3) captures transient behavior of the samples, which is an important special case of time-dependent functionals. These three points are illustrated by the application of UASFE-cp to random parameters in a mass-spring-damper system, the damped nonlinear Duffing oscillator, and an elastically mounted airfoil with nonlinearity in the flow and the structure. Results for different types of probability distributions are compared to those of UASFE-ti and Monte Carlo simulations. Keywords: Stochastic finite elements; Unsteady problems; Fluid-structure interaction; Random parameters; Uncertainty quantification PDF Back Efficient quantification of the effect of uncertainties in advection-diffusion problems using polynomial chaos, J.A.S. Witteveen, H. Bijl, Numer. Heat Tr. B-Fund. 53 (2008) 437-465. Uncertainties in advection-diffusion heat transfer problems are modeled using polynomial chaos to increase the basic understanding of the effect of physical variability. The polynomial chaos method approximates the effect of uncertain parameters using a polynomial expansion in probability space. Since the computational work of an uncertainty analysis increases rapidly with the number of uncertain parameters to the equivalence of many deterministic simulations, strategies for efficient quantification of the effect of multiple uncertain parameters are needed. Three strategies are studied in this article. Results are presented for advection-diffusion problems of heat transfer in one-dimensional and two-dimensional pipe flows. PDF Back An improved front tracking method for the Euler equations, J.A.S. Witteveen, B. Koren, P.G. Bakker, J. Comput. Phys. 224 (2007) 712-728. An improved front tracking method for hyperbolic conservation laws is presented. The improved method accurately resolves discontinuities as well as continuous phenomena. The method is based on an improved front interaction model for a physically more accurate modeling of the Euler equations, as compared to standard front tracking methods. The resulting algorithm is also more efficient than existing front tracking methods. The improved front tracking method is applied to the Euler equations for one-dimensional unsteady flow and two-dimensional steady supersonic flow. The results are compared to results of a standard front tracking method and a finite volume method. Keywords: Front tracking; Euler equations; Gas dynamics; Hyperbolic conservation laws PACS classification codes: 35L65; 35L67; 65M12; 76L05; 76N15 PDF Back Modeling physical uncertainties in dynamic stall induced fluid-structure interaction of turbine blades using arbitrary polynomial chaos, J.A.S. Witteveen, S. Sarkar, H. Bijl, Comput. Struct. 85 (2007) 866-878. A nonlinear dynamic problem of stall induced flutter oscillation subject to physical uncertainties is analyzed using arbitrary polynomial chaos. A single-degree-of-freedom stall flutter model with torsional oscillation is considered subject to nonlinear aerodynamic loads in the dynamic stall regime and nonlinear structural stiffness. The analysis of the deterministic aeroelastic response demonstrated that the problem is sensitive to variations in structural natural frequency and structural nonlinearity. The effect of uncertainties in these parameters is studied. Arbitrary polynomial chaos is employed in which appropriate expansion polynomials are constructed based on the statistical moments of the uncertain input. The arbitrary polynomial chaos results are compared with Monte Carlo simulations. Keywords: Dynamic stall; Stall flutter; Structural nonlinearity; Uncertainty quantification; Polynomial chaos expansion; Arbitrary uncertainties PDF Back Top of page |