Modellierung und numerische Simulation von Hangrutschungen

in Busch, W; Niemeier, W; Sörgel, U (Eds.) GeoMonitoring 2011 - Ein Paradigmenwechsel zur Beherrschung von Georisiken (2011)

A rheological interface model and its space-time finite element formulation for fluid-structure interaction

in International Journal for Numerical Methods in Engineering (2011), 86(6), 667-687

This contribution discusses extended physical interface models for fluid-structure interaction problems and investigates their phenomenological effects on the behavior of coupled systems by numerical ... [more ▼]

This contribution discusses extended physical interface models for fluid-structure interaction problems and investigates their phenomenological effects on the behavior of coupled systems by numerical simulation. Besides the various types of friction at the fluid-structure interface the most interesting phenomena are related to effects due to additional interface stiffness and damping. The paper introduces extended models at the fluid-structure interface on the basis of rheological devices (Hooke, Newton, Kelvin, Maxwell, Zener). The interface is decomposed into a Lagrangian layer for the solid-like part and an Eulerian layer for the fluid-like part. The mechanical model for fluid-structure interaction is based on the equations of rigid body dynamics for the structural part and the incompressible Navier-Stokes equations for viscous flow. The resulting weighted residual form uses the interface velocity and interface tractions in both layers in addition to the field variables for fluid and structure. The weak formulation of the whole coupled system is discretized using space-time finite elements with a discontinuous Galerkin method for time-integration leading to a monolithic algebraic system. The deforming fluid domain is taken into account by deformable space-time finite elements and a pseudo-structure approach for mesh motion. The sensitivity of coupled systems to modification of the interface model and its parameters is investigated by numerical simulation of flow induced vibrations of a spring supported fluid-immersed cylinder. It is shown that the presented rheological interface model allows to influence flow-induced vibrations. © 2010 John Wiley & Sons, Ltd. [less ▲]

Model order reduction of the aeroelastic response of a wind turbine rotor blade

Scientific Conference (2011)

The dynamic response of a wind turbine is mainly governed by the a􏰁ecting 􏰃ow forces of the wind. Concerning life expectancy, the vibration sensitivity of the rotor blades is of particular importance ... [more ▼]

The dynamic response of a wind turbine is mainly governed by the a􏰁ecting 􏰃ow forces of the wind. Concerning life expectancy, the vibration sensitivity of the rotor blades is of particular importance. In this contribution the dynamics of a rotating blade is described including the deformation-dependant aerodynamic forces [1]. Then, a reduced-order model for the coupled system of structure and 􏰃uid 􏰃ow is derived, which is more e􏰄cient concerning the calculation through the use of less degrees of freedom, but maintains the stability characteristics of the non-reduced-order model. A single rotor blade is described as a straight Bernoulli beam with a variable non-symmetric sectional pro􏰂le. The coordinate system refers to the current position of the blade. Besides the structural sti􏰁ness, mass inertia and aerodynamic loading according to potential 􏰃ow theory are included. The aerodynamic loading is linearised following the Scanlan model described in [2]. The linear equation of motion is formulated by means of the principle of virtual deformation assuming a constant rotational speed [3]. The quality of the model order reduction approach strongly depends on the chosen reduced basis. In this approach the basis is built by an appropriate selection of eigenmodes, which are dependent on the aerodynamic loading and parametrized on the rotational speed of the blade. The contribution discusses available methods [4] of creating reduced bases eligible to correctly represent the 􏰃utter characteristics in a spectrum of operating speeds. [less ▲]

Meshfree collocation method for implicit time integration of ODEs

in International Journal of Computational Methods (2011), 8(1), 119-137

An implicit time integration meshfree collocation method for solving linear and nonlinear ordinary differential equations (ODEs) based on interpolating moving least squares technique, which uses singular ... [more ▼]

An implicit time integration meshfree collocation method for solving linear and nonlinear ordinary differential equations (ODEs) based on interpolating moving least squares technique, which uses singular weights for constructing ansatz functions, is presented. On an example of a system of equations for Foucault pendulum, the flexibility of the proposed approach is shown and the accuracy, convergence, and stability properties are investigated. In a nonlinear case, the method gives accurate results, which is demonstrated by the solution of Lorenz equations. The typical trajectory patterns, e.g. butterfly pattern, were observed and the properties of the method are compared to those of a higher-order time integration method. © 2011 World Scientific Publishing Company. [less ▲]

Finite element method for strongly-coupled systems of fluid-structure interaction with application to granular flow in silos

in Proceedings of the 4th International Conference on Computational Methods for Coupled Problems in Science and Engineering, COUPLED PROBLEMS 2011 (2011)

A monolithic approach to fluid-structure interactions based on the space-time finite element method (STFEM) is presented. The method is applied to the investigation of stress states in silos filled with ... [more ▼]

A monolithic approach to fluid-structure interactions based on the space-time finite element method (STFEM) is presented. The method is applied to the investigation of stress states in silos filled with granular material during discharge. The thin-walled siloshell is modeled in a continuum approach as elastic solid material, whereas the flowing granular material is described by an enhanced viscoplastic non-Newtonian fluid model. The weak forms of the governing equations are discretized by STFEM for both solid and fluid domain. To adapt the matching mesh nodes of the fluid domain to the structural deformations, a mesh-moving scheme using a neo-Hookean pseudo-solid is applied. The finite element approximation of non-smooth solution characteristics is enhanced by the extended finite element method (XFEM). The proposed methodology is applied to the 4D (space-time) investigation of deformation-dependent loading conditions during silo discharge. [less ▲]

Finite element methods for strongly-coupled systems of fluid-structure interaction with application to granular flow in silos

in PAMM (2010), 10(1), 381--382

A monolithic approach to fluid-structure interactions based on the space-time finite element method is presented to investigate stress states in silos filled with granular material during discharge. The ... [more ▼]

A monolithic approach to fluid-structure interactions based on the space-time finite element method is presented to investigate stress states in silos filled with granular material during discharge. The thin-walled silo-shell is discretized by continuum based, mixed-hybrid finite elements, whereas the flowing granular material is described by an enhanced viscoplastic non-Newtonian fluid model. To adapt the mesh nodes of the fluid domain to the structural deformations, a mesh-moving scheme using a pseudo-solid is applied. The level-set-method involving XFEM is used, including a 4D split algorithm for the space-time finite elements, in order to describe free surfaces. The method is applied to 3D silo discharges. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [less ▲]

A localized mixed-hybrid method for imposing interfacial constraints in the extended finite element method (XFEM)

in International Journal for Numerical Methods in Engineering (2009), 79(6), 733-752

The paper proposes an approach for the imposition of constraints along moving or fixed immersed interfaces in the context of the extended finite element method. An enriched approximation space enables ... [more ▼]

The paper proposes an approach for the imposition of constraints along moving or fixed immersed interfaces in the context of the extended finite element method. An enriched approximation space enables consistent representation of strong and weak discontinuities in the solution fields along arbitrarily-shaped material interfaces using an unfitted background mesh. The use of Lagrange multipliers or penalty methods is circumvented by a localized mixed hybrid formulation of the model equations. In a defined region in the vicinity of the interface, the original problem is re-stated in its auxiliary formulation. The availability of the auxiliary variable enables the consideration of a variety of interface constraints in the weak form. The contribution discusses the weak imposition of Dirichlet- and Neumann-type interface conditions as well as continuity requirements not fulfilled a priori by the enriched approximation. The properties of the proposed approach applied to two-dimensional linear scalar- and vector-valued elliptic problems are investigated by studying the convergence behavior. © 2009 John Wiley & Sons,Ltd. [less ▲]

Space-Time Meshfree Collocation Method for PDEs

in PAMM (2009), 9(1), 651--652

An innovative Space-Time Meshfree Collocation Method (STMCM) for solving systems of nonlinear ordinary and partial differential equations by a consistent discretization in both space and time is proposed ... [more ▼]

An innovative Space-Time Meshfree Collocation Method (STMCM) for solving systems of nonlinear ordinary and partial differential equations by a consistent discretization in both space and time is proposed as an alternative to established mesh-based methods. The STMCM belongs to the class of truly meshfree methods, i.e. the methods which do not have any underlying mesh, but work on a set of nodes only, without an a priori node-to-node connectivity. A regularization technique to overcome the singularity-by-construction and to compute all necessary derivatives of the kernel functions is presented. The method combines the simplicity and straightforwardness of the strong-form computational techniques with the advantages of meshfree methods over the classical ones, especially for coupled engineering problems involving moving interfaces. The key features of the proposed approach are: (i) no need to generate a mesh, (ii) simplified imposition of boundary conditions, (iii) no need to evaluate integral forms of governing equations, (iv) applicability to complex irregularly-shaped domains. The proposed STMCM is applied to linear and nonlinear ordinary and partial differential equations of different types and its accuracy and convergence properties are studied. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [less ▲]

Numerical model for tsunami generation by subaerial landslides

in PAMM (2008), 8(1), 10519--10520

A discretization method based on stabilized space–time finite elements is presented for the numerical analysis of three–fluid flows of immiscible and incompressible fluids. Signed distance functions are ... [more ▼]

A discretization method based on stabilized space–time finite elements is presented for the numerical analysis of three–fluid flows of immiscible and incompressible fluids. Signed distance functions are used to assign the material properties to each spatial point in the domain. The motion and the change in topology of fluid–fluid interfaces are implicitly described by the level–set method. Strong and weak discontinuities in the fields of the physical state variables are captured by locally enriched approximations based on the partition–of–unity concept. An interior penalty method enforces interfacial conservation of mass and momentum. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [less ▲]

The enriched space-time finite element method (EST) for simultaneous solution of fluid-structure interaction

in International Journal for Numerical Methods in Engineering (2008), 75(3), 305-334

The paper introduces a weighted residual-based approach for the numerical investigation of the interaction of fluid flow and thin flexible structures. The presented method enables one to treat strongly ... [more ▼]

The paper introduces a weighted residual-based approach for the numerical investigation of the interaction of fluid flow and thin flexible structures. The presented method enables one to treat strongly coupled systems involving large structural motion and deformation of multiple-flow-immersed solid objects. The fluid flow is described by the incompressible Navier-Stokes equations. The current configuration of the thin structure of linear elastic material with non-linear kinematics is mapped to the flow using the zero iso-contour of an updated level set function. The formulation of fluid, structure and coupling conditions uniformly uses velocities as unknowns. The integration of the weak form is performed on a space-time finite element discretization of the domain. Interfacial constraints of the multi-field problem are ensured by distributed Lagrange multipliers. The proposed formulation and discretization techniques lead to a monolithic algebraic system, well suited for strongly coupled fluid-structure systems. Embedding a thin structure into a flow results in non-smooth fields for the fluid. Based on the concept of the extended finite element method, the space-time approximations of fluid pressure and velocity are properly enriched to capture weakly and strongly discontinuous solutions. This leads to the present enriched space-time (EST) method. Numerical examples of fluid-structure interaction show the eligibility of the developed numerical approach in order to describe the behavior of such coupled systems. The test cases demonstrate the application of the proposed technique to problems where mesh moving strategies often fail. Copyright © 2007 John Wiley & Sons, Ltd. [less ▲]