This paper proposes a computational methodology that allows a direct numerical simulation of hete... more This paper proposes a computational methodology that allows a direct numerical simulation of heterogeneous/functionally graded materials based on V-reps/V-models and the Finite Cell Method (FCM). The FCM is an embedded domain approach that employs higher-order finite elements. The basic idea is to embed a complex geometric model into a fictitious domain that is trivial to mesh. The complexity of the geometry is then recaptured by an adapted precise numerical integration scheme for the elements cut by the boundary. For this, only a robust point inclusion test is required, which can be provided by various Computer-Aided Design (CAD) models. V-rep is a geometric modeling framework that represents the entire volume based on tri-variate B-Splines. Consequently, not only a point inclusion test is provided – but also the possibility to represent and model the interior domain. This allows to apply functionally graded material based on the tri-variate basis functions. These material parameters...
International Journal of Structural Stability and Dynamics, 2015
In this contribution, the finite cell method (FCM) is applied to solve transient problems of line... more In this contribution, the finite cell method (FCM) is applied to solve transient problems of linear elastodynamics. The mathematical formulation of FCM for linear elastodynamics is presented, following from the weak formulation of the initial/boundary-value problem. Semi-discrete time integration schemes are briefly discussed, and the choice of implicit time integration is justified. A 1D benchmark problem is solved using FCM, illustrating the method's ability to solve problems of linear elastodynamics obtaining high rates of convergence. Furthermore, a numerical example of transient analysis from an industrial application is solved using FCM. The numerical results are compared to the results obtained using state-of-the-art commercial software, employing linear finite elements, in conjunction with explicit time integration. The results illustrate the potential of FCM as a powerful tool for transient analysis in elastodynamics, offering a high degree of accuracy at a moderate com...
Lecture Notes in Computational Science and Engineering
In this contribution the use of hexahedral elements for the structural simulation in a fluid stru... more In this contribution the use of hexahedral elements for the structural simulation in a fluid structure interaction framework is presented, resulting in a consistent kinematic and geometric description of the solid. In order to compensate the additional numerical effort of the three-dimensional approach, an anisotropic p-adaptive method for linear elastodynamic problems is proposed, resulting in a clearly higher efficiency and higher convergence rates than uniform p-extensions. Special emphasis is placed on the accurate transfer of loads considering the fluid discretization for computation of the surface load integrals. For a coupling with a cartesian grid based Lattice Boltzmann code it was found that oscillations in the interface tractions may excite higher structural modes possibly leading to a nonstable coupling behavior. A first remedy to this problem was a linear modal analysis of the structure, thus allowing to control the number of modes to be considered without disregarding bidirectional fluid structure interactions. Preliminary results are presented for the FSI benchmark configuration proposed in this book.
After a short discussion of recent discretization techniques for the lattice-Boltzmann equations ... more After a short discussion of recent discretization techniques for the lattice-Boltzmann equations we motivate and discuss some alternative approaches using implicit, nonuniform FD discretization and mesh refinement techniques. After presenting results of a stability analysis we use an implicit approach to simulate a boundary layer test problem. The numerical results compare well to the reference solution when using strongly refined meshes. Some basic ideas for a nonuniform mesh refinement (with non-cartesian mesh topology) are introduced using the standard discretization procedure of alternating collision and propagation.
The development of flow instabilities due to high Reynolds number flow in artificial heart valve ... more The development of flow instabilities due to high Reynolds number flow in artificial heart valve geometries inducing high strain rates and stresses often leads to hemolysis and related highly undesired effects. Geometric and functional optimization of artificial heart valves is therefore mandatory. In addition to experimental work in this field it is meanwhile possible to obtain increasing insight into flow dynamics by computer simulation of refined model problems. After giving an introductory overview we report the results of the simulation of three-dimensional transient physiological flows in fixed geometries similar to a CarboMedics bileaflet heart valve at different opening angles. The visualization of emerging complicated flow patterns gives detailed information about the transient history of the systems dynamical stability. Stress analysis indicates temporal shear stress peaks even far away from walls. The mathematical approach used is the Lattice Boltzmann method. We obtained reasonable results for velocity and shear stress fields. The code is implemented on parallel hardware in order to decrease computation time. Finally, we discuss problems, shortcomings and possible extensions of our approach.
... to give reasonable results, when the solids velocity is small compared to the lattice distanc... more ... to give reasonable results, when the solids velocity is small compared to the lattice distance times ... goal was to test the suitability of LB methods for a coupled fluidstructure flow problem in ... presented here using the LB method gave reasonable results for the prediction of velocity ...
This paper proposes a computational methodology that allows a direct numerical simulation of hete... more This paper proposes a computational methodology that allows a direct numerical simulation of heterogeneous/functionally graded materials based on V-reps/V-models and the Finite Cell Method (FCM). The FCM is an embedded domain approach that employs higher-order finite elements. The basic idea is to embed a complex geometric model into a fictitious domain that is trivial to mesh. The complexity of the geometry is then recaptured by an adapted precise numerical integration scheme for the elements cut by the boundary. For this, only a robust point inclusion test is required, which can be provided by various Computer-Aided Design (CAD) models. V-rep is a geometric modeling framework that represents the entire volume based on tri-variate B-Splines. Consequently, not only a point inclusion test is provided – but also the possibility to represent and model the interior domain. This allows to apply functionally graded material based on the tri-variate basis functions. These material parameters...
International Journal of Structural Stability and Dynamics, 2015
In this contribution, the finite cell method (FCM) is applied to solve transient problems of line... more In this contribution, the finite cell method (FCM) is applied to solve transient problems of linear elastodynamics. The mathematical formulation of FCM for linear elastodynamics is presented, following from the weak formulation of the initial/boundary-value problem. Semi-discrete time integration schemes are briefly discussed, and the choice of implicit time integration is justified. A 1D benchmark problem is solved using FCM, illustrating the method's ability to solve problems of linear elastodynamics obtaining high rates of convergence. Furthermore, a numerical example of transient analysis from an industrial application is solved using FCM. The numerical results are compared to the results obtained using state-of-the-art commercial software, employing linear finite elements, in conjunction with explicit time integration. The results illustrate the potential of FCM as a powerful tool for transient analysis in elastodynamics, offering a high degree of accuracy at a moderate com...
Lecture Notes in Computational Science and Engineering
In this contribution the use of hexahedral elements for the structural simulation in a fluid stru... more In this contribution the use of hexahedral elements for the structural simulation in a fluid structure interaction framework is presented, resulting in a consistent kinematic and geometric description of the solid. In order to compensate the additional numerical effort of the three-dimensional approach, an anisotropic p-adaptive method for linear elastodynamic problems is proposed, resulting in a clearly higher efficiency and higher convergence rates than uniform p-extensions. Special emphasis is placed on the accurate transfer of loads considering the fluid discretization for computation of the surface load integrals. For a coupling with a cartesian grid based Lattice Boltzmann code it was found that oscillations in the interface tractions may excite higher structural modes possibly leading to a nonstable coupling behavior. A first remedy to this problem was a linear modal analysis of the structure, thus allowing to control the number of modes to be considered without disregarding bidirectional fluid structure interactions. Preliminary results are presented for the FSI benchmark configuration proposed in this book.
After a short discussion of recent discretization techniques for the lattice-Boltzmann equations ... more After a short discussion of recent discretization techniques for the lattice-Boltzmann equations we motivate and discuss some alternative approaches using implicit, nonuniform FD discretization and mesh refinement techniques. After presenting results of a stability analysis we use an implicit approach to simulate a boundary layer test problem. The numerical results compare well to the reference solution when using strongly refined meshes. Some basic ideas for a nonuniform mesh refinement (with non-cartesian mesh topology) are introduced using the standard discretization procedure of alternating collision and propagation.
The development of flow instabilities due to high Reynolds number flow in artificial heart valve ... more The development of flow instabilities due to high Reynolds number flow in artificial heart valve geometries inducing high strain rates and stresses often leads to hemolysis and related highly undesired effects. Geometric and functional optimization of artificial heart valves is therefore mandatory. In addition to experimental work in this field it is meanwhile possible to obtain increasing insight into flow dynamics by computer simulation of refined model problems. After giving an introductory overview we report the results of the simulation of three-dimensional transient physiological flows in fixed geometries similar to a CarboMedics bileaflet heart valve at different opening angles. The visualization of emerging complicated flow patterns gives detailed information about the transient history of the systems dynamical stability. Stress analysis indicates temporal shear stress peaks even far away from walls. The mathematical approach used is the Lattice Boltzmann method. We obtained reasonable results for velocity and shear stress fields. The code is implemented on parallel hardware in order to decrease computation time. Finally, we discuss problems, shortcomings and possible extensions of our approach.
... to give reasonable results, when the solids velocity is small compared to the lattice distanc... more ... to give reasonable results, when the solids velocity is small compared to the lattice distance times ... goal was to test the suitability of LB methods for a coupled fluidstructure flow problem in ... presented here using the LB method gave reasonable results for the prediction of velocity ...
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