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Item type:Publication, Access status: with files , Coupled clustering in hierarchical matrices for the oseen problemFluid flow problems can be modelled by the Navier-Stokes or, after linearization, by the Oseen equations. Their discretization results in discrete saddle point problems. These systems of equations are typically very large and need to be solved iteratively. Standard (block-) preconditioning techniques for saddle point problems rely on an approximation of the Schur complement. Such an approximation can be obtained by a hierarchical ((Formula presented.) -) matrix LU-decomposition which first approximates the Schur complement explicitly. The computational complexity of this computation depends, among other things, on the hierarchical block structure of the involved hierarchical matrices. However, widely used techniques do not consider the connection between the discretization grids for the velocity field and the pressure, respectively. Here we present a hierarchical block structure for the finite element discretization of the gradient operator which is improved by considering the connection between the two involved grids. We prove a logarithmic depth estimate for cluster trees generated with the coupled clustering. Numerical results will show that the improved block structure allows for a faster computation of the Schur complement which is the bottleneck for the set-up of the (Formula presented.) -matrix LU-decomposition. The presented coupled clustering is also applicable to other types of mixed (finite element) problems.Publicationtype: Journal Article34 39 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Incremental model order reduction of smoothed-particle hydrodynamic simulationsEngineering simulations are usually based on complex, grid-based, or mesh-free methods for solving partial differential equations. The results of these methods cover large fields of physical quantities at very many discrete spatial locations and temporal points. Efficient compression methods can be helpful for processing and reusing such large amounts of data. A compression technique is attractive if it causes only a small additional effort and the loss of information with strong compression is low. The paper presents the development of an incremental singular value decomposition (SVD) strategy for compressing time-dependent particle simulation results. The approach is based on an algorithm that was previously developed for grid-based, regular snapshot data matrices. It is further developed here to process highly irregular data matrices generated by particle simulation methods during simulation. Various aspects important for information loss, computational effort, and storage requirements are discussed, and corresponding solution techniques are investigated. These include the development of an adaptive rank truncation approach, the assessment of imputation strategies to close snapshot matrix gaps caused by temporarily inactive particles, a suggestion for sequencing the data history into temporal windows as well as bundling the SVD updates. The simulation-accompanying method is embedded in a parallel, industrialized smoothed-particle hydrodynamics software and applied to several 2D and 3D test cases. The proposed approach reduces the memory requirement by about 90% and increases the computational effort by about 10%, while preserving the required accuracy. For the final application of a water turbine, the temporal evolution of the force and torque values for the compressed and simulated data is in excellent agreement.Publicationtype: Journal Article20 28 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , A two-phase volume of fluid approach to model rigid-perfectly plastic granular materialsGranular flow problems characterized by large deformations are widespread in various applications, including coastal and geotechnical engineering. The paper deals with the application of a rigid-perfectly plastic two-phase model extended by the Drucker–Prager yield criterion to simulate granular media with a finite volume flow solver (FV). The model refers to the combination of a Bingham fluid and an Eulerian strain measure to assess the failure region of granular dam slides. A monolithic volume-of-fluid (VoF) method is used to distinguish between the air and granular phases, both governed by the incompressible Navier–Stokes equations. The numerical framework enables modeling of large displacements and arbitrary shapes for large-scale applications. The displayed validation and verification focuses on the rigid-perfectly plastic material model for noncohesive and cohesive materials with varying angles of repose. Results indicate a good agreement of the predicted soil surface and strain results with experimental and numerical data.Publicationtype: Journal Article20 41 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Adjoint shape sensitivities of blood flows considering non-newtonian propertiesThis article discusses the derivation and numerical implementation of an adjoint system, to the primal Navier–Stokes equations, for the computation of shape sensitivities of ducted blood flows considering non-Newtonian fluid properties. The ever-growing advancements in blood flow simulations are, naturally, accompanied by an increased interest in the optimization of related medical devices. In the majority of the computational studies, the Newtonian assumption is used to describe the rheology of blood. While this assumption has been shown to satisfactorily capture the flow when it is governed by high shear rates, it falls short at low shear rates. A rich variety of viscosity models has been proposed to tackle this shortcoming. In this article we show how such models can be incorporated into an adjoint system targeting to produce the shape sensitivity which can be used by a gradient-based optimization method for the minimization of an objective functional. A general formulation of the adjoint equations is proposed, in which contributions of the non-Newtonian properties explicitly occur. The numerical implementation is discussed and the validity of the method is assessed by means of numerical experiments of steady blood flows in a 2D stenosed duct, where results are compared against second-order finite-difference (FD) studies. The proposed methodology is then applied to CAD-free, gradient-based shape optimizations of an idealized 3D arterial bypass-graft operating at three relevant Reynolds numbers. It is observed that the impact of the adjoint viscosity treatment is amplified in low shear-rate flow regimes while fades for higher shear-rates, analogous to its primal counterpart.Publicationtype: Journal ArticleScopus© Citations 1 46 199 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Periodic hill flow simulations with a parameterized cumulant lattice Boltzmann methodThe article is concerned with the assessment of a cumulant lattice Boltzmann method in wall-bounded, separated turbulent shear flows. The approach is of interest for its resolution-spanning success in turbulent channel flows without using a specific turbulence treatment. The assessment focuses upon the flow over a periodic hill, which offers a rich basis of numerical and experimental data, for Reynolds numbers within (Formula presented.). The analysis involves the mean flow field, second moments and their invariants, as well as spectral data obtained for a wide range of resolutions with (Formula presented.). With the emphasis on a recently published parameterized cumulant collision operator, the universality of the value assigned to a stability preserving regularization parameter is assessed. Reported results guide resolution-dependent optimized values and indicate a required minimum resolution of (Formula presented.). Analog to the findings for attached turbulent shear flows, the approach appears to adequately resolve complex turbulent flows without the need for ad hoc modeling for a range of scale resolving resolutions.Publicationtype: Journal ArticleScopus© Citations 4 79 558 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , The simulation of turbulent particle-laden channel flow by the Lattice Boltzmann method(Wiley, 2015-06-01); ; ; ; We perform direct numerical simulation of three-dimensional turbulent flows in a rectangular channel, with a lattice Boltzmann method, efficiently implemented on heavily parallel general purpose graphical processor units. After validating the method for a single fluid, for standard boundary layer problems, we study changes in mean and turbulent properties of particle-laden flows, as a function of particle size and concentration. The problem of physical interest for this application is the effect of water droplets on the turbulent properties of a high-speed air flow, near a solid surface. To do so, we use a Lagrangian tracking approach for a large number of rigid spherical point particles, whose motion is forced by drag forces caused by the fluid flow; particle effects on the latter are in turn represented by distributed volume forces in the lattice Boltzmann method. Results suggest that, while mean flow properties are only slightly affected, unless a very large concentration of particles is used, the turbulent vortices present near the boundary are significantly damped and broken down by the turbulent motion of the heavy particles, and both turbulent Reynolds stresses and the production of turbulent kinetic energy are decreased because of the particle effects. We also find that the streamwise component of turbulent velocity fluctuations is increased, while the spanwise and wall-normal components are decreased, as compared with the single fluid channel case. Additionally, the streamwise velocity of the carrier (air) phase is slightly reduced in the logarithmic boundary layer near the solid walls.Publicationtype: Journal Article34 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , ℋ-LU factorization in preconditioners for augmented Lagrangian and grad-div stabilized saddle point systemsThe (mixed finite element) discretization of the linearized Navier-Stokes equations leads to a linear system of equations of saddle point type. The iterative solution of this linear system requires the construction of suitable preconditioners, especially in the case of high Reynolds numbers. In the past, a stabilizing approach has been suggested which does not change the exact solution but influences the accuracy of the discrete solution as well as the effectiveness of iterative solvers. This stabilization technique can be performed on the continuous side before the discretization, where it is known as 'grad-div' (GD) stabilization, as well as on the discrete side where it is known as an 'augmented Lagrangian' (AL) technique (and does not change the discrete solution). In this paper, we study the applicability of ℋ-LU factorizations to solve the arising subproblems in the different variants of stabilized saddle point systems. We consider both the saddle point systems that arise from the stabilization in the continuous as well as on the discrete setting. Recently, a modified AL preconditioner has been proposed for the system resulting from the discrete stabilization. We provide a straightforward generalization of this approach to the GD stabilization. We conclude the paper with numerical tests for a variety of problems to illustrate the behavior of the considered preconditioners as well as the suitability of ℋ-LU factorization in the preconditioners.Publicationtype: Journal Article174