arXiv subjects

Wolfgang A. Wall

Publications and source records attributed to Wolfgang A. Wall.

96 records · Page 6Linked to original sources

arXiv2016

A Unified Approach for Beam-to-Beam Contact

Existing beam contact formulations can be categorized in point contact models that consider a discrete contact force at the closest point of the beams, and line contact models that assume distributed contact forces. In this work, it will be shown that line contact formulations provide accurate and robust mechanical models in the range of small contact angles, whereas the computational efficiency considerably decreases with increasing contact angles. On the other hand, point contact formulations serve as sufficiently accurate and very efficient models in the regime of large contact angles, while they are not applicable for small contact angles as a consequence of non-unique closest point projections. In order to combine the advantages of these basic formulations, a novel all-angle beam contact (ABC) formulation is developed that applies a point contact formulation for large contact angles and a recently developed line contact formulation for small contact angles, the two being smoothly connected by means of a variationally consistent model transition. Based on a stringent analysis, two different transition laws are investigated, optimal algorithmic parameters are suggested and conservation of energy and momentum is shown. All configuration-dependent quantities are consistently linearized, thus allowing for their application within implicit time integration schemes. Furthermore, a step size control of the nonlinear solution scheme that allows for large displacement increments per time step and an efficient two-stage contact search based on dynamically adapted search segments are proposed. A series of numerical test cases is analyzed in order to verify the accuracy and consistency of the proposed contact model transition regarding contact force distributions and conservation properties, but also for quantifying the efficiency gains as compared to standard beam contact formulations.

cs.CE↗

arXiv2016

Unified computational framework for the efficient solution of n-field coupled problems with monolithic schemes

In this paper, we propose and evaluate the performance of a unified computational framework for preconditioning systems of linear equations resulting from the solution of coupled problems with monolithic schemes. The framework is composed by promising application-specific preconditioners presented previously in the literature with the common feature that they are able to be implemented for a generic coupled problem, involving an arbitrary number of fields, and to be used to solve a variety of applications. The first selected preconditioner is based on a generic block Gauss-Seidel iteration for uncoupling the fields, and standard algebraic multigrid (AMG) methods for solving the resulting uncoupled problems. The second preconditioner is based on the semi-implicit method for pressure-linked equations (SIMPLE) which is extended here to deal with an arbitrary number of fields, and also results in uncoupled problems that can be solved with standard AMG. Finally, a more sophisticated preconditioner is considered which enforces the coupling at all AMG levels, in contrast to the other two techniques which resolve the coupling only at the finest level. Our purpose is to show that these methods perform satisfactory in quite different scenarios apart from their original applications. To this end, we consider three very different coupled problems: thermo-structure interaction, fluid-structure interaction and a complex model of the human lung. Numerical results show that these general purpose methods are efficient and scalable in this range of applications.

math.NA↗

arXiv2016

A high-order semi-explicit discontinuous Galerkin solver for 3D incompressible flow with application to DNS and LES of turbulent channel flow

We present an efficient discontinuous Galerkin scheme for simulation of the incompressible Navier-Stokes equations including laminar and turbulent flow. We consider a semi-explicit high-order velocity-correction method for time integration as well as nodal equal-order discretizations for velocity and pressure. The non-linear convective term is treated explicitly while a linear system is solved for the pressure Poisson equation and the viscous term. The key feature of our solver is a consistent penalty term reducing the local divergence error in order to overcome recently reported instabilities in spatially under-resolved high-Reynolds-number flows as well as small time steps. This penalty method is similar to the grad-div stabilization widely used in continuous finite elements. We further review and compare our method to several other techniques recently proposed in literature to stabilize the method for such flow configurations. The solver is specifically designed for large-scale computations through matrix-free linear solvers including efficient preconditioning strategies and tensor-product elements, which have allowed us to scale this code up to 34.4 billion degrees of freedom and 147,456 CPU cores. We validate our code and demonstrate optimal convergence rates with laminar flows present in a vortex problem and flow past a cylinder and show applicability of our solver to direct numerical simulation as well as implicit large-eddy simulation of turbulent channel flow at $Re_τ=180$ as well as $590$.

math.NA↗

arXiv2016

A Finite Element Approach for the Line-to-Line Contact Interaction of Thin Beams with Arbitrary Orientation

The objective of this work is the development of a novel finite element formulation describing the contact interaction of slender beams in complex 3D configurations involving arbitrary beam-to-beam orientations. It is shown in a mathematically concise manner that standard beam contact models based on a point-wise contact force fail to describe a considerable range of configurations, which are, however, likely to occur in practical applications. On the contrary, the formulation proposed here models beam-to-beam contact by means of distributed line forces, a procedure that is shown to be applicable for arbitrary geometrical configurations. The proposed formulation is based on a Gauss-point-to-segment type contact discretization and a penalty regularization of the contact constraint. By means of detailed theoretical and numerical investigations, it is shown that this approach is more suitable for beam contact than possible alternatives based on mortar type contact discretizations or constraint enforcement by means of Lagrange multipliers. The proposed formulation is enhanced by a consistently linearized integration interval segmentation avoiding numerical integration across strong discontinuities. In combination with a smoothed contact force law and the employed C1-continuous beam elements, this procedure drastically reduces the numerical integration error, an essential prerequisite for optimal spatial convergence rates. The resulting line-to-line contact algorithm is supplemented by contact contributions of the beam endpoints, which represent boundary minima of the underlying minimal distance problem. Finally, a series of numerical test cases is analyzed in order to investigate the accuracy and consistency of the proposed formulation regarding integration error, spatial convergence behavior and resulting contact force distributions.

cs.CE↗

arXiv2015

A cut-cell finite volume - finite element coupling approach for fluid-structure interaction in compressible flow

We present a loosely coupled approach for the solution of fluid-structure interaction problems between a compressible flow and a deformable structure. The method is based on staggered Dirichlet-Neumann partitioning. The interface motion in the Eulerian frame is accounted for by a conservative cut-cell Immersed Boundary method. The present approach enables sub-cell resolution by considering individual cut-elements within a single fluid cell, which guarantees an accurate representation of the time-varying solid interface. The cut-cell procedure inevitably leads to non-matching interfaces, demanding for a special treatment. A Mortar method is chosen in order to obtain a conservative and consistent load transfer. We validate our method by investigating two-dimensional test cases comprising a shock-loaded rigid cylinder and a deformable panel. Moreover, the aeroelastic instability of a thin plate structure is studied with a focus on the prediction of flutter onset. Finally, we propose a three-dimensional fluid-structure interaction test case of a flexible inflated thin shell interacting with a shock wave involving large and complex structural deformations.

math.NA↗

arXiv2015

A new approach to wall modeling in LES of incompressible flow via function enrichment

A novel approach to wall modeling for the incompressible Navier-Stokes equations including flows of moderate and large Reynolds numbers is presented. The basic idea is that a problem-tailored function space allows prediction of turbulent boundary layer gradients with very coarse meshes. The proposed function space consists of a standard polynomial function space plus an enrichment, which is constructed using Spalding's law-of-the-wall. The enrichment function is not enforced but "allowed" in a consistent way and the overall methodology is much more general and also enables other enrichment functions. The proposed method is closely related to detached-eddy simulation as near-wall turbulence is modeled statistically and large eddies are resolved in the bulk flow. Interpreted in terms of a three-scale separation within the variational multiscale method, the standard scale resolves large eddies and the enrichment scale represents boundary layer turbulence in an averaged sense. The potential of the scheme is shown applying it to turbulent channel flow of friction Reynolds numbers from $Re_τ=590$ and up to $5,000$, flow over periodic constrictions at the Reynolds numbers $Re_H=10,595$ and $19,000$ as well as backward-facing step flow at $Re_h=5,000$, all with extremely coarse meshes. Excellent agreement with experimental and DNS data is observed with the first grid point located at up to $y_1^+=500$ and especially under adverse pressure gradients as well as in separated flows.

physics.flu-dyn↗