arXiv subjects

Ulrich Rüde

Publications and source records attributed to Ulrich Rüde.

At least 73 records · Page 4Linked to original sources

arXiv2016

Curvature estimation from a volume of fluid indicator function for the simulation of surface tension and wetting with a free surface lattice Boltzmann method

The free surface lattice Boltzmann method (FSLBM) is a combination of the hydrodynamic lattice Boltzmann method (LBM) with a volume of fluid (VOF) interface apturing technique for the simulation of incompressible free surface flows. Capillary effects are modeled by extracting the curvature of the interface from the VOF indicator function and imposing a pressure jump at the free boundary. However, obtaining accurate curvature estimates from a VOF description can introduce significant errors. This article reports numerical results for three different surface tension models in standard test cases, and compares the according errors in the velocity field (spurious currents). Furthermore, the FSLBM is shown to be suited to simulate wetting effects at solid boundaries. To this end, a new method is developed to represent wetting boundary conditions in a least squares curvature econstruction technique. The main limitations of the current FSLBM are analyzed and are found to be caused by its simplified advection scheme. Possible improvements are suggested.

physics.flu-dyn↗

arXiv2016

Massively Parallel Algorithms for the Lattice Boltzmann Method on Non-uniform Grids

The lattice Boltzmann method exhibits excellent scalability on current supercomputing systems and has thus increasingly become an alternative method for large-scale non-stationary flow simulations, reaching up to a trillion grid nodes. Additionally, grid refinement can lead to substantial savings in memory and compute time. These saving, however, come at the cost of much more complex data structures and algorithms. In particular, the interface between subdomains with different grid sizes must receive special treatment. In this article, we present parallel algorithms, distributed data structures, and communication routines that are implemented in the software framework waLBerla in order to support large-scale, massively parallel lattice Boltzmann-based simulations on non-uniform grids. Additionally, we evaluate the performance of our approach on two current petascale supercomputers. On an IBM Blue Gene/Q system, the largest weak scaling benchmarks with refined grids are executed with almost two million threads, demonstrating not only near-perfect scalability but also an absolute performance of close to a trillion lattice Boltzmann cell updates per second. On an Intel-based system, the strong scaling of a simulation with refined grids and a total of more than 8.5 million cells is demonstrated to reach a performance of less than one millisecond per time step. This enables simulations with complex, non-uniform grids and four million time steps per hour compute time.

cs.DC↗

arXiv2015

A Python Extension for the Massively Parallel Multiphysics Simulation Framework waLBerla

We present a Python extension to the massively parallel HPC simulation toolkit waLBerla. waLBerla is a framework for stencil based algorithms operating on block-structured grids, with the main application field being fluid simulations in complex geometries using the lattice Boltzmann method. Careful performance engineering results in excellent node performance and good scalability to over 400,000 cores. To increase the usability and flexibility of the framework, a Python interface was developed. Python extensions are used at all stages of the simulation pipeline: They simplify and automate scenario setup, evaluation, and plotting. We show how our Python interface outperforms the existing text-file-based configuration mechanism, providing features like automatic nondimensionalization of physical quantities and handling of complex parameter dependencies. Furthermore, Python is used to process and evaluate results while the simulation is running, leading to smaller output files and the possibility to adjust parameters dependent on the current simulation state. C++ data structures are exported such that a seamless interfacing to other numerical Python libraries is possible. The expressive power of Python and the performance of C++ make development of efficient code with low time effort possible.

cs.DC↗

arXiv2015

Solution Techniques for the Stokes System: A priori and a posteriori modifications, resilient algorithms

This article proposes modifications to standard low order finite element approximations of the Stokes system with the goal of improving both the approximation quality and the parallel algebraic solution process. Different from standard finite element techniques, we do not modify or enrich the approximation spaces but modify the operator itself to ensure fundamental physical properties such as mass and energy conservation. Special local a~priori correction techniques at re-entrant corners lead to an improved representation of the energy in the discrete system and can suppress the global pollution effect. Local mass conservation can be achieved by an a~posteriori correction to the finite element flux. This avoids artifacts in coupled multi-physics transport problems. Finally, hardware failures in large supercomputers may lead to a loss of data in solution subdomains. Within parallel multigrid, this can be compensated by the accelerated solution of local subproblems. These resilient algorithms will gain importance on future extreme scale computing systems.

math.NA↗

arXiv2015

A quantitative performance analysis for Stokes solvers at the extreme scale

This article presents a systematic quantitative performance analysis for large finite element computations on extreme scale computing systems. Three parallel iterative solvers for the Stokes system, discretized by low order tetrahedral elements, are compared with respect to their numerical efficiency and their scalability running on up to $786\,432$ parallel threads. A genuine multigrid method for the saddle point system using an Uzawa-type smoother provides the best overall performance with respect to memory consumption and time-to-solution. The largest system solved on a Blue Gene/Q system has more than ten trillion ($1.1 \cdot 10 ^{13}$) unknowns and requires about 13 minutes compute time. Despite the matrix free and highly optimized implementation, the memory requirement for the solution vector and the auxiliary vectors is about 200 TByte. Brandt's notion of "textbook multigrid efficiency" is employed to study the algorithmic performance of iterative solvers. A recent extension of this paradigm to "parallel textbook multigrid efficiency" makes it possible to assess also the efficiency of parallel iterative solvers for a given hardware architecture in absolute terms. The efficiency of the method is demonstrated for simulating incompressible fluid flow in a pipe filled with spherical obstacles.

cs.CE↗

arXiv2015

Pore-scale lattice Boltzmann simulation of laminar and turbulent flow through a sphere pack

The lattice Boltzmann method can be used to simulate flow through porous media with full geometrical resolution. With such a direct numerical simulation, it becomes possible to study fundamental effects which are difficult to assess either by developing macroscopic mathematical models or experiments. We first evaluate the lattice Boltzmann method with various boundary handling of the solid-wall and various collision operators to assess their suitability for large scale direct numerical simulation of porous media flow. A periodic pressure drop boundary condition is used to mimic the pressure driven flow through the simple sphere pack in a periodic domain. The evaluation of the method is done in the Darcy regime and the results are compared to a semi-analytic solution. Taking into account computational cost and accuracy, we choose the most efficient combination of the solid boundary condition and collision operator. We apply this method to perform simulations for a wide range of Reynolds numbers from Stokes flow over seven orders of magnitude to turbulent flow. Contours and streamlines of the flow field are presented to show the flow behavior in different flow regimes. Moreover, unknown parameters of the Forchheimer, the Barree--Conway and friction factor models are evaluated numerically for the considered flow regimes.

cs.CE↗

arXiv2015

Large scale lattice Boltzmann simulation for the coupling of free and porous media flow

In this work, we investigate the interaction of free and porous media flow by large scale lattice Boltzmann simulations. We study the transport phenomena at the porous interface on multiple scales, i.e., we consider both, computationally generated pore-scale geometries and homogenized models at a macroscopic scale. The pore-scale results are compared to those obtained by using different transmission models. Two-domain approaches with sharp interface conditions, e.g., of Beavers--Joseph--Saffman type, as well as a single-domain approach with a porosity depending viscosity are taken into account. For the pore-scale simulations, we use a highly scalable communication-reducing scheme with a robust second order boundary handling. We comment on computational aspects of the pore-scale simulation and on how to generate pore-scale geometries. The two-domain approaches depend sensitively on the choice of the exact position of the interface, whereas a well-designed single-domain approach can significantly better recover the averaged pore-scale results.

cs.CE↗

arXiv2015

Resilience for Multigrid Software at the Extreme Scale

Fault tolerant algorithms for the numerical approximation of elliptic partial differential equations on modern supercomputers play a more and more important role in the future design of exa-scale enabled iterative solvers. Here, we combine domain partitioning with highly scalable geometric multigrid schemes to obtain fast and fault-robust solvers in three dimensions. The recovery strategy is based on a hierarchical hybrid concept where the values on lower dimensional primitives such as faces are stored redundantly and thus can be recovered easily in case of a failure. The lost volume unknowns in the faulty region are re-computed approximately with multigrid cycles by solving a local Dirichlet problem on the faulty subdomain. Different strategies are compared and evaluated with respect to performance, computational cost, and speed up. Especially effective are strategies in which the local recovery in the faulty region is executed in parallel with global solves and when the local recovery is additionally accelerated. This results in an asynchronous multigrid iteration that can fully compensate faults. Excellent parallel performance on a current peta-scale system is demonstrated.

cs.MS↗

arXiv2015

Massively Parallel Phase-Field Simulations for Ternary Eutectic Directional Solidification

Microstructures forming during ternary eutectic directional solidification processes have significant influence on the macroscopic mechanical properties of metal alloys. For a realistic simulation, we use the well established thermodynamically consistent phase-field method and improve it with a new grand potential formulation to couple the concentration evolution. This extension is very compute intensive due to a temperature dependent diffusive concentration. We significantly extend previous simulations that have used simpler phase-field models or were performed on smaller domain sizes. The new method has been implemented within the massively parallel HPC framework waLBerla that is designed to exploit current supercomputers efficiently. We apply various optimization techniques, including buffering techniques, explicit SIMD kernel vectorization, and communication hiding. Simulations utilizing up to 262,144 cores have been run on three different supercomputing architectures and weak scalability results are shown. Additionally, a hierarchical, mesh-based data reduction strategy is developed to keep the I/O problem manageable at scale.

cs.DC↗

arXiv2015

Numerical Investigations on Hatching Process Strategies for Powder Bed Based Additive Manufacturing using an Electron Beam

This paper investigates in hatching process strategies for additive manufacturing using an electron beam by numerical simulations. The underlying physical model and the corresponding three dimensional thermal free surface lattice Boltzmann method of the simulation software are briefly presented. The simulation software has already been validated on the basis of experiments up to 1.2 kW beam power by hatching a cuboid with a basic process strategy, whereby the results are classified into `porous', `good' and `uneven', depending on their relative density and top surface smoothness. In this paper we study the limitations of this basic process strategy in terms of higher beam powers and scan velocities to exploit the future potential of high power electron beam guns up to 10 kW. Subsequently, we introduce modified process strategies, which circumvent these restrictions, to build the part as fast as possible under the restriction of a fully dense part with a smooth top surface. These process strategies are suitable to reduce the build time and costs, maximize the beam power usage and therefore use the potential of high power electron beam guns.

cs.CE↗

arXiv2015

Two Computational Models for Simulating the Tumbling Motion of Elongated Particles in Fluids

Suspensions with fiber-like particles in the low Reynolds number regime are modeled by two different approaches that both use a Lagrangian representation of individual particles. The first method is the well-established formulation based on Stokes flow that is formulated as integral equations. It uses a slender body approximation for the fibers to represent the interaction between them directly without explicitly computing the flow field. The second is a new technique using the 3D lattice Boltzmann method on parallel supercomputers. Here the flow computation is coupled to a computational model of the dynamics of rigid bodies using fluid-structure interaction techniques. Both methods can be applied to simulate fibers in fluid flow. They are carefully validated and compared against each other, exposing systematically their strengths and weaknesses regarding their accuracy, the computational cost, and possible model extensions.

cs.CE↗

arXiv2015

Boundary Conditions for Free Interfaces with the Lattice Boltzmann Method

In this paper we analyze the boundary treatment of the lattice Boltzmann method (LBM) for simulating 3D flows with free surfaces. The widely used free surface boundary condition of Körner et al. (2005) is shown to be first order accurate. The article presents a new free surface boundary scheme that is suitable for second order accurate simulations based on the LBM. The new method takes into account the free surface position and its orientation with respect to the computational lattice. Numerical experiments confirm the theoretical findings and illustrate the different behavior of the original method and the new method.

math.NA↗

arXiv2015

Resilience for Exascale Enabled Multigrid Methods

With the increasing number of components and further miniaturization the mean time between faults in supercomputers will decrease. System level fault tolerance techniques are expensive and cost energy, since they are often based on redundancy. Also classical check-point-restart techniques reach their limits when the time for storing the system state to backup memory becomes excessive. Therefore, algorithm-based fault tolerance mechanisms can become an attractive alternative. This article investigates the solution process for elliptic partial differential equations that are discretized by finite elements. Faults that occur in the parallel geometric multigrid solver are studied in various model scenarios. In a standard domain partitioning approach, the impact of a failure of a core or a node will affect one or several subdomains. Different strategies are developed to compensate the effect of such a failure algorithmically. The recovery is achieved by solving a local subproblem with Dirichlet boundary conditions using local multigrid cycling algorithms. Additionally, we propose a superman strategy where extra compute power is employed to minimize the time of the recovery process.

cs.CE↗

arXiv2015

Ultrascale Simulations of Non-smooth Granular Dynamics

This article presents new algorithms for massively parallel granular dynamics simulations on distributed memory architectures using a domain partitioning approach. Collisions are modelled with hard contacts in order to hide their micro-dynamics and thus to extend the time and length scales that can be simulated. The multi-contact problem is solved using a non-linear block Gauss-Seidel method that is conforming to the subdomain structure. The parallel algorithms employ a sophisticated protocol between processors that delegate algorithmic tasks such as contact treatment and position integration uniquely and robustly to the processors. Communication overhead is minimized through aggressive message aggregation, leading to excellent strong and weak scaling. The robustness and scalability is assessed on three clusters including two peta-scale supercomputers with up to 458752 processor cores. The simulations can reach unprecedented resolution of up to ten billion non-spherical particles and contacts.

cs.CE↗

arXiv2014

Parallel Multiphysics Simulations of Charged Particles in Microfluidic Flows

The article describes parallel multiphysics simulations of charged particles in microfluidic flows with the waLBerla framework. To this end, three physical effects are coupled: rigid body dynamics, fluid flow modelled by a lattice Boltzmann algorithm, and electric potentials represented by a finite volume discretisation. For solving the finite volume discretisation for the electrostatic forces, a cell-centered multigrid algorithm is developed that conforms to the lattice Boltzmann meshes and the parallel communication structure of waLBerla. The new functionality is validated with suitable benchmark scenarios. Additionally, the parallel scaling and the numerical efficiency of the algorithms are analysed on an advanced supercomputer.

cs.CE↗

arXiv2014

Drag correlation for dilute and moderately dense fluid-particle systems using the lattice Boltzmann method

This paper presents a numerical study of flow through static random assemblies of monodisperse, spherical particles. A lattice Boltzmann approach based on a two relaxation time collision operator is used to obtain reliable predictions of the particle drag by direct numerical simulation. From these predictions a closure law $F(Re, φ)$ of the drag force relationship to the bed density $φ$ and the particle Reynolds number $Re$ is derived. The present study includes densities $φ$ ranging from $0.01$ to $0.35$ with Re ranging up to $300$, that is compiled into a single drag correlation valid for the whole range. The corelation has a more compact expression compared to others previously reported in literature. At low particle densities, the new correlation is close to the widely used Wen & Yu - correlation. Recently, there has been reported a discrepancy between results obtained using different numerical methods, namely the comprehensive lattice Boltzmann study of Beetstra et al. (2007) and the predictions based on an immersed boundary - pseudo-spectral Navier-Stokes approach (Tenneti et al., 2011). The present study excludes significant finite resolution effects, which have been suspected to cause the reported deviations, but does not coincide exactly with either of the previous studies. This indicates the need for yet more accurate simulation methods in the future.

physics.flu-dyn↗

arXiv2014

Validation Experiments for LBM Simulations of Electron Beam Melting

This paper validates 3D simulation results of electron beam melting (EBM) processes comparing experimental and numerical data. The physical setup is presented which is discretized by a three dimensional (3D) thermal lattice Boltzmann method (LBM). An experimental process window is used for the validation depending on the line energy injected into the metal powder bed and the scan velocity of the electron beam. In the process window the EBM products are classified into the categories, porous, good and swelling, depending on the quality of the surface. The same parameter sets are used to generate a numerical process window. A comparison of numerical and experimental process windows shows a good agreement. This validates the EBM model and justifies simulations for future improvements of EBM processes. In particular numerical simulations can be used to explain future process window scenarios and find the best parameter set for a good surface quality and dense products.

cs.CE↗

arXiv2012

Permeability of porous materials determined from the Euler characteristic

We study the permeability of quasi two-dimensional porous structures of randomly placed overlapping monodisperse circular and elliptical grains. Measurements in microfluidic devices and lattice Boltzmann simulations demonstrate that the permeability is determined by the Euler characteristic of the conducting phase. We obtain an expression for the permeability that is independent of the percolation threshold and shows agreement with experimental and simulated data over a wide range of porosities. Our approach suggests that the permeability explicitly depends on the overlapping probability of grains rather than their shape.

physics.flu-dyn↗