Jonas Tölke

TeraFLOP computing on a desktop PC with GPUs for 3D CFD

A very efficient implementation of a lattice Boltzmann (LB) kernel in 3D on a graphical processing unit using the compute unified device architecture interface developed by nVIDIA is presented. By exploiting the explicit parallelism offered by the graphics hardware, we obtain an efficiency gain of up to two orders of magnitude with respect to the computational performance of a PC. A non-trivial example shows the performance of the LB implementation, which is based on a D3Q13 model that is described in detail.

Implementation of a Lattice Boltzmann kernel using the Compute Unified Device Architecture developed by nVIDIA

In this article a very efficient implementation of a 2D-Lattice Boltzmann kernel using the Compute Unified Device Architecture (CUDA™) interface developed by nVIDIA® is presented. By exploiting the explicit parallelism exposed in the graphics hardware we obtain more than one order in performance gain compared to standard CPUs. A non-trivial example, the flow through a generic porous medium, shows the performance of the implementation.

LARGE-EDDY SIMULATIONS WITH A MULTIPLE-RELAXATION-TIME LBE MODEL

We include Smagorinskys algebraic eddy viscosity approach into the multiple-relaxation-time (MRT) lattice Boltzmann equation (LBE) for large-eddy simulations (LES) of turbulent flows. The main advantage of the MRT-LBE model over the popular lattice BGK model is a significant improvement of numerical stability which leads to a substantial reduction of oscillations in the pressure field, especially for turbulent flow simulations near the numerical stability limit. The MRT-LBE model for LES is validated with a benchmark case of a surface mounted cube in a channel at Re = 40 000. Our preliminary results agree well with experimental data.

A LB-BASED APPROACH FOR ADAPTIVE FLOW SIMULATIONS

This paper presents an approach for adaptive flow simulations based on Lattice-Boltzmann (LB) models in the sense, that in addition to an a priori distribution of degrees of freedom (DOF) a dynamic modification of the computational grid (coarsening and/or refinement) in the course of the transient computation is initiated, based on the local evaluation of error indicators in order to optimize the ratio of accuracy versus absolute number of DOF. Using quadtree-based data structures, both arbitrarily formed grid interfaces of different resolutions as well as their dynamic modification are facilitated. Efficiency aspects will be discussed based on laminar two-dimensional flow simulations. The obtained results compare well to reference solutions cited in the literature and indicate the usefulness and computational efficiency of the approach.

An Agent-Based Coupling Platform for Complex Automata

The ability to couple distinct computational models of science and engineering systems is still a recurring challenge when developing multiphysics applications. The applied coupling technique is often dictated by various constraints (such as hard- and software requirements for the submodels to be coupled). This may lead to different coupling strategies/implementations in case a submodel has to be replaced in an existing coupled setup. Additional efforts are required when it comes to multiscale coupling. At least one of the submodels has to be modified to provide a matching interface on a specific spatial and temporal scale. In the present paper we describe a generic coupling mechanism/framework to reduce these common problems and to facilitate the development of multiscale simulations consisting of a multitude of submodels. The resulting implementation allows the coupling of legacy as well as dedicated codes with only minor adjustments. As the system is being build upon the JADE library, our platform fully supports computations on distributed heterogeneous hardware. We discuss the platforms capabilities by demonstrating the coupling of several cellular-automata kernels to model a coupled transport problem.

Lattice-Boltzmann simulations in reconstructed parametrized porous media

Computations of flows in explicitly resolved porous media reported in the literature so far are based on binarized porous media data mapped to uniform Cartesian grids. The voxel set is directly being used as the computational grid and thus the geometrical representation is usually only first-order accurate due to stair-case patterns. In this work, we pursue a more elaborate approach: starting from a highly resolved tomographic grey value data set we utilize a Marching Cube algorithm to reconstruct the surface of the porous medium as a set of planar triangles. The numerical resolution of the Cartesian grid for the simulation can then be chosen independently from the voxel set. As we take into account the subgrid distances between the nodes of the Cartesian grid and the planar triangle surfaces, one can utilize a second-order accurate lattice Boltzmann flow solver to efficiently compute, e.g. permeabilities. As these interpolation-based no-slip boundary conditions are not mass preserving, we also present a local modification of the no-slip boundary condition restoring mass conservation. Our numerical results demonstrate that for saturated flow simulations this coupled approach allows a substantial acceleration of saturated flow computations in porous media.

A Multigrid-Solver for the Discrete Boltzmann Equation

This paper introduces a nonlinear multigrid solution approach for the discrete Boltzmann equation discretized by an implicit second-order Finite Difference scheme. For simplicity we restrict the discussion to the stationary case. A numerical example shows the drastically improved efficiency in comparison to the widely used Lattice–Bathnagar–Gross–Krook (LBGK) approach.

Advection-diffusion lattice Boltzmann scheme for hierarchical grids

In this paper we describe an extension of a recently developed lattice Boltzmann method for solving the advection-diffusion equation. Our proposed approach allows to couple grids of different grid resolutions and includes a staggered timestepping scheme, interpolations in space and time and finally a scaling step ensuring the continuity of the desired macroscopic quantities across the grid interface. After validating the basic lattice Boltzmann method on a uniform grid by a convergence study of analytic problems we demonstrate the consistency of our approach by solving benchmark problems and comparing results on uniform grids and multiply locally refined grids.

Lattice-Boltzmann Method on Quadtree-Type Grids for Fluid-Structure Interaction

In this work a Lattice Boltzmann (LB) fluid flow solver based on unstructured quadtree/octree type Eulerian grids is coupled with a spectral Finite Element (p-FEM) structural mechanics solver based on a Lagrangian description to predict bidirectional fluid-structure interaction (FSI). The methods and algorithms are described in detail. Benchmark computations of a coupled transient problem of a 2D beam-like structure in a channel as defined by the DFG-Research Unit 493 are presented.

Second order interpolation of the flow field in the lattice Boltzmann method

We propose a scheme to reconstruct the flow field up to second order in a cell composed of four lattices nodes in 2 dimensions. The information contained in the higher order moments of the distribution functions is used to construct an interpolation scheme of second order for the velocity field.