Sabine Roller

Linearized acoustic perturbation equations for low Mach number flow with variable density and temperature

When the Mach number tends to zero the compressible Navier-Stokes equations converge to the incompressible Navier-Stokes equations, under the restrictions of constant density, constant temperature and no compression from the boundary. This is a singular limit in which the pressure of the compressible equations converges at leading order to a constant thermodynamic background pressure, while a hydrodynamic pressure term appears in the incompressible equations as a Lagrangian multiplier to establish the divergence-free condition for the velocity. In this paper we consider the more general case in which variable density, variable temperature and heat transfer are present, while the Mach number is small. We discuss first the limit equations for this case, when the Mach number tends to zero. The introduction of a pressure splitting into a thermodynamic and a hydrodynamic part allows the extension of numerical methods to the zero Mach number equations in these non-standard situations. The solution of these equations is then used as the state of expansion extending the expansion about incompressible flow proposed by Hardin and Pope [J.C. Hardin, D.S. Pope, An acoustic/viscous splitting technique for computational aeroacoustics, Theor. Comput. Fluid Dyn. 6 (1995) 323-340]. The resulting linearized equations state a mathematical model for the generation and propagation of acoustic waves in this more general low Mach number regime and may be used within a hybrid aeroacoustic approach.

Complex fluid simulations with the parallel tree-based Lattice Boltzmann solver Musubi

Abstract We present the open source Lattice Boltzmann solver Musubi . It is part of the parallel simulation framework APES , which utilizes octrees to represent sparse meshes and provides tools from automatic mesh generation to post-processing. The octree mesh representation enables the handling of arbitrarily complex simulation domains, even on massively parallel systems. Local grid refinement is implemented by several interpolation schemes in Musubi . Various kernels provide different physical models based on stream-collide algorithms. These models can be computed concurrently and can be coupled with each other. This paper explains our approach to provide a flexible yet scalable simulation environment and elaborates its design principles and implementation details. The efficiency of our approach is demonstrated with a performance evaluation on two supercomputers and a comparison to the widely used Lattice Boltzmann solver Palabos .

An Adaptable Simulation Framework Based on a Linearized Octree

This work presents the basic concepts of the simulation framework Apes, which allows for large scale distributed computations. The main idea of this framework is a commonly used data structure to represent the geometry for various physical solvers and their pre- and post- processing tools. To enable highly parallel computations in a mesh based simulation it is desirable to minimize the necessary local knowledge on each partition of the mesh about the global mesh and remote partitions. In order to achieve this goal of minimal required global information, an octree structure is chosen in the framework. This tree based elemental mesh builds the basis of the presented framework and is available as a Fortran library. Flexible configuration of the simulations is achieved by using the Lua scripting language for configuration files, which is wrapped in a convenience library to easily retrieve configuration data from the scripts in Fortran.

Lattice Boltzmann Simulation of non-Darcy Flow in Porous Media

Abstract Flow through porous media at low Reynolds numbers has been studied in detail with the Lattice Boltzmann Method (LBM) for applications such as groundwater flow, pollution transport or adsorption processes. In contrast to that, medium to high Reynolds number flow through porous media, which occurs in many areas of industrial engineering, has not yet widely been investigated on a microscopic level by detailed numerical simulations.In this paper, we focus on air flow through a porous medium, because our far goal entails the simulation of acoustic excitations from the turbulent flow leaving the porous medium. We validate the LBM at Reynolds numbers beyond the limit of Darcys law, and compare the results of direct numerical simulation with those achieved by applying a Smagorinsky-type large eddy turbulence model. For this, we performed flow simulations through a generic (periodic) porous medium at a variety of resolutions to investigate the effect of LES modelling at lower mesh sizes, where the subgrid scale effects become important.

Three-Dimensional Numerical Simulation of a 30-GHz Gyrotron Resonator With an Explicit High-Order Discontinuous-Galerkin-Based Parallel Particle-In-Cell Method

Fast design codes for the simulation of the particle-field interaction in the interior of gyrotron resonators are available. They procure their rapidity by making strong physical simplifications and approximations, which are not known to be valid for many variations of the geometry and the operating setup. For the first time, we apply a fully electromagnetic (EM) transient 3-D high-order discontinuous Galerkin particle-in-cell method solving the complete self-consistent nonlinear Vlasov-Maxwell equations to simulate a 30-GHz high-power millimeter-wave gyrotron resonator without physical reductions. This is a computational expensive endeavor, which requires todays high-performance computing capacity. However, this enables a detailed analysis of the EM field, the excited TE2,3 mode, the frequencies, and the azimuthal particle bunching in the beam. Therefrom, we present new insights into the complex particle-field interaction of the electron cyclotron maser instability transferring kinetic energy from the electron beam to the EM field.

Comparison of coupling techniques in a high-order discontinuous Galerkin-based particle-in-cell solver.

Highly rarefied plasma flows in technical devices are physically modelled by the Maxwell?Lorentz equations. They combine the solution of the Maxwell equations, where the electric field E and magnetic induction B are determined, with the Lorentz system, accounting for the movement of charged particles due to the electromagnetic forces. To solve these equations for complex-shaped domains, a fully electromagnetic particle-in-cell (PIC) code has been developed using high-order discontinuous Galerkin methods for the Maxwell equations on a computational mesh, coupled with a Lorentz solver on the basis of a second-order leapfrog scheme, acting on the particles at their current positions. Since the particles move freely in space, the mesh-based and the mesh-free values have to be coupled. This coupling includes the deposition of the charge and current densities from the current particle positions onto the mesh as well as the interpolation of the electromagnetic fields from the mesh to the actual particle positions. Both steps have to be computed with appropriate accuracy. Different approaches to particle-grid coupling within the PIC solver have been investigated. In this paper, these concepts are described and corresponding simulation results with respect to accuracy and computational demand are presented.

Dynamic Load Balancing for Unstructured Meshes on Space-Filling Curves

Load imbalance is an important impediment on the path towards higher degrees of parallelism - especially for engineering codes with their highly unstructured problem domains. In particular, when load conditions change dynamically, efficient mesh partitioning becomes an indispensable ingredient of scalable design. However, popular graph-based methods such as those used by ParMetis require global knowledge, which effectively limits the problem size on distributed-memory machines. On such architectures, space-filling curves (SFCs) offer a memory-efficient alternative and many sophisticated schemes have already been proposed. In this paper, we present a simple strategy based on SFCs that is custom-tailored to the needs of static meshes with dynamically changing computational load. Exploiting the properties of this class of problems, it is not only easy to implement but also reduces memory requirements substantially. Moreover, exclusively relying on MPI collective operations, our load-balancing scheme also offers portable performance across a broad range of HPC systems. Experimental evaluation shows excellent scaling behavior for up to 16,384 cores on a Nehalem-Infiniband system and up to 294,912 processes on a Blue Gene/P system.

CAF versus MPI - applicability of coarray fortran to a flow solver

We investigate how to use coarrays in Fortran (CAF) for parallelizing a flow solver and the capabilities of current compilers with coarray support. Usability and performance of CAF in mesh-based applications is examined and compared to traditional MPI strategies. We analyze the influence of the memory layout, the usage of communication buffers against direct access to the data used in the computation and different methods of the communication itself. Our objective is to provide insights on how common communication patterns have to be formulated when using coarrays.

A Multiscale Approach for the Coupled Simulation of Blood Flow and Thrombus Formation in Intracranial Aneurysms

This paper considers a multiscale description of thrombus formation and its simplified numerical implementation in the case of cerebral aneurysms. In particular, we extend previously introduced generic 2D models towards 3D patient specific aneurysm geometries. The multiscale amplification method contributes to considerably reducing simulation time. This allows us to achieve a mesh resolution high enough to resolve details of the stent geometry which is triggering flow conditions to induce clotting. Simulation results presented in this paper are qualitatively in a good agreement with clinical observations.

Towards aeroacoustic sound generation by flow through porous media

In this work, we present single-step aeroacoustic calculations using the Lattice Boltzmann method (LBM). Our application case consists of the prediction of an acoustic field radiating from the outlet of a porous media silencer. It has been proved that the LBM is able to simulate acoustic wave generation and propagation. Our particular aim is to validate the LBM for aeroacoustics in porous media. As a validation case, we consider a spinning vortex pair emitting sound waves as the vortices rotate around a common centre. Non-reflective boundary conditions based on characteristics have been adopted from Navier–Stokes methods and are validated using the time evolution of a Gaussian pulse. We show preliminary results of the flow through the porous medium.