Manfred Krafczyk

Analysis of 3D transient blood flow passing through an artificial aortic valve by Lattice–Boltzmann methods

The development of flow instabilities due to high Reynolds number flow in artificial heart valve geometries inducing high strain rates and stresses often leads to hemolysis and related highly undesired effects. Geometric and functional optimization of artificial heart valves is therefore mandatory. In addition to experimental work in this field it is meanwhile possible to obtain increasing insight into flow dynamics by computer simulation of refined model problems. After giving an introductory overview we report the results of the simulation of three-dimensional transient physiological flows in fixed geometries similar to a CarboMedics bileaflet heart valve at different opening angles. The visualization of emerging complicated flow patterns gives detailed information about the transient history of the systems dynamical stability. Stress analysis indicates temporal shear stress peaks even far away from walls. The mathematical approach used is the Lattice Boltzmann method. We obtained reasonable results for velocity and shear stress fields. The code is implemented on parallel hardware in order to decrease computation time. Finally, we discuss problems, shortcomings and possible extensions of our approach.

Two-dimensional simulation of fluid–structure interaction using lattice-Boltzmann methods

Abstract The development of flow instabilities due to high Reynolds number flow in artificial heart-value geometries inducing high strain rates and stresses often leads to hemolysis and related highly undesired effects. Geometric and functional optimization of artificial heart valves is therefore mandatory. In addition to experimental work in this field it is meanwhile possible to obtain increasing insight into flow dynamics by computer simulation of refined model problems. Here we present two-dimensional simulation results of the coupled fluid–structure problem defined by a model geometry of an artificial heart value with moving leaflets exposed to a channel flow driven by transient boundary conditions representing a physiologically relevant regime. A modified lattice-Boltzmann approach is used to solve the coupled problem.

Parallelization Strategies and Efficiency of CFD Computations in Complex Geometries Using Lattice Boltzmann Methods on High-Performance Computers

A frequently stated property of the Lattice Boltzmann (LB) method is, that it is easy to implement and that the generation of computational grids is trivial even for three-dimensional problems. This is mainly due to the usually chosen approach of using full matrices to store the primary variables of the scheme. However this kind of implementation has severe disadvantages for simulations, where the volume of the bounding box of the flow domain is large compared to the actual volume of the flow domain. Thus the authors developed data structures which allow to discretize only the fluid volume including boundary conditions to minimize memory requirements, while retaining the excellent performance with respect to vectorization of standard LB-implementations on supercomputers. Due to extensive communication hiding using asynchronous non-blocking message transfer an almost linear parallel speedup is achieved

Discretization of the Boltzmann equation in velocity space using a Galerkin approach

A method for the discretization of the Boltzmann equation in velocity space via a Galerkin procedure with Hermite polynomials as trial and test functions is proposed. This procedure results in a set of partial differential equations, which is an alternative to the lattice-Boltzmann equations. These PDEs are discretized using an explicit finite difference scheme and a numerical example shows the validity of the approach.

Lattice‐gas simulations of two‐phase flow in porous media

Nearly all CFD methods can be considered as discretization methods for partial differential equations, such as finite difference, finite volume, finite element, spectral or boundary integral element methods. Virtually unrecognized by the scientific mainstream in computational fluid dynamics (CFD) during the last decade, a completely different approach to flow simulation has been developed in computational physics. n n n nThe basic idea of lattice-gas solvers (LGS) goes back to the cellular automation concept of John von Neumann. LGS use objects (‘cells’), being extremely simple compared to finite boxes or finite elements. The state of a cell is usually described by only a few bits therefore often two orders of magnitude more cells are used for a simulation with LGS than ‘elements’ in a finite element computation. LGS are explicit time-stepping procedures; no equation systems have to be solved. Thus every time-step is extremely cheap in terms of CPU power compared to standard procedures, yet again much shorter time-steps have to be used. LGS are inherently parallel and are suitable to coarse-grain as well as to fine-grain parallelization. n n n nThe paper will discuss some advantages and disadvantages of lattice-gas solvers and present LG simulation results of two-phase flow with moving boundaries on a microscope scale for a two-dimensional test geometry of randomly distributed equally sized disks where the effect of surface tension on the steady-state saturation will be demonstrated.

Efficient Simulation of Transient Heat Transfer Problems in Civil Engineering

Heat transport problems arise in many fields of civil engineering e.g. indoor climate comfort, building insulation, HVAC (heating, ventilating, and air conditioning) or fire prevention to name a few. An a priori and precise knowledge of the thermal behavior is indispensable for an efficient optimization and planning process. The complex space-time behavior of heat transfer in 3D domains can only be achieved with extensive computer simulations (or prohibitively complex experiments). In this article we describe approaches to simulate the transient coupled modes of heat transfer (convection, conduction and radiation) applicable to many fields in civil engineering. The numerical simulation of these coupled multi-scale, multi-physics problems are still very challenging and require great care in modeling the different spatio-temporal scales of the problem. One approach in this direction is offered by the Lattice-Boltzmann method (LBM) which is known to be a viable Ansatz for simulating physically complex problems. For the simulation of radiation a radiosity method is used which also has already proven its suitability for modeling radiation based heat transfer. The coupling and some typical applications of both methods are discussed in this chapter.