SC²S Colloquium - October 13, 2011

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Date: October 6, 2011
Room: 02.07.014
Time: 15:00 am, s.t.

Denis Jarema: Comparison and Coupling of a Lattice-Boltzmann Fluid-Structure Interaction Code with the Faxen Correction Approach (MA)

The number of applications that involve multiple physical models or multiple simultaneous physical phenomena is constantly growing. The main reason is that many interesting natural phenomena are complex and the only way to understand them is to couple different models. In this thesis, we treat a multi-physical problem of particle transport phenomena in a channel with a complex wall geometry and laminar fluid flow. We start from two independent ways of describing the particle transport. While a Lattice Boltzmann fluid-structure interaction code provides precise computations of the particle motion, a Navier-Stokes' equations solver with the Faxen's postprocessing force estimation is computationally fast. The idea of this thesis is to combine the best properties of the two approaches. To accomplish this goal we developed an application that exploits the precision of the Lattice Boltzmann regime, when the particle is close to the walls or moves in the dynamically changing flow and gains performance, from the Navier-Stokes' regime, when the particle does not experience the impact of the walls and the flow is almost steady. In the thesis we provide a theoretical model of the fluid forces acting on the particle. For the postprocessing force computations, we derive the Faxen's theorems for the two-dimensional system. This enables us to test our application with two-dimensional models before experimenting with more computationally demanding three-dimensional systems. We compare the computed forces with the ones obtained from the fluid-structure interaction simulations. The drift ratchet model was used for testing purposes. We implemented the application in the Peano framework, a framework that was initially developed to support multi-physical simulations and that provides all necessary tools to accomplish our goals.

Till Rohrmann: Comparison and Coupling of a Lattice-Boltzmann Fluid-Structure Interaction Code with the Faxen Correction Approach (BA)

  Due to its kinetic origin and the demand for a simulation model 

capable of predicting microflows for microelectromechanical systems (MEMS), the lattice Boltzmann method (LBM) has spurred considerable research interest during the last years. The multiple relaxation times lattice Boltzmann method (MRT-LBM) has emerged to be best suited for this task, combining efficient computability and applicability to a wide range of scales. Therefore, this model together with appropriate boundary conditions to model first-order and second-order slip velocity models are implemented within the Peano framework, a framework for solving partial differential equations. To further account for rarefaction effects occuring at microscales, a Bosanquet-type effective viscosity approximation is real- ized. This approximation incorporates the shortening of the molecular mean free path in confined environments into the lattice Boltzmann method.

  The implementation is validated by simulating distinct 

pressure-driven Poiseuille flow scenarios and comparing the data with results obtained by the information-preservation direct simulation Monte Carlo (IP-DSMC) method, solving the Navier-Stokes equation with first- and second-order slip velocity boundary condition and solving the linearized Boltzmann equation directly. The numerical data for the streamwise velocity, spanwise velocity and the pressure deviation from the linear distribution, using the first-order slip velocity consistent MRT-LBM, are in good accordance with the reference data in the slip flow regime. To further increase the Knudsen number range the approach is applicable to, the MRT-LBM employing the second-order slip velocity boundary condition and effective viscosity calculation is utilized. The computed data based on this model agrees very well with results of the IP-DSMC even in the transitional regime, thus indicating the proper modelling of microflow dynamics.

  Besides investigating the modelling capabilities of flows in the 

finite Knudsen number range, the numerical stability properties of the MRT-LBM are examined and compared to the widely used Bhatnagar-Gross-Krook lattice Boltzmann model (BGK-LBM). This model serves as well as a reference to evaluate the computational costs of the MRT-LBM which slightly derogates the overall performance within Peano. In contrast, the new bounce back specular reflection, bounce back diffusive reflection and consistent flow field pressure boundary conditions inflict insignificantly more computational costs.

  The implemented approach is also applied to a complex fluid scenario 

in form of a microreactor as it would appear in realistic engineering scenarios. The calculated data is validated against pressure-driven Poiseuille flow results and the validity of the presented approach for the microreactor scenario is discussed.