SC²S Colloquium - October 11, 2011

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Date: October 11, 2011
Room: 02.07.023
Time: 15:00 am, s.t.

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.