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The lattice Boltzmann method, a kinetic-theory based approach to computational fluid dynamics (CFD), has evolved into a mature and, due to the simplicity of the underlying kinetic equation, highly efficient approach for complex flows in regimes ranging from incompressible turbulence, multiphase, thermal, and compressible flows up to micro-flows and relativistic hydrodynamics. However, stability and accuracy issues precluded a significant impact of LBM on fluid dynamics so far. Among various suggestions, this issue was resolved by introducing a discrete H-function and restoring the second law of thermodynamics, resulting in the locally adaptive, parameter-free and non-linearly stable entropic LBM [2]. Notable is the recent extension to multiple relaxation times, the so-called KBC model [1].
In this contribution, we show that the local adaptivity in combination with excellent implicit subgrid features of the KBC model enables the simulation of complex flows of engineering and fundamental relevance. On one hand, a drastic reduction of computational cost is achieved by exploiting the local adaptivity of entropy-based LB models in a novel multi-domain grid refinement technique with entropic time stepping in the domain interface [3]. On the other hand, we provide evidence that the implicit subgrid features supplied with consistent boundary conditions for complex moving and deformable geometries [5, 4] allow for severely under-resolved simulations, while retaining accuracy and a second-order limit to direct numerical simulation (DNS) [6].
The combination of all its features make these models attractive as a unified approach, which is able to bridge the gap between various regimes, where modeling is not appropriate and the computational cost of DNS prohibitive. In this talk, this will be illustrated on various examples ranging from classical benchmarks such as turbulent channel flow, flow past a sphere to transitional flows and bio-fluidmechanical applications including self-propelled swimmers and flyers in three dimensions.
References
[1] I. V. Karlin, F. Bösch, S. S. Chikatamarla, Gibbs’ principle for the lattice-kinetic theory of fluid
dynamics, Physical Review E 90 (2014) 31302.
[2] I. V. Karlin, A. Ferrante, H. C. Öttinger, Perfect entropy functions of the Lattice Boltzmann method,
Europhysics Letters 47 (1999) 182-188.
[3] B. Dorschner, N. Frapolli, S. Chikatamarla, I. Karlin, Grid Refinement for Entropic Lattice Boltz-
mann Models, Physical Review E 94 (2016) 053311.
[4] B. Dorschner, S. Chikatamarla, I. Karlin, Entropic Lattice Boltzmann Method for Moving and De-
forming Geometries in Three Dimensions, arXiv:1608.04658 (2016) (submitted to Journal of Com-
putational Physics)
[5] B. Dorschner, S. Chikatamarla, F. Bösch, I. Karlin, Grad’s approximation for moving and stationary
walls in entropic lattice Boltzmann simulations, Journal of Computational Physics 295 (2015) 340-
354.
[6] B. Dorschner, F. Bösch, S. Chikatamarla, K. Boulouchos, I. Karlin, Entropic Multi-Relaxation Time
Lattice Boltzmann Model for Complex Flows, Journal of Fluid Mechanics 801 (2016) 623-651.
[7] B. Dorschner, S. Chikatamarla, K. Boulouchos, I. Karlin, Transitional Flows with the Entropic
Lattice Boltzmann Method, (submitted to Journal of Fluid Mechanics).
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