
Polynomial Projection and Immersed Quadrature for Boundary-Condition Enforcement in Lattice Boltzmann
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Aeroacoustics studies the noise generated by (turbulent) flow phenomena. This commonly features challenging computations due to the different time and length scales involved in the turbulent eddies, acoustic waves, simulated object, and sound propagation distance. To capture the noise produced by turbulent fluctuations, simulations must often resolve turbulent structures instead of statistically modelling these. For this reason, computational aeroacoustics generally applies highly-parallelizable and explicit fluid-dynamics solvers, with Lattice Boltzmann one of the most-applied techniques. The most difficult aspect of this technique is the enforcement of boundary conditions. Lattice Boltzmann requires a (perfectly straight) equidistant Cartesian grid, making it impossible to align the grid with the simulated geometry. Here, a parallel can be drawn with Isogeometric analysis, where often immersed boundaries must be treated that cut through the grid at arbitrary locations. While multiple approaches to enforce boundary conditions in Lattice Boltzmann exist, none of those combines high (at least quadratic) accuracy, conservation of mass, being exempt from oscillations, and a low computational cost. In this contribution we assess whether existing techniques in immersed Isogeometric analysis can be applied to enforce boundary conditions in Lattice Boltzmann. We define an immersed basis on the existing grid on which we project the flow-field. Subsequently, we employ immersed quadrature techniques to translate the space-continuous boundary conditions (dictated by the space-continuous Boltzmann equation) to the discrete mesh. Accuracy, conservation, and stability are assessed.