Lattice Boltzmann simulations on irregular grids: Introduction of the NATriuM library

Krämer, Andreas; Wilde, Dominik; Küllmer, Knut; Reith, Dirk; Foysi, Holger; Joppich, Wolfgang

doi:10.1016/j.camwa.2018.10.041

Cited by 15 publications

(22 citation statements)

References 64 publications

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“…The interpolation error of semi-Lagrangian advection schemes has been investigated, for instance, by Einkemmer and Ostermann [52] or Falcone and Ferretti [53]. For the SLLBM used in the present work, we have previously discussed the nontrivial behavior of the temporal discretization error [28], which is of order, This means in practice that the error has a minimum for intermediate CFL numbers and is bounded by the spatial discretization error in the limit of small time steps.…”

Section: E Semi-lagrangian Streaming Stepmentioning

confidence: 98%

“…The problems that arise with interpolation-based schemes have been discussed in earlier works, e.g., by Chen [10], like the issue that interpolation-based LBM do not conserve mass, momentum, and energy. However, this effect can be at least reduced by using high-order interpolation polynomials, which we showed in a recent work [28].…”

Section: Introductionmentioning

confidence: 94%

“…All SLLBM simulations in this manuscript have been performed with the NATRIUM library [28], which makes use of the finite element library DEAL.II [54]. See [28] for further details concerning the implementation.…”

Section: E Semi-lagrangian Streaming Stepmentioning

confidence: 99%

“…The physical and numerical parameters can be decoupled in an off-lattice framework, where the velocity set does not need to match the computational grid. In the field of off-lattice Boltzmann methods the semi-Lagrangian lattice Boltzmann method (SLLBM) was recently introduced [24] and further investigated in a number of subsequent works [25][26][27][28][29]. To formulate the streaming step the algorithm follows the trajectories of the lattice Boltzmann equation along their characteristics to find the cells of the corresponding departure points.…”

Section: Introductionmentioning

confidence: 99%

“…In common with Eulerian-based off-lattice Boltzmann solvers the SLLBM enables the use of non-integer-based velocity sets. Yet, compared to Eulerian-based off-lattice Boltzmann schemes, the streaming step is computationally more efficient [28], reduces numerical dissipation, and is still close to the original formulation of the LBM, as it also follows the trajectories of the discrete Boltzmann equation back in time [24]. The problems that arise with interpolation-based schemes have been discussed in earlier works, e.g., by Chen [10], like the issue that interpolation-based LBM do not conserve mass, momentum, and energy.…”

Section: Introductionmentioning

confidence: 99%

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Semi-Lagrangian lattice Boltzmann method for compressible flows

et al. 2020

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This work thoroughly investigates a semi-Lagrangian lattice Boltzmann (SLLBM) solver for compressible flows. In contrast to other LBM for compressible flows, the vertices are organized in cells, and interpolation polynomials up to fourth order are used to attain the off-vertex distribution function values. Differing from the recently introduced Particles on Demand (PoD) method [Dorschner, Bösch, and Karlin, Phys. Rev. Lett. 121, 130602 (2018)], the method operates in a static, nonmoving reference frame. Yet the SLLBM in the present formulation grants supersonic flows and exhibits a high degree of Galilean invariance. The SLLBM solver allows for an independent time step size due to the integration along characteristics and for the use of unusual velocity sets, like the D2Q25, which is constructed by the roots of the fifth-order Hermite polynomial. The properties of the present model are shown in diverse example simulations of a two-dimensional Taylor-Green vortex, a Sod shock tube, a two-dimensional Riemann problem, and a shock-vortex interaction. It is shown that the cell-based interpolation and the use of Gauss-Lobatto-Chebyshev support points allow for spatially high-order solutions and minimize the mass loss caused by the interpolation. Transformed grids in the shock-vortex interaction show the general applicability to nonuniform grids.

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Section: E Semi-lagrangian Streaming Stepmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 94%

Section: E Semi-lagrangian Streaming Stepmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Semi-Lagrangian lattice Boltzmann method for compressible flows

et al. 2020

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Multistep lattice Boltzmann methods: Theory and applications

Wilde

Krämer

Küllmer

et al. 2019

Numerical Methods in Fluids

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Summary This paper presents a framework for incorporating arbitrary implicit multistep schemes into the lattice Boltzmann method. While the temporal discretization of the lattice Boltzmann equation is usually derived using a second‐order trapezoidal rule, it appears natural to augment the time discretization by using multistep methods. The effect of incorporating multistep methods into the lattice Boltzmann method is studied in terms of accuracy and stability. Numerical tests for the third‐order accurate Adams‐Moulton method and the second‐order backward differentiation formula show that the temporal order of the method can be increased when the stability properties of multistep methods are considered in accordance with the second Dahlquist barrier.

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