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Journal Articles Journal of Computational Physics Year : 2021

Spurious interface and boundary behaviour beyond physical solutions in lattice Boltzmann schemes


The scalar field and the non-equilibrium solutions of the linear advection-diffusion d2Q9 Lattice Boltzmann (LBM) two-relaxation-times (TRT) scheme are constructed analytically. The scheme copes with an infinite number of suitable, second-order accurate, equilibrium weights. Here, the simplest, translation-invariant geometry with an implicitly located, straight or diagonal, grid-aligned interface (boundary) is addressed. We show that these two interface (boundary) orientations are accommodated with the help of two distinctive, anisotropic, discrete-exponential algebraic solution components, referred to as the A-layer and the B-layer. Being unpredicted by the perturbative analysis, such as the ChapmanEnskog, asymptotic or truncation, their solution is derived symbolically from the TRT recurrence equations, subject to the local mass conservation solvability and effective closure conditions. When the interface (boundary) is "diagonal", the A-layer perturbs the simplest physical solutions, like the piece-wise linear, polynomial or exponential scalar field, rendering the macroscopic solution weight-dependent and delaying its convergence to the first order; the A-layer base depends upon the weights, free relaxation parameter A and physical numbers. In contrast, the B-layer, invisible to the scalar field, typically accommodates the non-equilibrium discrepancy between the normal and diagonal directions on the "straight" interface (boundary); the B-layer base is fixed by A alone. The A-layer and B-layer may coexist and degrade the physical solution gradient and its convergence. Only the D2Q5 model is free from all these effects in the straight and diagonal orientations, while the diagonally-rotated D2Q5 model is unsuitable because of the "checkerboard" effect. These spurious corrections are not the Knudsen layers, but they present the LBM response for any-order bulk mismatch with the implicit or explicit interface (boundary) treatment; the A-layer and B-layer bring them in evidence and provide excellent benchmarks for their attenuation through interface-conjugate or adaptive refinement techniques. Our approach extends to any lattice, linear collision, source term, heterogeneity and LBM problem class.
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hal-03508079 , version 1 (10-03-2023)


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Irina Ginzburg. Spurious interface and boundary behaviour beyond physical solutions in lattice Boltzmann schemes. Journal of Computational Physics, 2021, 431, ⟨10.1016/j.jcp.2020.109986⟩. ⟨hal-03508079⟩
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