Lattice Boltzmann model for weakly compressible flows

Abstract

We present an energy conserving lattice Boltzmann model based on a crystallographic lattice for simulation of weakly compressible flows. The theoretical requirements and the methodology to construct such a model are discussed. We demonstrate that the model recovers the isentropic sound speed in addition to the effects of viscous heating and heat flux dynamics. Several test cases for acoustics, thermal and thermoacoustic flows are simulated to show the accuracy of the proposed model. :1909.08406v1 [physics.comp-ph] arXiv

Efficient supersonic flow simulations using lattice Boltzmann methods based on numerical equilibria

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Lattice Boltzmann Method for wave propagation in elastic solids with a regular lattice: Theoretical analysis and validation

“…The LB method presented here is based on the one proposed by Murthy et al [14] which employs higherorder Crystallographic Lattices [16,17]. These lattices were shown to result in a gain in terms of compactness of the computational stencil and number of unknowns per node.…”

“…O'Brien et al [13] uses a D2Q13 (D2Q9 + (±2, 0) form vectors) in 2D or a D3Q25 (D3Q19 + (±2, 0, 0)) in 3D. Murthy et al [14] uses crystallographic lattices [16]: RD3Q27 (a D3Q27 including half-speeds) and RD3Q41 [17]: (D3Q27 + 8 half-speeds + 6 double-speeds). Such sets have a higher-order truncation, so they are sometimes necessary to recover the good macroscopic behaviour.…”

Essentially entropic lattice Boltzmann model: Theory and simulations

“…However, this polynomial form of discrete equilibrium permits the populations to attain negative values thus making the simulations numerically unstable [12,13]. A method that resolves the issue of nonpositive form of equilibrium distribution is to construct the discrete equilibrium f eq as the minimizer of the convex H function under the constraint that the mass density, the momentum density, and the energy density (ignored for isothermal scenarios) are conserved [12,14,32,33]. The discrete entropic equilibrium thus obtained is of the form…”