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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 and thermal and thermoacoustic flows are simulated to show the accuracy of the proposed model. [ABSTRACT FROM AUTHOR]

We present an energy conserving lattice Boltzmann model on a body-centered-cubic arrangement for thermohydrodynamics. It exhibits accurate thermohydrodynamic behavior with a high degree of accuracy and is therefore capable of simulating compressible and thermal hydrodynamics. The theoretical requirements and the methodology to construct this model have been described in detail and can be employed to construct even more accurate models. Simulations of canonical test cases related to compressible flows like shock tube and thermoacoustic convection and thermal flows like viscous heat dissipation and the Rayleigh-Bénard convection are performed to demonstrate the effectiveness of the model. [ABSTRACT FROM AUTHOR]

The entropic lattice Boltzmann model (ELBM), a discrete space-time kinetic theory for hydrodynamics, ensures nonlinear stability via the discrete time version of the second law of thermodynamics (the H theorem). Compliance with the H theorem is numerically enforced in this methodology and involves a search for the maximal discrete path length corresponding to the zero dissipation state by iteratively solving a nonlinear equation. We demonstrate that an exact solution for the path length can be obtained by assuming a natural criterion of negative entropy change, thereby reducing the problem to solving an inequality. This inequality is solved by creating a new framework for construction of Padé approximants via quadrature on appropriate convex function. This exact solution also resolves the issue of indeterminacy in case of nonexistence of the entropic involution step. Since our formulation is devoid of complex mathematical library functions, the computational cost is drastically reduced. To illustrate this, we have simulated a model setup of flow over the NACA-0012 airfoil at a Reynolds number of 2.88×106. [ABSTRACT FROM AUTHOR]

We present a detailed description of the essentially entropic lattice Boltzmann model. The entropic lattice Boltzmann model guarantees unconditional numerical stability by iteratively solving the nonlinear entropy evolution equation. In this paper we explain the construction of closed-form analytic solutions to this equation. We demonstrate that near equilibrium this analytic solution reduces to the standard lattice Boltzmann model. We consider a few test cases to show that the analytic solution does not exhibit any significant deviation from the iterative solution. We also extend the analytical solution for the Ellipsoidal Statistical (ES)-Bhatnagar-Gross-Krook model to remove the limitation on the Prandtl number for heat transfer problems. The simplicity of the analytic solution removes the computational overhead and algorithmic complexity associated with the entropic lattice Boltzmann models.