Adaptive lattice Boltzmann model for compressible flows: Viscous and conductive properties

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Abstract
This paper presents an adaptive lattice Boltzmann model of higher accuracy for viscous compressible flows with heat conduction. The proper heat conduction term in the energy equation is recovered by a modification of the kinetic energy transported by particles. The accuracy of the model is improved by introducing a term of fluctuating velocity in the collision-invariant vector. The Navier-Stokes equations are derived by the Chapman-Enskog method from the Bhatnagar-Gross-Krook Boltzmann equation. The advantage of an adaptive lattice Boltzmann model over the standard ones is that the particle velocities are no longer constant, varying with the mean velocity and internal energy. Therefore, the mean flow can have a high Mach number. To investigate the viscous and conductive properties of the model, a one-dimensional flow with a sinusoidal velocity distribution and Couette flow were simulated, showing good agreement with the analytical solutions. The simulation of an oblique shock impinging on a solid wall has captured the complex feature of the interaction between the shock and boundary layer.