Viscous multi-species lattice Boltzmann solver for simulating shock-wave structure. (15th May 2020)

• Record Type: Journal Article
• Authors: Sashi Kumar, G.N.; Maheshwari, N.K.
• Is Part Of: Computers & fluids. Volume 203(2020)
• Publication Date: 2020-05-15
• Subjects: Lattice Boltzmann method -- Compressible viscous flow -- Multi-species flow -- Onsager BGK kinetic model -- MEPP -- Richtmyer Meshkov instability -- Euler viscous comparison -- Binary shock structure; Fluid dynamics -- Data processing -- Periodicals; 532.050285
• DOI: 10.1016/j.compfluid.2020.104539
• Languages: English
• ISSNs: 0045-7930

Abstract

Highlights: Extension of Onsager-BGK kinetic model to multi-species viscous compressible flows. It ensures addition of correct amount of entropy as per the Onsager's MEP principle. It can handle species with different specific heat ratio, mol. Wt., Prandtl numbers. Single perturbation RMI shows bigger mushroom structure with NS compared to Euler. Unable to differentiate dissipation of 5th - WENO and 3rd - MUSCL due to fluid viscosity. Abstract: The Onsager Bhatnagar Gross Krook kinetic model proposed by Mahendra et al. [32, 33] has been extended to arrive at the viscous compressible flow equations for a multi-species diffusion problem. The multi-species model ensures (i) correct exchange coefficients, (ii) positivity, (iii) that it follows indifferentiability principle and (iv) that correct amount of entropy get added as per the Onsager's maximum entropy production principle (MEPP). A Lattice Boltzmann method (LBM) has been developed using the derived methodology within the framework of finite volume method (FVM). This solver incorporates the physics of polyatomic gases with internal degrees of freedom with flexible Prandl number. This solver can simulate the problem with species having different specific heat ratio and molecular weights. Although the equations are derived for multi-species, only binary test cases have been considered in this paper. The solver has been validated against binary shock-wave structure problems using experimental and theoretical data. Two dimensional Richtmyer Meshkov instability test case has been compared with and without viscous effects. The diffusive (viscous and mass diffusion) effects are manifested in the reduction in amplitude and increment in width of the mushroom structure. In the framework of FVM, the proposed scheme of LBM is efficient with good resolution of solutions and is easily adaptable.