Abstract
This article details a novel numerical algorithm to simulate compressible flow in the supersonic regime using the kinetic theory based lattice Boltzmann equation (LBE) method. In order to achieve higher-order accuracy, a fifth-order weighted essentially non-oscillatory (WENO) scheme with third-order Runge-Kutta (RK3) time integration is utilized. The LBE is solved using finite-differences on regular lattice structures with the discrete Bhatnager-Gross-Krook (BGK) approximation. A discrete velocity model given by Kataoka and Tsutahara (T. Kataoka and M. Tsutahara. Lattice Boltzmann method for the compressible Euler equations. Physical Review E, 69(5):056702, 2004) has been used, along with additional dissipation and artificial viscosity terms in order to account for the high Mach number problems. The most commonly studied benchmark two-dimensional, forward-facing step problem with a step-height of 0.2 and Mach number (Ma = 3) is used for validation. Further, the effect of change in the step-height on various parameters such as shock stand-off distance, Mach stems height, and triple points location are studied.
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Acknowledgements
Authors hereby acknowledge the support of ‘AnantGanak: HPC facility at IIT Dharwad’, to enable them to carry the reported work. S.G. Nayak and D.V. Patil acknowledge the support of ISRO-RESPOND and VSSC for project ‘RESPOND-VSSC002’.
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Shirsat, A.U., Nayak, S.G., Patil, D.V. (2023). Supersonic Inviscid Flow Over 2D Forward-Facing Step Using RK3 + WENO and Finite-Difference Lattice Boltzmann Equation Method. In: Bhattacharyya, S., Chattopadhyay, H. (eds) Fluid Mechanics and Fluid Power (Vol. 1). FMFP 2021. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-19-7055-9_16
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DOI: https://doi.org/10.1007/978-981-19-7055-9_16
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