A Novel Approach of Unsteady Adjoint Lattice Boltzmann Method Based on Circular Function Scheme
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A Novel Approach of Unsteady Adjoint Lattice Boltzmann Method Based on Circular Function Scheme Hamed Jalali Khouzani1 · Ramin Kamali Moghadam1 Received: 14 March 2020 / Revised: 16 September 2020 / Accepted: 18 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract A new approach of combination of the LBM and adjoint method based on the circular function idea is developed for optimization of unsteady incompressible/compressible inviscid flow in 1D and 2D problems. The circular function distribution is used for capturing the compressibility effect in the flowfield and the continuous adjoint method allows designers to implement large number of design variables in actual optimization problems. The adjoint approach is successfully derived for the first time based on the compressible LBM with terminal conditions for estimation of the cost function gradient vector in 1D/2D flow inverse design problem. To validate the new derived flow solver with new lattice, firstly, accuracy of the flow simulation is shown for the inviscid compressible discontinuous flows with shock wave. Secondly, for validation of novel derived adjoint optimization algorithm, three optimization problems in form of the inverse design, including the smooth and shock wave inviscid compressible flowfields, are presented. Also, trend of optimization algorithm is studied in all cases. The results indicate that the presented numerical optimization approach gives desirable accuracy in 1D/2D inverse design of inviscid unsteady compressible flowfields. Keywords Lattice Boltzmann method · Unsteady adjoint method · Inverse design · Circular function · Inviscid compressible flows · Finite volume method
1 Introduction The Lattice Boltzmann method (LBM) has been applied as an alternative for the computational fluid dynamics (CFD) approaches in simulation of fluid flows [1–4]. Specific features of the LBM compared to traditional CFD methods such as inherent parallelizability, simple explicit governing equation, easy access to solve pressure field, avoidance of nonlinear convective terms unlike the Navier–Stokes/Euler equations and so on, result in its vastly using, development and improvement in numerical simulations [5]. Based on the LBM abilities, simulation of the inviscid compressible flows and study of physical phenomena like shock waves has been interested by researchers.
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Ramin Kamali Moghadam [email protected] A&S Research Institute, Ministry of Science, Research and Technology, Tehran, Iran 0123456789().: V,-vol
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Journal of Scientific Computing
(2020) 85:38
The standard LBM is extremely limited to simulate incompressible flows [1] because it is constructed base on the Maxwellian expansion which originally develops for low Mach number. However, there are many numerical efforts for developing the LB models to simulate compressible and high Mach number flows. Firstly, the collision rules on the lattice Boltzmann equation (LBE) was constructed by [6]. Implemented the LBM to analysis compress
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