Central Moment Lattice Boltzmann Method on a Rectangular Lattice

Abstract

Simulating inhomogeneous flows with different characteristic scales in different coordinate directions using the collide-and-stream based lattice Boltzmann methods (LBM) can be accomplished efficiently using rectangular lattice grids. We develop and investigate a new rectangular central moment LBM based on non-orthogonal moment basis (referred to as RC-LBM). The equilibria to which the central moments relax under collision in this approach are obtained from matching with those corresponding to the continuous Maxwell distribution. A Chapman-Enskog analysis is performed to derive the correction terms to the second order moment equilibria involving the grid aspect ratio and velocity gradients that restores the isotropy of the viscous stress tensor and eliminates the non-Galilean invariant cubic velocity terms of the resulting hydrodynamical equations. A special case of this rectangular formulation involving the raw moments (referred to as the RNR-LBM) is also constructed. The resulting schemes represent a considerable simplification, especially for the transformation matrices and isotropy corrections, and improvement over the existing MRT-LB schemes on rectangular lattice grids that use orthogonal moment basis. Numerical validation study of both the RC-LBM and RNR-LBM for a variety of benchmark flow problems are performed that show good accuracy at various grid aspect ratios. The ability of our proposed schemes to simulate flows using relatively lower grid aspect ratios than considered in prior rectangular LB approaches is demonstrated. Furthermore, simulations reveal the superior stability characteristics of the RC-LBM over RNR-LBM in handling shear flows at lower viscosities and/or higher characteristic velocities. In addition, computational advantages of using our rectangular LB formulation in lieu of that based on the square lattice is shown.

arXiv comment41 pages, 16 figures

References in corpus (5)

• Incorporating Forcing Terms in Cascaded Lattice-Boltzmann Approach by Method of Central Moments
• On the Three-dimensional Central Moment Lattice Boltzmann Method
• Modeling incompressible thermal flows using a central-moment-based lattice Boltzmann method
• Galilean Invariant Preconditioned Central Moment Lattice Boltzmann Method without Cubic Velocity Errors for Efficient Steady Flow Simulations
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Cited by in corpus (3)

• Rectangular multiple-relaxation-time lattice Boltzmann method for the Navier-Stokes and nonlinear convection-diffusion equations: General equilibrium and some important issues
• Shaping the equation of state to improve numerical accuracy and stability of the pseudopotential lattice Boltzmann method
• Preconditioned Central Moment Lattice Boltzmann Method on a Rectangular Lattice Grid for Accelerated Computations of Inhomogeneous Flows