Abstract
Compressible lattice Boltzmann model on standard lattices [M.H. Saadat, F. Bösch, and I.V. Karlin, Phys. Rev. E 99, 013306 (2019).2470-004510.1103/PhysRevE.99.013306] is extended to deal with complex flows on unstructured grid. Semi-Lagrangian propagation [A. Krämer et al., Phys. Rev. E 95, 023305 (2017).2470-004510.1103/PhysRevE.95.023305] is performed on an unstructured second-order accurate finite-element mesh and a consistent wall boundary condition is implemented which makes it possible to simulate compressible flows over complex geometries. The model is validated through simulation of Sod shock tube, subsonic and supersonic flow over NACA0012 airfoil and shock-vortex interaction in Schardin's problem. Numerical results demonstrate that the present model on standard lattices is able to simulate compressible flows involving shock waves on unstructured meshes with good accuracy and without using any artificial dissipation or limiter.
Highlights
Lattice Boltzmann method (LBM) [1,2] as a kinetic theory approach to computational fluid dynamics (CFD) is a well-established tool for simulation of complex fluid flows ranging from turbulence [3,4] and multiphase [5] and multicomponent flows [6] to rarefied gas flows [7], magnetohydrodynamics [8], relativistic hydrodynamics [9], and others
The evolution of populations is based on simple rules of propagation along the discrete velocities C and relaxation to a local equilibrium
The most common LB models used in the literature suffer from a limited Galilean invariance and lack of isotropy at high-speed flows, which make their application limited to low-speed incompressible flows
Summary
Lattice Boltzmann method (LBM) [1,2] as a kinetic theory approach to computational fluid dynamics (CFD) is a well-established tool for simulation of complex fluid flows ranging from turbulence [3,4] and multiphase [5] and multicomponent flows [6] to rarefied gas flows [7], magnetohydrodynamics [8], relativistic hydrodynamics [9], and others. We extend the model formulation to unstructured finite-element mesh using a semi-Lagrangian propagation scheme and introduce consistent wall boundary conditions for the simulation of complex geometries. Finite-element-based interpolation schemes are good candidates as they allow to have body-conforming meshes which give more flexibility in handling complex geometries and are more efficient in capturing small scale structure of the flow near the wall. Another advantage of the semi-Lagrangian scheme is that the time step can be chosen arbitrarily and it remains stable at large Courant-FriedrichsLewy (CFL) numbers.
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