Unification of the lattice Boltzmann method and finite volume method
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This work proposes a general framework, the unified lattice Boltzmann finite volume scheme (ULBFVS), to unify the two methods, without losing their advantages. The ULBFVS on uniform meshes is mathematically equivalent to the standard LBM and thus preserves all its advantages in numerical stability and extraordinarily low dissipation. It can also be naturally extended to non-uniform meshes, incorporating the conservation properties and mesh flexibility of FVM. The general framework is built on the general collision and streaming steps of LBM and applies to all LBM models.
