A unified lattice Boltzmann finite volume framework: Direct numerical simulation of acoustics and low-Mach-number flows

The lattice Boltzmann method (LBM) has intrinsic mechanisms for stabilizing computation and extraordinarily low acoustic dissipation, while the finite volume method (FVM) applies to nonuniform meshes and ensures conservation naturally. Their advantages complement each other, and many approaches have been proposed to integrate the two methods. However, existing integrations compromise the stability or low-dissipation properties of LBM. This paper proposes a general framework, the unified lattice Boltzmann finite volume scheme (ULBFVS), to unify the two methods, without losing their advantages. On uniform meshes, ULBFVS is mathematically equivalent to LBM, thereby fully preserving its numerical stability and extraordinarily low acoustic dissipation. Moreover, the framework can be naturally extended to nonuniform meshes, inheriting the conservation property and mesh flexibility of FVM. The framework is based on the LBM collision and streaming steps and extends general LBM models to conservative simulations on nonuniform meshes. As an example, the present paper proposes ULBFVS based on the recursive regularized LBM for low-Mach-number flows. Numerical tests validate its good numerical stability, accuracy, and extraordinarily low acoustic dissipation.