Consistent lattice Boltzmann model with body force and heat source for compressible flows of generic fluids

Abstract

This work presents a consistent formulation of body-force and heat-source terms within a double-distribution-function lattice Boltzmann framework for simulating compressible flows of generic fluids. The proposed approach extends a recently developed kinetic framework for non-ideal compressible fluid dynamics by incorporating external forcing and volumetric heating through shifted quasi-equilibrium states. The standard lattice Boltzmann discretization is applied with a second-order accurate integration along characteristics and product-form equilibria on nearest-neighbor lattices are employed, supplemented by necessary correction terms. This formulation ensures the consistent recovery of the Navier-Stokes-Fourier equations, including the Korteweg stress tensor, across arbitrary equations of state, while maintaining independently controllable thermodynamic and transport coefficients. The methodology is rigorously validated and applied for two different flow regimes, with ideal-gas compressible flows and non-ideal/multiphase compressible flows, respectively, where a broad hierarchy of benchmarks is employed, including non-classical shock tubes, thermal Couette flows, and force-driven Poiseuille and Womersley flows. The framework's ability to capture complex thermodynamic processes using forcing and heating is further demonstrated through Rayleigh and Fanno flows, Joule-Thomson effects, and throttling processes. Furthermore, the model is validated for multiphase phenomena, including interface consistency and liquid-vapor co-existence. The results demonstrate excellent agreement with analytical solutions and reference data, while spatio-temporal grid-refinement studies confirm the expected second-order accuracy of the scheme. This establishes the model as a robust and efficient foundation for simulating highly compressible flows of generic fluids in the presence of numerical and physical s...