The transport phenomena within multiphase flows plays a key role in the operation of catalytic reactors, calciners, fluidized beds, and porous media. However, a fundamental understanding of the physics within these complicated systems still remains elusive. Direct numerical simulation has been shown to be an effective method for obtaining high fidelity predictions of the heat transfer within multiphase flows. Most commonly, particle-resolved immersed boundary [4, 5] or thermal lattice Boltzmann  methods are employed. Here we utilize a hybrid framework where the velocity field is resolved by the lattice Boltzmann method and temperature field by random walk particle tracking (Brownian tracers). Due to the simplicity of the algorithm and boundary conditions, random walk particle tracking offers an efficient means of simulating scalar transport within complex geometries. However, interfaces pose a significant challenge to the random walk framework [1, 2], due to the discontinuous change in material properties â e.g., a particle and fluid with different diffusivities. We derive a technique for handling discontinuities in the diffusivity, arising at a particle-fluid interface, and implement said method within the tracer algorithm. Verification of the code is completed against a host of systems: dispersion within a stagnant particle-fluid assembly, a hot sphere in contact with an unbounded fluid, a cooling sphere in contact with an unbounded fluid, and unbounded flow past a hot sphere. Predictions made by the new code are found to be in agreement with analytical solutions and previous works.
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