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This paper presents a kinetic model for the coupled evolution of radiation, electrons, and ions in a radiation plasma system. The model is solved using two methods. The gas-kinetic scheme (GKS) for electron and ion hydrodynamics and the unified gas-kinetic scheme (UGKS) for non-equilibrium radiative transfer. The UGKS accurately captures multiscale photon transport from free streaming to diffusion across varying fluid opacities. This approach enables the scheme to model equilibrium plasma with non-equilibrium radiation transport. The model is validated through several test cases, including radiative transfer in kinetic and diffusion regimes, Marshak wave, Radiative shock, 3T(three-temperature) double lax shock tube problem, two-dimensional Sedov blast wave, and two-dimensional tophat based problem. These tests demonstrate the current scheme's capability to handle diverse radiation plasma scenarios.

The multi-frequency radiation transport equation (RTE) system models the photon transport and the energy exchange process between the background material and different frequency photons. In this paper, the unified gas-kinetic wave-particle (UGKWP) method for multi-frequency RTE is developed to capture the multiscale non-equilibrium transport in different optical regimes. In the UGKWP, a multiscale evolution process is properly designed to obtain both non-equilibrium transport in the optically thin regime and thermal diffusion process in the optically thick regime automatically. At the same time, the coupled macroscopic energy equations for the photon and material are solved implicitly by the matrix-free source iteration method. With the wave-particle decomposition strategy, the UGKWP method has a dynamic adaptivity for different regime physics. In the optically thick regime, no particles will be sampled in the computational domain and the thermal diffusion solution for the photon transport will be recovered. While in the optically thin regime, stochastic particles will play a dominant role in the evolution and the non-equilibrium free transport of photon is automatically followed. In the frequency-dependent transport, the frequency carried by the simulating particle will be determined by a linear-frequency sampling strategy. In addition, to better resolve the sharp of opacity in the photon transport across a cell interface, the free streaming time of simulating particle in the UGKWP method will be reset when it passes through the interface. Moreover, the numerical relaxation time is properly defined to increase the particle proportion in the sharp opacity transition region in order to avoid numerical oscillation. Several typical test cases for the RTE system have been calculated to demonstrate the accuracy and reliability of the current frequency-dependent UGKWP method.

In this paper, a unified algorithm will be proposed for the study of gas-solid particle multiphase flow. The gas-kinetic scheme (GKS) is used to simulate the continuum gas phase and the multiscale unified gas-kinetic wave-particle (UGKWP) method is developed for the multiple dispersed solid particle phase. At the same time, the momentum and energy exchanges between gas-particle phases will be included under the GKS-UGKWP framework. For each disperse solid particle phase, the decomposition of deterministic wave and statistic particle in UGKWP is based on the local cell's Knudsen number. This is very significant for simulating dispersed particle phases at different Knudsen numbers due to the variation of physical properties in individual particle phase, such as the particle diameter, material density, and the corresponding mass fraction inside each control volume. For the gas phase, the GKS is basically an Eulerian approach for the NS solution. Therefore, the GKS-UGKWP method for the gas-particle flow unifies the Eulerian-Eulerian (EE) and Eulerian-Lagrangian (EL) methods. An optimal strategy can be obtained for the solid particle phase with the consideration of physical accuracy and numerical efficiency. Two cases of gas-solid fluidization system, i.e., one circulating fluidized bed and one turbulent fluidized bed, are simulated. The typical flow structures of the fluidized particles are captured, and the time-averaged variables of the flow field agree well with the experimental measurements. In addition, the shock particle-bed interaction is studied by the proposed GKS-UGKWP, which validates the method for polydisperse gas-particle system in the supersonic case, where the dynamic evolution process of the particle cloud is investigated., Comment: arXiv admin note: text overlap with arXiv:2112.01829, arXiv:2206.13824

The gas-solid particle two-phase flow in a fluidized bed shows complex physics. Following our previous work, the multi-scale framework based on gas-kinetic scheme (GKS) and unified gas-kinetic wave-particle method (UGKWP) for the gas-particle system is firstly extended to the three-dimensional simulation of the fluidized bed. For the solid particle evolution, different from the widely-used Eulerian and Lagrangian approaches, the UGKWP unifies the wave (dense particle region) and discrete particle (dilute particle region) formulation seamlessly according to a continuous variation of particle cell's Kundsen number ($Kn$). The GKS-UGKWP for the coupled gas-particle evolution system can automatically become an Eulerian-Eulerian (EE) method in the high particle collision regime and Eulerian-Lagrangian (EL) formulation in the collisionless particle regime. In the transition regime, the UGKWP can achieve a smooth transition between the Eulerian and Lagrangian limiting formulation. More importantly, the weights of mass distributions from analytical wave and discrete particle are related to the local $Kn$ by $\exp(-1/Kn)$ for wave and $(1-\exp(-1/Kn))$ for discrete particle. As a result, the UGKWP provides an optimal modeling for capturing the particle phase in terms of physical accuracy and numerical efficiency. In the numerical simulation, the UGKWP does not need any prior division of dilute/dense regions, which makes it suitable for the fluidized bed problem, where the dilute/transition/dense regions instantaneously coexist and are dynamically interconvertible. In this paper, based on the GKS-UGKWP formulation two lab-scale fluidization cases are simulated in 3D and the simulation results are compared with the experimental measurements. The typical heterogeneous flow features of the fluidized bed are well captured and the statistics are in good agreement with experiment data., Comment: arXiv admin note: substantial text overlap with arXiv:2112.01829

In this paper, a unified framework for particulate two-phase flow will be presented with a wide range of solid-particle concentration from dilute to dense limit. The two phase flow is simulated by two coupled flow solvers, i.e., the gas-kinetic scheme (GKS) for the gas phase and unified gas-kinetic wave-particle method (UGKWP) for the particle phase. The GKS is a second-order Navier-Stokes flow solver for the continuum flow. The UGKWP is a multiscale method for all flow regimes. The wave and particle decomposition in UGKWP depends on the cell's Knudsen number (Kn). At a small Kn number, the high concentrated solid particle phase will be modeled by the Eulerian hydrodynamic wave due to the intensive particle-particle collisions. At a large Kn number, the dilute solid particle will be sampled and followed by the Lagrangian particle formulation to capture the non-equilibrium transport. In the transition regime, the distribution and evolution of particle and wave in UGKWP are controlled by the local Kn number with a smooth transition between the above limits. In the current scheme, the two phase model improves the previous one in all following aspects: drag force model for different solid particle concentrations; the frictional pressure in inter-particle contacts at high solid-particle concentration; a flux limiting model to avoid solid particles' over-packing; additional non-conservative nozzle and work terms for the gas phase. Besides, the inter-particle collisions have been refined numerically for the dense particle flow through the discretization of the collision term and numerical flux function. The numerical scheme is tested in a series of typical gas-particle problems. The results validate the accuracy and reliability of the proposed method for gas-particle flow., Comment: arXiv admin note: text overlap with arXiv:2107.05075

In this paper, a unified gas-kinetic wave-particle scheme (UGKWP) for the disperse dilute gas-particle multiphase flow is proposed. The gas phase is always in the hydrodynamic regime. However, the particle phase covers different flow regimes from particle trajectory crossing to the hydrodynamic wave interaction with the variation of local particle phase Knudsen number. The UGKWP is an appropriate method for the capturing of the multiscale transport mechanism in the particle phase through its coupled wave-particle formulation. In the regime with intensive particle collision, the evolution of solid particle will be followed by the analytic wave with quasi-equilibrium distribution; while in the rarefied regime the non-equilibrium particle phase will be captured through particle tracking and collision, which plays a decisive role in recovering particle trajectory crossing behavior. The gas-kinetic scheme (GKS) is employed for the simulation of gas flow. In the highly collision regime for the particles, no particles will be sampled in UGKWP and the wave formulation for solid particle with the hydrodynamic gas phase will reduce the system to the two-fluid Eulerian model. On the other hand, in the collisionless regime for the solid particle, the free transport of solid particle will be followed in UGKWP, and coupled system will return to the Eulerian-Lagrangian formulation for the gas and particle. The scheme will be tested for in all flow regimes, which include the non-equilibrium particle trajectory crossing, the particle concentration under different Knudsen number, and the dispersion of particle flow with the variation of Stokes number. A experiment of shock-induced particle bed fluidization is simulated and the results are compared with experimental measurements. These numerical solutions validate suitability of the proposed scheme for the simulation of gas-particle multiphase flow.

In this paper, a comparison of the performance of two high-order finite volume methods based on the gas-kinetic scheme (GKS) and HLLC fluxes is carried out in structured rectangular mesh. For both schemes, the fifth-order WENO-AO reconstruction is adopted to achieve a high-order spatial accuracy. In terms of temporal discretization, a two-stage fourth-order (S2O4) time marching strategy is adopted for WENO5-AO-GKS scheme, and the fourth-order Runge-Kutta (RK4) method is employed for WENO5-AO-HLLC scheme. For the viscous flow computation, the GKS includes both inviscid and viscous fluxes in the evolution of a single cell interface gas distribution function. While for the WENO5-AO-HLLC scheme, the inviscid flux is provided by HLLC Riemann solver, and the viscous flux is discretized by a sixth-order central difference method. Based on the tests of forward Mach step and viscous shock tube, both schemes show outstanding shock capturing property. From the Titarev-Toro and double shear layer tests, WENO5-AO-GKS scheme seems to have a better resolution than WENO5-AO-HLLC scheme. Both schemes show excellent robustness in extreme cases, such as the Le Blanc problem. From the cases of the Noh problem and the compressible isotropic turbulence, WENO5-AO-GKS scheme shows favorite robustness. In the compressible isotropic turbulence and three-dimensional Taylor-Green vortex problems, WENO-AO-GKS can use a CFL number up to 0.5, instead of 0.3 for WENO5-AO-HLLC. In terms of computational efficiency, WENO5-AO-HLLC scheme is about 27% more expensive than WENO5-AO-GKS scheme in the two-dimensional viscous flow problems, but is about 15% faster in the three-dimensional case. Due to the multi-dimensionality, WENO5-AO-GKS scheme performs better than WENO5-AO-HLLC scheme in the laminar boundary layer and the double shear layer test.