A HWENO reconstruction based high-order compact gas-kinetic scheme on unstructured mesh

Ji, Xing; Zhao, Fengxiang; Shyy, Wei; Xu, Kun

doi:10.1016/j.jcp.2020.109367

Cited by 37 publications

(20 citation statements)

References 74 publications

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“…In recent years, a class of high-order compact gas-kinetic scheme (CGKS) [23,15] has been developed from the second-order gas-kinetic scheme (GKS) [34]. The time-dependent interface evolution solution in CGKS is based on an analytical integral solution of the Bhatnagar-Gross-Krook equation [5], which recovers a transition process from the kinetic scale flux vector splitting to the central difference Lax-Wendroff type discretization.…”

Section: Introductionmentioning

confidence: 99%

A p-multigrid compact gas-kinetic scheme for steady-state acceleration

Xing¹,

Shyy²,

Xu³

2021

Preprint

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In this paper, the high-order compact gas-kinetic scheme (CGKS) on three-dimensional hybrid unstructured mesh is further developed with the p-multigrid technique for steadystate solution acceleration. The p-multigrid strategy is a two-level algorithm. On the highorder level, the high-order CGKS is used to evolve both cell-averaged conservative flow variables and their gradients under high-order compact initial reconstruction at the beginning of next time step. On the low-order level, starting from the high-order level solution the cell-averaged conservative flow variables is evolved by a first-order scheme, where implicit backward Euler smoother is adopted for accelerating the convergence of steady-state solution. The final iterative updating scheme becomes numerically simple and computationally efficient. The effectiveness of the p-multigrid method is validated in both subsonic and supersonic flow simulations in two-and three-dimensional space with hybrid unstructured mesh. One order of magnitude speedup in the convergence rate has be achieved by the approach in comparison with the explicit counterpart.

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Section: Introductionmentioning

confidence: 99%

A p-multigrid compact gas-kinetic scheme for steady-state acceleration

Xing¹,

Shyy²,

Xu³

2021

Preprint

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“…Due to their differences in the updating schemes, the compact GKS can use a larger time step and has better robustness than the corresponding DG methods. For example, a CFL number around 0.5 can be taken for the third-order compact GKS [9] while it is restricted to be less than 0.33 for the third-order P1P2-rDG scheme. The P1P2-rDG is claimed to be unstable on tetrahedral mesh with smooth reconstruction.…”

Section: Introductionmentioning

confidence: 99%

Two-step multi-resolution reconstruction-based compact gas-kinetic scheme on tetrahedral mesh

Ji¹,

Zhao²,

Shyy³

et al. 2021

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In this paper, a third-order compact gas-kinetic scheme (GKS) on unstructured tetrahedral mesh is constructed for the compressible Euler and Navier-Stokes solutions. The timedependent gas distribution function at a cell interface is used to calculate the fluxes for the updating the cell-averaged flow variables and to evaluate the time accurate cell-averaged flow variables as well for evolving the cell-averaged gradients of flow variables. With the accurate evolution model for both flow variables and their slopes, the quality of the scheme depends closely on the accuracy and reliability of the initial reconstruction of flow variables. The reconstruction scheme becomes more challenge on tetrahedral mesh, where the conventional second-order unlimited least-square reconstruction can make the scheme be linearly unstable when using cell-averaged conservative variables alone with von Neumann neighbors. Benefiting from the evolved cell-averaged slopes, on tetrahedral mesh the GKS is linearly stable from a compact third-order smooth reconstruction with a large CFL number. In order to further increase the robustness of the high-order compact GKS for capturing discontinuous solution, a new two-step multi-resolution weighted essentially non-oscillatory (WENO) reconstruction will be proposed. The novelty of the reconstruction includes the following. Firstly, it releases the stability issue from a second-order compact reconstruction through the introduction of a pre-reconstruction step. Secondly, in the third-order non-linear reconstruction, only one more large stencil is added beside those in the second-order one, which significantly simplifies the high-order reconstruction. At the same time, the high-order wall boundary treatment is carefully designed by combining the constrained least-square technique and the WENO procedure, where a quadratic element is adopted in the reconstruction for the curved boundary. Numerical tests for both inviscid and viscous flow at low and high speed are presented from the second-order and third-order compact GKS. The proposed third-order scheme shows good robustness in high speed flow computation and favorable mesh adaptability in cases with complex geometry.

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“…In this paper, a multiscale method will be developed for the system with the gas-kinetic scheme (GKS) for the gas phase and the UGKWP for the particle phase [61,60]. The GKS is a gas-kinetic theory-based Navier-Stokes solver which is basically the limiting scheme of UGKWP in the continuum flow regime [24,67,25]. For the continuum flow, the GKS has been used in the turbulence flow [5,6], acoustic wave [66], multi-component flow [59,44], and hypersonic flow studies [27].…”

Section: Introductionmentioning

confidence: 99%

Unified gas-kinetic wave-particle methods VI: Disperse dilute gas-particle multiphase flow

Yang,

Liu,

et al. 2021

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In this paper, a unified gas-kinetic wave-particle scheme (UGKWP) for the disperse dilute gas-particle multiphase flow is proposed. In this study, 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 phase in the multiphase system is assumed to be stay in the continuum flow regime, and its evolution is mainly controlled by the Navier-Stokes equations with the interaction with particle phase. 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.

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A HWENO reconstruction based high-order compact gas-kinetic scheme on unstructured mesh

Cited by 37 publications

References 74 publications

A p-multigrid compact gas-kinetic scheme for steady-state acceleration

A p-multigrid compact gas-kinetic scheme for steady-state acceleration

Two-step multi-resolution reconstruction-based compact gas-kinetic scheme on tetrahedral mesh

Unified gas-kinetic wave-particle methods VI: Disperse dilute gas-particle multiphase flow

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