Discrete unified gas kinetic scheme for all Knudsen number flows: II. Compressible case

Abstract

This paper is a continuation of our earlier work [Z.L. Guo {\it et al.}, Phys. Rev. E {\bf 88}, 033305 (2013)] where a multiscale numerical scheme based on kinetic model was developed for low speed isothermal flows with arbitrary Knudsen numbers. In this work, a discrete unified gas-kinetic scheme (DUGKS) for compressible flows with the consideration of heat transfer and shock discontinuity is developed based on the Shakhov model with an adjustable Prandtl number. The method is an explicit finite-volume scheme where the transport and collision processes are coupled in the evaluation of the fluxes at cell interfaces, so that the nice asymptotic preserving (AP) property is retained, such that the time step is limited only by the CFL number, the distribution function at cell interface recovers to the Chapman-Enskog one in the continuum limit while reduces to that of free-transport for free-molecular flow, and the time and spatial accuracy is of second-order accuracy in smooth region. These features make the DUGKS an ideal method for multiscale compressible flow simulations. A number of numerical tests, including the shock structure problem, the Sod tube problem with different degree of non-equilibrium, and the two-dimensional Riemann problem in continuum and rarefied regimes, are performed to validate the scheme. The comparisons with the results of DSMC and other benchmark data demonstrate that the DUGKS is a reliable and efficient method for multiscale compressible flow computation.

18 pages

Cited by in corpus (24)

• A three-dimensional unified gas-kinetic wave-particle solver for flow computation in all regimes
• A simplified discrete unified gas kinetic scheme for incompressible flow
• Compressible lattice Boltzmann methods with adaptive velocity stencils: An interpolation-free formulation
• Unified gas-kinetic scheme with simplified multi-scale numerical flux for thermodynamic non-equilibrium flow in all flow regimes
• High-order semi-Lagrangian kinetic scheme for compressible turbulence
• Computational Study of Rarefied Gas Flow and Heat Transfer in Lid-driven Cylindrical Cavities
• Particles on Demand for flows with strong discontinuities
• Central-moment discrete unified gas-kinetic scheme for incompressible two-phase flows with large density ratio
• GPU-based compressible lattice Boltzmann simulations on non-uniform grids using standard C++ parallelism: From best practices to aerodynamics, aeroacoustics and supersonic flow simulations
• A gas-surface interaction algorithm for discrete velocity methods in predicting rarefied and multi-scale flows: For Maxwell boundary model
• The first decade of unified gas kinetic scheme
• Simulation of two-phase flows at large density ratios and high Reynolds numbers using a discrete unified gas kinetic scheme
• Efficient methods for particle-resolved direct numerical simulation
• High-order Unified Gas-kinetic Scheme
• Implementation of the force term in half-range lattice Boltzmann models
• A novel Cercignani-Lampis boundary model for discrete velocity methods in predicting rarefied and multi-scale flows
• Discrete unified gas kinetic scheme on unstructured meshes
• A fully conservative discrete velocity Boltzmann solver with parallel adaptive mesh refinement for compressible flows
• A unified gas-kinetic framework from Boltzmann to Navier-Stokes scales
• Computational Fluid Dynamics with the Coupled Discrete Unified Gas Kinetic Scheme (CDUGKS)
• Multiscale discrete Maxwell boundary condition for the discrete unified gas kinetic scheme for all Knudsen number flows
• Implementation of Asymptotic Preserving Discrete Velocity Methods into the Simulation Code PICLas
• A coupled discrete unified gas-kinetic scheme for Boussinesq flows
• A Log-Gaussian Scale-Space Limiter for Hybrid Continuum--Ballistic Gas Dynamics