scholarly journals A two-stage fourth-order gas-kinetic scheme on unstructured hybrid mesh

2019 ◽  
Vol 235 ◽  
pp. 75-87
Author(s):  
Dongxin Pan ◽  
Chengwen Zhong ◽  
Congshan Zhuo ◽  
Sha Liu
Keyword(s):  
Fourth Order ◽  
Kinetic Scheme ◽  
Two Stage ◽  
Hybrid Mesh

A Two-Stage Fourth-Order Gas-Kinetic Scheme for Compressible Multicomponent Flows

2017 ◽  
Vol 22 (4) ◽  
pp. 1123-1149 ◽  
Author(s):  
Liang Pan ◽  
Junxia Cheng ◽  
Shuanghu Wang ◽  
Kun Xu
Keyword(s):  
Fourth Order ◽  
Kinetic Scheme ◽  
Second Order ◽  
Individual Species ◽  
Bgk Model ◽  
Weno Reconstruction ◽  
Two Stage ◽  
Flux Function ◽  
Temporal Discretization ◽  
Multicomponent Flows

AbstractWith the use of temporal derivative of flux function, a two-stage temporal discretization has been recently proposed in the design of fourth-order schemes based on the generalized Riemann problem (GRP) [21] and gas-kinetic scheme (GKS) [28]. In this paper, the fourth-order gas-kinetic scheme will be extended to solve the compressible multicomponent flow equations, where the two-stage temporal discretization and fifth-order WENO reconstruction will be used in the construction of the scheme. Based on the simplified two-species BGK model [41], the coupled Euler equations for individual species will be solved. Each component has its individual gas distribution function and the equilibrium states for each component are coupled by the physical requirements of total momentum and energy conservation in particle collisions. The second-order flux function is used to achieve the fourth-order temporal accuracy, and the robustness is as good as the second-order schemes. At the same time, the source terms, such as the gravitational force and the chemical reaction, will be explicitly included in the two-stage temporal discretization through their temporal derivatives. Many numerical tests from the shock-bubble interaction to ZND detonative waves are presented to validate the current approach.

scholarly journals Large-eddy simulation of wall-bounded turbulent flow with high-order discrete unified gas-kinetic scheme

2020 ◽  
Vol 2 (1) ◽  
Author(s):  
Rui Zhang ◽  
Chengwen Zhong ◽  
Sha Liu ◽  
Congshan Zhuo
Keyword(s):  
Turbulent Flow ◽  
Turbulent Flows ◽  
Parallel Implementation ◽  
Kinetic Scheme ◽  
Cavity Flow ◽  
Equilibrium Distribution Function ◽  
Third Order ◽  
Two Stage ◽  
Large Eddy ◽  
Unified Gas Kinetic Scheme

AbstractIn this paper, we introduce the discrete Maxwellian equilibrium distribution function for incompressible flow and force term into the two-stage third-order Discrete Unified Gas-Kinetic Scheme (DUGKS) for simulating low-speed turbulent flows. The Wall-Adapting Local Eddy-viscosity (WALE) and Vreman sub-grid models for Large-Eddy Simulations (LES) of turbulent flows are coupled within the present framework. Meanwhile, the implicit LES are also presented to verify the effect of LES models. A parallel implementation strategy for the present framework is developed, and three canonical wall-bounded turbulent flow cases are investigated, including the fully developed turbulent channel flow at a friction Reynolds number (Re) about 180, the turbulent plane Couette flow at a friction Re number about 93 and lid-driven cubical cavity flow at a Re number of 12000. The turbulence statistics, including mean velocity, the r.m.s. fluctuations velocity, Reynolds stress, etc. are computed by the present approach. Their predictions match precisely with each other, and they are both in reasonable agreement with the benchmark data of DNS. Especially, the predicted flow physics of three-dimensional lid-driven cavity flow are consistent with the description from abundant literature. The present numerical results verify that the present two-stage third-order DUGKS-based LES method is capable for simulating inhomogeneous wall-bounded turbulent flows and getting reliable results with relatively coarse grids.

A High-Order Accurate Gas-Kinetic Scheme for One- and Two-Dimensional Flow Simulation

2014 ◽  
Vol 15 (4) ◽  
pp. 911-943 ◽  
Author(s):  
Na Liu ◽  
Huazhong Tang
Keyword(s):  
Velocity Distribution ◽  
Particle Velocity ◽  
Fourth Order ◽  
Velocity Distribution Function ◽  
Kinetic Scheme ◽  
High Order ◽  
Third Order ◽  
Quartic Polynomial ◽  
Two Dimensional Flow ◽  
Cell Interface

AbstractThis paper develops a high-order accurate gas-kinetic scheme in the framework of the finite volume method for the one- and two-dimensional flow simulations, which is an extension of the third-order accurate gas-kinetic scheme [Q.B. Li, K. Xu, and S. Fu, J. Comput. Phys., 229(2010), 6715-6731] and the second-order accurate gas-kinetic scheme [K. Xu, J. Comput. Phys., 171(2001), 289-335]. It is formed by two parts: quartic polynomial reconstruction of the macroscopic variables and fourth-order accurate flux evolution. The first part reconstructs a piecewise cell-center based quartic polynomial and a cell-vertex based quartic polynomial according to the “initial” cell average approximation of macroscopic variables to recover locally the non-equilibrium and equilibrium single particle velocity distribution functions around the cell interface. It is in view of the fact that all macroscopic variables become moments of a single particle velocity distribution function in the gas-kinetic theory. The generalized moment limiter is employed there to suppress the possible numerical oscillation. In the second part, the macroscopic flux at the cell interface is evolved in fourth-order accuracy by means of the simple particle transport mechanism in the microscopic level, i.e. free transport and the Bhatnagar-Gross-Krook (BGK) collisions. In other words, the fourth-order flux evolution is based on the solution (i.e. the particle velocity distribution function) of the BGK model for the Boltzmann equation. Several 1D and 2D test problems are numerically solved by using the proposed high-order accurate gas-kinetic scheme. By comparing with the exact solutions or the numerical solutions obtained the second-order or third-order accurate gas-kinetic scheme, the computations demonstrate that our scheme is effective and accurate for simulating invisid and viscous fluid flows, and the accuracy of the high-order GKS depends on the choice of the (numerical) collision time.

Numerical studies of a thermokinetic model for oscillatory cool flame and complex ignition phenomena in ethanal oxidation under well-stirred flowing conditions

1989 ◽  
Vol 422 (1863) ◽  
pp. 289-310 ◽  
Keyword(s):  
Numerical Study ◽  
Thermal Characteristics ◽  
Kinetic Scheme ◽  
Ambient Conditions ◽  
Two Stage ◽  
Experimental Conditions ◽  
Cool Flame ◽  
Cool Flames ◽  
Spatial Uniformity ◽  
Acetyl Radical

A numerical study has been undertaken to predict quantitatively each of the non-isothermal reaction modes (stationary-state reaction, oscillatory cool flames and oscillatory two-stage and multiple-stage ignitions) associated with the oxidation of ethanal in a non-adiabatic well-stirred flow system (0.5 dm 3 ) at a mean residence time of 3 s. The kinetic scheme comprises 28 species involved in 60 reactions and it is coupled to the thermal characteristics through enthalpy change in each step, heat capacities of the major components and a heat transfer coefficient appropriate to heat loss through the reaction vessel wall. Spatial uniformity of temperature and concentrations is assumed, matching the experimental conditions. Very satisfactory accord is obtained between the experimentally measured and predicted location of the different reaction modes in the ( p - T a ) ignition diagram (where p is pressure and T a is temperature at ambient conditions), and the time-dependent patterns for oscillatory reaction agree with experimental measurements. The competition between degenerate branching and non-branching reaction modes is governed ultimately by the equilibrium CH 3 +O 2 ⇌CH 3 O 2 . The predicted behaviour is found also to be especially sensitive to the rate of decomposition of the acetyl radical CH 3 CO + M → CH 3 + CO + M. Corrections for its pressure dependence are essential if the predicted form of the oscillatory cool flame region in the ( p - T a ) diagram is to match the experimental results. Variations of the rate of this reaction also give new kinetic insight into the origins of complex oscillatory wave-forms for cool flames that have been observed experimentally. Relationships between the results of the detailed kinetic computations and the predictions from a three-variable, thermokinetic model are examined. This model is the simplest of all reduced schemes that makes successful predictions of two-stage ignition phenomena.

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