Discrete unified gas-kinetic scheme for the conservative Allen-Cahn equation

Zhang，Chunhua1; Liang，Hong2; Guo，Zhaoli3; Wang，Lian Ping1,4,5

2022-04-01

10.1103/PhysRevE.105.045317

Physical Review E   影响因子和分区

2470-0045

2470-0053

In this paper, two discrete unified gas-kinetic scheme (DUGKS) methods with piecewise-parabolic flux reconstruction are presented for the conservative Allen-Cahn equation (CACE). One includes a temporal derivative of the order parameter in the force term while the other does not include temporal derivative in the force term but results in a modified CACE with additional terms. In the context of DUGKS, the continuum equations recovered from the piecewise-linear and piecewise-parabolic reconstructions for the fluxes at cell faces are subsequently derived. It is proved that the resulting equation with the piecewise-linear reconstruction is a first-order approximation to the discrete velocity kinetic equation due to the presence of the force term and the nonconservation property of the momentum of the collision model. To guarantee second-order accuracy of DUGKS, the piecewise-parabolic reconstruction for numerical flux is proposed. To validate the accuracy of the present DUGKS with the proposed flux evaluation, several benchmark problems, including the diagonal translation of a circular interface, the rotation of a Zalesak disk and the deformation of a circular interface, have been simulated. Numerical results show that the accuracy of both proposed DUGKS methods is almost comparable and improved compared with the DUGKS with linear flux reconstruction scheme.

SCI ; EI

英语

第一

National Natural Science Foundation of China[51836003,11972142,51806142,91852205,91741101,11961131006] ; NSFC Basic Science Center Program[11988102] ; Guangdong Provincial Key Laboratory of Turbulence Re-search and Applications[2019B21203001] ; Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications[2020B1212030001] ; Shenzhen Science and Tech-nology Program[KQTD20180411143441009]

Physics

Physics, Fluids & Plasmas ; Physics, Mathematical

WOS:000796449100004

AMER PHYSICAL SOC

20222012103114

Integral equations ; Kinetics ; Numerical methods

Fluid Flow, General:631.1 ; Calculus:921.2 ; Combinatorial Mathematics, Includes Graph Theory, Set Theory:921.4 ; Numerical Methods:921.6 ; Classical Physics; Quantum Theory; Relativity:931

PHYSICS

2-s2.0-85129732880

Scopus

1.Guangdong Provincial Key Laboratory of Turbulence Research and Applications,Department of Mechanics and Aerospace Engineering,Southern University of Science and Technology,Guangdong,Shenzhen,518055,China
2.Department of Physics,Hangzhou Dianzi University,Hangzhou,310018,China
3.State Key Laboratory of Coal Combustion,Huazhong University of Science and Technology,Wuhan,430074,China
4.Center for Complex Flows and Soft Matter Research,Southern University of Science and Technology,Guangdong,Shenzhen,518055,China
5.Guangdong-Hong Kong-Macao Jt. Lab. for Data-Driven Fluid Mechanics and Engineering Applications,Southern University of Science and Technology,Guangdong,Shenzhen,518055,China

Zhang，Chunhua,Liang，Hong,Guo，Zhaoli,et al. Discrete unified gas-kinetic scheme for the conservative Allen-Cahn equation[J]. Physical Review E,2022,105(4).

Zhang，Chunhua,Liang，Hong,Guo，Zhaoli,&Wang，Lian Ping.(2022).Discrete unified gas-kinetic scheme for the conservative Allen-Cahn equation.Physical Review E,105(4).

Zhang，Chunhua,et al."Discrete unified gas-kinetic scheme for the conservative Allen-Cahn equation".Physical Review E 105.4(2022).