The approach to optimization of finite-difference schemes for the advective stage of finite-difference-based lattice Boltzmann method

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The approach to optimization of finite-difference schemes for the advective stage of finite-difference-based lattice Boltzmann method. / Krivovichev, Gerasim V.; Marnopolskaya, Elena S.

In: International Journal of Modeling, Simulation, and Scientific Computing, Vol. 11, No. 1, 2050002, 01.02.2020.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{60dc53f40ecb4dae93ba5c251318ebb2,

title = "The approach to optimization of finite-difference schemes for the advective stage of finite-difference-based lattice Boltzmann method",

abstract = "The approach to optimization of finite-difference (FD) schemes for the linear advection equation (LAE) is proposed. The FD schemes dependent on the scalar dimensionless parameter are considered. The parameter is included in the expression, which approximates the term with spatial derivatives. The approach is based on the considering of the dispersive and dissipative characteristics of the schemes as the functions of the parameter. For the proper choice of the parameter, these functions are minimized. The approach is applied to the optimization of two-step schemes with an asymmetric approximation of time derivative and with various approximations of the spatial term. The cases of schemes from first to fourth approximation orders are considered. The optimal values of the parameter are obtained. Schemes with the optimal values are applied to the solution of test problems with smooth and discontinuous initial conditions. Also, schemes are used in the FD-based lattice Boltzmann method (LBM) for modeling of the compressible gas flow. The obtained numerical results demonstrate the convergence of the schemes and decaying of the numerical dispersion.",

keywords = "dispersion, dissipation, finite-difference schemes, Lattice Boltzmann method, optimization, NATURAL-CONVECTION, CONVERGENCE, SIMULATION, EQUATION, FLOW, BINGHAM FLUID",

author = "Krivovichev, {Gerasim V.} and Marnopolskaya, {Elena S.}",

year = "2020",

month = feb,

day = "1",

doi = "10.1142/S1793962320500026",

language = "English",

volume = "11",

journal = "International Journal of Modeling, Simulation, and Scientific Computing",

issn = "1793-9623",

publisher = "Taylor & Francis",

number = "1",

}

RIS

TY - JOUR

T1 - The approach to optimization of finite-difference schemes for the advective stage of finite-difference-based lattice Boltzmann method

AU - Krivovichev, Gerasim V.

AU - Marnopolskaya, Elena S.

PY - 2020/2/1

Y1 - 2020/2/1

N2 - The approach to optimization of finite-difference (FD) schemes for the linear advection equation (LAE) is proposed. The FD schemes dependent on the scalar dimensionless parameter are considered. The parameter is included in the expression, which approximates the term with spatial derivatives. The approach is based on the considering of the dispersive and dissipative characteristics of the schemes as the functions of the parameter. For the proper choice of the parameter, these functions are minimized. The approach is applied to the optimization of two-step schemes with an asymmetric approximation of time derivative and with various approximations of the spatial term. The cases of schemes from first to fourth approximation orders are considered. The optimal values of the parameter are obtained. Schemes with the optimal values are applied to the solution of test problems with smooth and discontinuous initial conditions. Also, schemes are used in the FD-based lattice Boltzmann method (LBM) for modeling of the compressible gas flow. The obtained numerical results demonstrate the convergence of the schemes and decaying of the numerical dispersion.

AB - The approach to optimization of finite-difference (FD) schemes for the linear advection equation (LAE) is proposed. The FD schemes dependent on the scalar dimensionless parameter are considered. The parameter is included in the expression, which approximates the term with spatial derivatives. The approach is based on the considering of the dispersive and dissipative characteristics of the schemes as the functions of the parameter. For the proper choice of the parameter, these functions are minimized. The approach is applied to the optimization of two-step schemes with an asymmetric approximation of time derivative and with various approximations of the spatial term. The cases of schemes from first to fourth approximation orders are considered. The optimal values of the parameter are obtained. Schemes with the optimal values are applied to the solution of test problems with smooth and discontinuous initial conditions. Also, schemes are used in the FD-based lattice Boltzmann method (LBM) for modeling of the compressible gas flow. The obtained numerical results demonstrate the convergence of the schemes and decaying of the numerical dispersion.

KW - dispersion

KW - dissipation

KW - finite-difference schemes

KW - Lattice Boltzmann method

KW - optimization

KW - NATURAL-CONVECTION

KW - CONVERGENCE

KW - SIMULATION

KW - EQUATION

KW - FLOW

KW - BINGHAM FLUID

UR - http://www.scopus.com/inward/record.url?scp=85079013967&partnerID=8YFLogxK

U2 - 10.1142/S1793962320500026

DO - 10.1142/S1793962320500026

M3 - Article

AN - SCOPUS:85079013967

VL - 11

JO - International Journal of Modeling, Simulation, and Scientific Computing

JF - International Journal of Modeling, Simulation, and Scientific Computing

SN - 1793-9623

IS - 1

M1 - 2050002

ER -

ID: 60401755