The Boltzmann-Bhatnagar-Gross-Krook（BGK）model is investigated for its validity regarding the collision term approximation through relaxation evaluation. The evaluation is based on theoretical analysis and numerical ...The Boltzmann-Bhatnagar-Gross-Krook（BGK）model is investigated for its validity regarding the collision term approximation through relaxation evaluation. The evaluation is based on theoretical analysis and numerical comparison between the BGK and direct simulation Monte Carlo（DSMC） results for three specifically designed relaxation problems. In these problems, one or half component of the velocity distribution is characterized by another Maxwellian distribution with a different temperature. It is analyzed that the relaxation time in the BGK model is unequal to the molecular mean collision time. Relaxation of component distribution fails to involve enough contribution from other component distributions, which makes the BGK model unable to capture details of velocity distribution, especially when discontinuity exists in distribution. The BGK model,however, predicts satisfactory results including fluxes during relaxation when the temperature difference is small. Particularly, the model-induced error in the BGK model increases with the temperature difference, thus the model is more reliable for low-speed rarefied flows than for hypersonic flows.展开更多
By further generalizing Frommer's results in the sense of nonlinear multisplitting, we build a class of nonlinear multisplitting AOR-type methods, which covers many rather practical nonlinear multisplitting relaxa...By further generalizing Frommer's results in the sense of nonlinear multisplitting, we build a class of nonlinear multisplitting AOR-type methods, which covers many rather practical nonlinear multisplitting relaxation methods such as multisplitting AOR-Newton method, multisplitting AOR-chord method and multisplitting AOR-Steffensen method, etc.. Furthermore,a general convergence theorem for the nonlinear multisplitting AOR-type methods and the local convergence for the multisplitting AOR-Newton method are discussed in detail.A lot of numerical tests show that our new methods are feasible and satisfactory.展开更多
We extend the SCGS smoothing procedure (Symmetrical Collective Gauss-Seidel relaxation) proposed by S. P. Vanka[4], for multigrid solvers of the steady viscous incompressible Navier-Stokes equations, to corresponding ...We extend the SCGS smoothing procedure (Symmetrical Collective Gauss-Seidel relaxation) proposed by S. P. Vanka[4], for multigrid solvers of the steady viscous incompressible Navier-Stokes equations, to corresponding line-wise versions. The resulting relaxation schemes are integrated into the multigrid solver based on second-order upwind differencing presented in [5]. Numerical comparisons on the efficiency of point-wise and line-wise relaxations are presented展开更多
基金supported by the National Natural Science Foundation of China(91116013,11372325,and 11111120080)
文摘The Boltzmann-Bhatnagar-Gross-Krook（BGK）model is investigated for its validity regarding the collision term approximation through relaxation evaluation. The evaluation is based on theoretical analysis and numerical comparison between the BGK and direct simulation Monte Carlo（DSMC） results for three specifically designed relaxation problems. In these problems, one or half component of the velocity distribution is characterized by another Maxwellian distribution with a different temperature. It is analyzed that the relaxation time in the BGK model is unequal to the molecular mean collision time. Relaxation of component distribution fails to involve enough contribution from other component distributions, which makes the BGK model unable to capture details of velocity distribution, especially when discontinuity exists in distribution. The BGK model,however, predicts satisfactory results including fluxes during relaxation when the temperature difference is small. Particularly, the model-induced error in the BGK model increases with the temperature difference, thus the model is more reliable for low-speed rarefied flows than for hypersonic flows.
文摘By further generalizing Frommer's results in the sense of nonlinear multisplitting, we build a class of nonlinear multisplitting AOR-type methods, which covers many rather practical nonlinear multisplitting relaxation methods such as multisplitting AOR-Newton method, multisplitting AOR-chord method and multisplitting AOR-Steffensen method, etc.. Furthermore,a general convergence theorem for the nonlinear multisplitting AOR-type methods and the local convergence for the multisplitting AOR-Newton method are discussed in detail.A lot of numerical tests show that our new methods are feasible and satisfactory.
文摘We extend the SCGS smoothing procedure (Symmetrical Collective Gauss-Seidel relaxation) proposed by S. P. Vanka[4], for multigrid solvers of the steady viscous incompressible Navier-Stokes equations, to corresponding line-wise versions. The resulting relaxation schemes are integrated into the multigrid solver based on second-order upwind differencing presented in [5]. Numerical comparisons on the efficiency of point-wise and line-wise relaxations are presented
