This paper presents two uniformly convergent numerical schemes for the two dimensional steady state discrete ordinates transport equation in the diffusive regime,which is valid up to the boundary and interface layers....This paper presents two uniformly convergent numerical schemes for the two dimensional steady state discrete ordinates transport equation in the diffusive regime,which is valid up to the boundary and interface layers.A five-point nodecentered and a four-point cell-centered tailored finite point schemes(TFPS)are introduced.The schemes first approximate the scattering coefficients and sources by piecewise constant functions and then use special solutions to the constant coefficient equation as local basis functions to formulate a discrete linear system.Numerically,both methods can not only capture the diffusion limit,but also exhibit uniform convergence in the diffusive regime,even with boundary layers.Numerical results show that the five-point scheme has first-order accuracy and the four-point scheme has second-order accuracy,uniformly with respect to the mean free path.Therefore a relatively coarse grid can be used to capture the two dimensional boundary and interface layers.展开更多
In this paper some common used numerical schemes for solving discrete ordinate equations are considered and the error estimates are studied for the combined spatial and angular approximations. The conclusions show tha...In this paper some common used numerical schemes for solving discrete ordinate equations are considered and the error estimates are studied for the combined spatial and angular approximations. The conclusions show that the error order of scalar flux in all of these schemes can not be second order even if the source term f is smooth enough. In addition, when we introduce a kind of graded grids, the simple step character scheme has same accuracy as "high order" ones.展开更多
基金supported by the NSFC Project No.10971116.M.Tang is supported by Natural Science Foundation of Shanghai under Grant No.12ZR1445400Shanghai Pujiang Program 13PJ1404700+1 种基金supported in part by the National Natural Science Foundation of China under Grant DMS-11101278the Young Thousand Talents Program of China.
文摘This paper presents two uniformly convergent numerical schemes for the two dimensional steady state discrete ordinates transport equation in the diffusive regime,which is valid up to the boundary and interface layers.A five-point nodecentered and a four-point cell-centered tailored finite point schemes(TFPS)are introduced.The schemes first approximate the scattering coefficients and sources by piecewise constant functions and then use special solutions to the constant coefficient equation as local basis functions to formulate a discrete linear system.Numerically,both methods can not only capture the diffusion limit,but also exhibit uniform convergence in the diffusive regime,even with boundary layers.Numerical results show that the five-point scheme has first-order accuracy and the four-point scheme has second-order accuracy,uniformly with respect to the mean free path.Therefore a relatively coarse grid can be used to capture the two dimensional boundary and interface layers.
文摘In this paper some common used numerical schemes for solving discrete ordinate equations are considered and the error estimates are studied for the combined spatial and angular approximations. The conclusions show that the error order of scalar flux in all of these schemes can not be second order even if the source term f is smooth enough. In addition, when we introduce a kind of graded grids, the simple step character scheme has same accuracy as "high order" ones.
