Two high-order splitting schemes based on the idea of the operators splitting method are given. The three-dimensional advection-diffusion equation was split into several one-dimensional equations that were solved by t...Two high-order splitting schemes based on the idea of the operators splitting method are given. The three-dimensional advection-diffusion equation was split into several one-dimensional equations that were solved by these two schemes, only three computational grid points were needed in each direction but the accuracy reaches the spatial fourth-order. The third scheme proposed is based on the classical ADI scheme and the accuracy of the advection term of it can reach the spatial fourth-order. Finally, two typical numerical experiments show that the solutions of these three schemes compare well with that given by the analytical solution when the Peclet number is not bigger than 5.展开更多
A refined numerical method, based upon time-line interpolation, for the simulation of advection and diffusion has been tentatively explored. A complete set of temporal reachback numerical scheme in applying the method...A refined numerical method, based upon time-line interpolation, for the simulation of advection and diffusion has been tentatively explored. A complete set of temporal reachback numerical scheme in applying the method of characteristics has been derived, and the favorable accuracy of the method demonstrated. The use of interpolations in time, rather than the more widely used interpolations in space, demonstrates that it generates a much smaller numerical error.展开更多
文摘Two high-order splitting schemes based on the idea of the operators splitting method are given. The three-dimensional advection-diffusion equation was split into several one-dimensional equations that were solved by these two schemes, only three computational grid points were needed in each direction but the accuracy reaches the spatial fourth-order. The third scheme proposed is based on the classical ADI scheme and the accuracy of the advection term of it can reach the spatial fourth-order. Finally, two typical numerical experiments show that the solutions of these three schemes compare well with that given by the analytical solution when the Peclet number is not bigger than 5.
文摘A refined numerical method, based upon time-line interpolation, for the simulation of advection and diffusion has been tentatively explored. A complete set of temporal reachback numerical scheme in applying the method of characteristics has been derived, and the favorable accuracy of the method demonstrated. The use of interpolations in time, rather than the more widely used interpolations in space, demonstrates that it generates a much smaller numerical error.
