| Convection equations is a kind of partial differential equations.Therefore,solving these equations has very important theoretical and practical significance.This paper establishes high-order compact difference scheme for solving convection equations.First of all,For the one-dimensional convection equation,assuming that the one dimensional equation is established at(xi,tn+1/2),Taylor series expansion and correction for the third derivative in the truncation error remainder of the central difference scheme are used for discretization of time and space.So a two-level implicit compact difference scheme for solving this convection equation is proposed.It is named in HOC1.it is the fourth-order accuracy in both time and space.Secondly,expending the one dimensional equation at(xi,ti),a three-level compact difference scheme for solving the one-dimensional convection equation is proposed.It is named in HOC2.These stabilities are obtained by the von Neumann method.The accuracy and the stability of the two schemes are validated by some numerical experiments.Then,For the two-dimensional and three-dimensional convection equations,using the Local one-dimensional(LOD)method to making the two-dimensional and three-dimensional problems split some one-dimensional equations.The one-dimensional convection equations use taylor series expansion and correction for the third derivative in the truncation error remainder of the central difference scheme in discretization of time and space.We can establish high-order compact LOD schemes for solving two-dimensional and three-dimensional convection equations.The stability are obtained by the von Neumann method.Then,the accuracy and reliability of these schemes are validated by some numerical experiments.Finally,these schemes deduced in this paper are integrated into the software of"PHOEBESolver",which makes it easier for scholars in numerical solutions of partial differential equations to use these schemes in this paper. |
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