The Research Of Numerical Perturbation Algorithm For A Class Of The Convective-diffusion Equation With Source Term

The convective-diffusion equation with source term is found in many ap-plications of fluid dynamics. Sometimes, the existence of source term makes some schemesreducing calculation accuracy. The numerical perturbation algo-rithm proposed by professor Gao Zhi has improved the some schemes’ calculation accuracy of the convective-diffusion equation. However, there are many worthy of further research works in this respect. The main contents of this thesis are as follows:Firstly, the schemes, including the exponent scheme, numerical perturbation finite difference method and numerical perturbation finite volume method, are introduced for convective-diffusion equation without source term. Then, for the convective-diffusion equation with source term, the diffusion term is discretized by using second-order central scheme, while the convection term is discretized by using third-order upwind scheme and fourth-order central scheme, respective-ly. Based on which, two kinds of numerical perturbation difference schemes are obtained by reconstructing discrete part of convection term and source term. Fur-thermore, for the convective-diffusion equation with source term, the numerical perturbation central finite volume scheme is obtained by reconstructing discrete part of convection term and source term. Finally, the numerical results show that the numerical perturbation difference schemes and numerical perturbation finite volume schemes are higher calculation accuracy than the original schemes.