Numerical manifold scheme for convection diffusion equation and its stability analysis

作者：Zhang Zhengrong^*; Zhang Xiangwei

来源：Journal of Xi'an Jiaotong University, 2010, 44(1): 117-124.

• Analytic solution
• Comparative analysis
• Computational accuracy
• Convection diffusion problems
• Convection-diffusion equations
• Cover system
• Diffusion effects
• Finite element solution
• First order
• Free convections
• Galerkin
• In-pipe
• Numerical manifold method
• Numerical stabilities
• Rectangular finite element
• Stability analysis
• Thermal convections
• Unconditionally stable
• Weighted residuals method

The manifold method was employed to solve convection diffusion problems and the numerical manifold schemes for the convection diffusion equation were derived based on the Galerkin weighted residuals method. The standard manifold schemes with the first order polynomial function for physical cover were proved to be unconditionally stable, and the stability and adaptability of the present manifold schemes were confirmed by comparative analysis of numerical manifold solutions, finite element solutions and analytic solutions for one-dimensional steady source-free convection diffusion. The manifold schemes based on a four-node rectangular finite element cover system were used to simulate two-dimensional thermal convection-diffusion in pipe entry flow. The results show that the numerical manifold method can significantly improve computational accuracy at low element Peclet number (Pe<2) compared with the finite element method. However, severe false diffusion effects at high element Peclet number will reduce computational accuracy and lead to erroneous results.

• 出版日期2010