A new weighted upwind finite volume element method based on non-standard covolume for time-dependent convection-diffusion problems

作者：Gao, Fuzheng^*; Liang, Dong

来源：International Journal for Numerical Methods in Fluids, 2013, 73(11): 953-975.

DOI：10.1002/fld.3830

• convection-diffusion
• weighted upwind FVEM
• nonstandard covolume
• high-order accuracy
• mass conservation
• stability

In modern numerical simulation of problems in energy resources and environmental science, it is important to develop efficient numerical methods for time-dependent convection-diffusion problems. On the basis of nonstandard covolume grids, we propose a new kind of high-order upwind finite volume element method for the problems. We first prove the stability and mass conservation in the discrete forms of the scheme. Optimal second-order error estimate in L-2-norm in spatial step is then proved strictly. The scheme is effective for avoiding numerical diffusion and nonphysical oscillations and has second-order accuracy. Numerical experiments are given to verify the performance of the scheme.

• 出版日期2013-12-20
• 单位山东大学