Numerical Scheme Improvement of Three Dimensional Mass Transport Equation

Smolarkiewicz upwind scheme is improved based on commonl upwind scheme, in which anti-diffusive velocities are added. Central scheme, upwind scheme, and Smolarkiewicz upwind scheme are used to discretize 1-D and 3-D convection equation. Relative mean square deviations between simulated values and exact ones are analyzed. Errors of central scheme, upwind scheme, and Smolarkiewicz upwind scheme are 2.11~7.25%, 3.62~9.65%, and 2.15~6.21%, which are produced by time and spatial discretization. Central scheme is more precise than upwind scheme because of its second-order truncation error. Smolarkiewicz upwind scheme is more precise than common one because of anti-diffusive velocities added. Plane distribution figure of mass concentration in the flume shows that numerical oscillations and negative values appear in central scheme condition, and upwind scheme has the lowest precision due to heavy dissipation. Smolarkiewicz upwind scheme overcomes the weaknesses of above two schemes, and it is the recommended scheme to be applied in water quality model based on POM.