Augmented upwind numerical schemes for the groundwater transport advection-dispersion equation with local operators

作者：Allwright A^*; Atangana A^*

来源：International Journal for Numerical Methods in Fluids, 2018, 87(9): 437-462.

DOI：10.1002/fld.4497

• advection-dispersion equation
• Crank-Nicolson scheme
• local operators
• upwind schemes
• weighted upwind-downwind scheme

When solute transport is advection-dominated, the advection-dispersion equation approximates to a hyperbolic-type partial differential equation, and finite difference and finite element numerical approximation methods become prone to artificial oscillations. The upwind scheme serves to correct these responses to produce a more realistic solution. The upwind scheme is reviewed and then applied to the advection-dispersion equation with local operators for the first-order upwinding numerical approximation scheme. The traditional explicit and implicit schemes, as well as the Crank-Nicolson scheme, are developed and analyzed for numerical stability to form a comparison base. Two new numerical approximation schemes are then proposed, namely, upwind-Crank-Nicolson scheme, where only for the advection term is applied, and weighted upwind-downwind scheme. These newly developed schemes are analyzed for numerical stability and compared to the traditional schemes. It was found that an upwind-Crank-Nicolson scheme is appropriate if the Crank-Nicolson scheme is only applied to the advection term of the advection-dispersion equation. Furthermore, the proposed explicit weighted upwind-downwind finite difference numerical scheme is an improvement on the traditional explicit first-order upwind scheme, whereas the implicit weighted first-order upwind-downwind finite difference numerical scheme is stable under all assumptions when the appropriate weighting factor () is assigned.

• 出版日期2018-7-30