MOSQUITO: An efficient finite difference scheme for numerical simulation of 2D advection

An explicit finite difference method for the treatment of the advective terms in the 2D equation of unsteady scalar transport is presented. The scheme is a conditionally stable extension to two dimensions of the popular QUICKEST scheme. It is deduced imposing the vanishing of selected components of the truncation error for the case of steady uniform flow. The method is then extended to solve the conservative form of the depth-averaged transport equation. Details of the accuracy and stability analysis of the numerical scheme with test case results are given, together with a comparison with other existing schemes suitable for the long-term computations needed in environmental modelling. Although with a truncation error of formal order 0(ΔxΔt, ΔyΔt, Δt2), the present scheme is shown actually to be of an accuracy comparable with schemes of third-order in space, while requiring a smaller computational effort and/or having better stability properties. In principle, the method can be easily extended to the 3D case. Copyright © 1999 John Wiley & Sons, Ltd.

[1]  D. Webb,et al.  IMPROVED ADVECTION SCHEMES FOR OCEAN MODELS , 1998 .

[2]  Thomas J. R. Hughes,et al.  A Petrov-Galerkin finite element method for convection-dominated flows: An accurate upwinding technique for satisfying the maximum principle☆ , 1985 .

[3]  Jeffrey W. Gartner,et al.  Tidal, Residual, Intertidal Mudflat (TRIM) Model and its Applications to San Francisco Bay, California , 1993 .

[4]  Patrick J. Roache,et al.  On artificial viscosity , 1972 .

[5]  P. Gaskell,et al.  Curvature‐compensated convective transport: SMART, A new boundedness‐ preserving transport algorithm , 1988 .

[6]  George Em Karniadakis,et al.  Spectral element‐FCT method for scalar hyperbolic conservation laws , 1992 .

[7]  J. Crank,et al.  A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type , 1947 .

[8]  D. Bradley,et al.  A Taylor-series approach to numerical accuracy and a third-order scheme for strong convective flows , 1988 .

[9]  A. K. Runchal,et al.  Convergence and accuracy of three finite difference schemes for a two‐dimensional conduction and convection problem , 1972 .

[10]  Dennis N. Assanis,et al.  Evaluation of various high-order-accuracy schemes with and without flux limiters , 1993 .

[11]  A. Arakawa,et al.  Numerical methods used in atmospheric models , 1976 .

[12]  B. P. Leonard,et al.  A stable and accurate convective modelling procedure based on quadratic upstream interpolation , 1990 .

[13]  W. Rodi,et al.  A higher order numerical scheme for scalar transport , 1982 .

[14]  Jay P. Boris,et al.  Flux-corrected transport. I. SHASTA, a fluid transport algorithm that works , 1973 .

[15]  F. Holly,et al.  Dispersion Simulation in Two‐dimensional Tidal Flow , 1984 .

[16]  D. Spalding.  A novel finite difference formulation for differential expressions involving both first and second derivatives , 1972 .

[17]  Roger Alexander Falconer,et al.  Modified forms of the third-order convection, second-order diffusion scheme for the advection-diffusion equation , 1994 .

[18]  E. Baskharone,et al.  A monotone streamline upwind method for quadratic finite elements , 1993 .

[19]  Zhong Ji,et al.  Semi‐implicit Skew Upwind Method for problems in environmental hydraulics , 1993 .

[20]  Roger Alexander Falconer,et al.  Advection-diffusion modelling using the modified QUICK scheme , 1992 .