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Solution of the flow and mass transport equations by means of spectral elements
Author(s) -
Goblet P.,
Cordier E.
Publication year - 1993
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/93wr00926
Subject(s) - interpolation (computer graphics) , computation , mathematics , term (time) , spectral method , flow (mathematics) , basis (linear algebra) , finite element method , spectral element method , basis function , convection–diffusion equation , mathematical optimization , mathematical analysis , algorithm , physics , mixed finite element method , geometry , classical mechanics , motion (physics) , quantum mechanics , thermodynamics
A new numerical approach is proposed to solve the equations of flow and mass transport. This approach relies on a finite‐element type formulation using basis functions of arbitrary order (spectral elements). An appropriate choice of the nodal points and the integration points leads to a very effective computation of the element matrices. The transport equation is solved by combining a spectral approximation for the dispersion term with a backtracking algorithm for the advection term, which is aided by the most precise interpolation possible with the spectral method. The formulation is shown to yield an accurate description of very steep fronts with reasonable computer resources.