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A new collocation method for the solution of the convection‐dominated transport equation
Author(s) -
Pinder George E.,
Shapiro Allen
Publication year - 1979
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/wr015i005p01177
Subject(s) - collocation (remote sensing) , convection–diffusion equation , orthogonal collocation , basis (linear algebra) , mathematics , collocation method , convection , basis function , mathematical analysis , dispersion (optics) , function (biology) , derivative (finance) , mechanics , physics , geometry , computer science , differential equation , optics , ordinary differential equation , machine learning , evolutionary biology , financial economics , economics , biology
A modified Hermitian basis function is developed as a means of enhancing numerical solutions to the convection‐dominated transport equation using orthogonal collocation. An asymmetric approximation to the first‐order spatial derivative is provided so that oscillations in the numerical solution are eliminated while introducing a minimum amount of numerical dispersion. The degree of assymetry in the basis function required to achieve a smooth solution is shown to be dependent upon the magnitude of the convective and dispersive terms.