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A single‐node characteristic collocation method for unsteady‐state convection‐diffusion equations in three‐dimensional spaces
Author(s) -
Wu Li,
Wang Kaixin
Publication year - 2011
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20552
Subject(s) - piecewise , mathematics , collocation (remote sensing) , collocation method , orthogonal collocation , hermite polynomials , partial differential equation , node (physics) , reduction (mathematics) , partial derivative , diffusion , convection–diffusion equation , mathematical analysis , differential equation , ordinary differential equation , computer science , geometry , physics , machine learning , thermodynamics , quantum mechanics
We develop a nonconventional single‐node characteristic collocation method with piecewise‐cubic Hermite polynomials for the numerical simulation to unsteady‐state advection‐diffusion transport partial differential equations. This method greatly reduces the number of unknowns in the conventional collocation method, and generates accurate numerical solutions even if very large time steps are taken. The reduction of number of nodes has great potential for problems defined on high space dimensions, which appears in such problems as quantification of uncertainties in subsurface porous media. The method developed here is easy to formulate. Numerical experiments are presented to show the strong potential of the method. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 786–802, 2011