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A monotone predictor-corrector scheme for advection

Trębiński J.

Computer Assisted Mechanics and Engineering Sciences

2002

Vol. 9, No. 2

271-290

A monotone predictor-corrector finite difference scheme solving the advection equation has been proposed. A geometrical interpretation of the Burstein scheme forms a basis for construction of the new scheme. The main idea consists in defining a proper limitation algorithm in the predictor step preventing formation of new extremes of the solution profile. Various variants of the scheme have been tested for the linear advection equation and an optimum version has been chosen for further developments. Extensions to the nonlinear case and inhomogenous, solution independent velocity field have been made. Application of the time splitting procedure enables the scheme to be applied for multidimensional advection problems. For chosen test problems the scheme behaves better than schemes proposed in the literature.