A very high-order finite volume method for the time-dependent convection–diffusion problem with Butcher Tableau extension

• Published in: Computers & mathematics with applications (1987) Vol. 68; no. 10; pp. 1292 - 1311
• Main Authors: Clain, S., Machado, G.J.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.11.2014
• Subjects: Accuracy; Butcher Tableau; Computer simulation; Convection–diffusion; Discretization; Finite volume; Finite volume method; Mathematical models; Polynomial reconstruction; Polynomials; Runge-Kutta method; Very high-order; Finite volume; Convection–diffusion; Very high-order; Polynomial reconstruction; Butcher Tableau

The time discretization of a very high-order finite volume method may give rise to new numerical difficulties resulting into accuracy degradations. Indeed, for the simple one-dimensional unstationary convection–diffusion equation for instance, a conflicting situation between the source term time dis...