Limiting strategies for polynomial reconstructions in the finite volume approximation of the linear advection equation

Authors:
Enrico Bertolazzi;Gianmarco Manzini
Affiliations:
Dipartimento di Ingegneria Meccanica e Strutturale, Università di Trento, via Mesiano 77, I-38050 Trento, Italy;Istituto di Analisi Numerica IAN-CNR, via Ferrata 1, I-27100 Pavia, Italy
Venue:
Applied Numerical Mathematics - Special issue: Applied scientific computing - Grid generation, approximated solutions and visualization
Year:
2004

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Abstract

A cell-centered semi-discrete finite volume method is proposed to accurately solve the time-dependent scalar advection equation. The spatial accuracy is ensured by a piecewise linear reconstruction which requires a suitable limiting strategy to control spurious numerical oscillations. Three different approaches are conceived to limit the approximate solution.