A linear stability analysis of the cell-wise relaxation implicit discontinuous Galerkin method for wave propagation

Keisuke Sawada; Kanako Yasue

doi:10.1088/0169-5983/43/4/041402

A linear stability analysis of the cell-wise relaxation implicit discontinuous Galerkin method for wave propagation

Keisuke Sawada, Kanako Yasue

ENG - Aerospace Engineering

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1 Citation (Scopus)

Abstract

A linear stability analysis of the cell-wise relaxation implicit discontinuous Galerkin method proposed in our previous work was carried out for a scalar advection equation using three different generating patterns of triangular cells in two-dimensional space. A detailed mathematical formulation of the stability analysis is presented in this paper. It is shown that the present cell-wise implicit method with spatial accuracies up to fourth order is stable with very large Courant-Friedrichs-Lewy (CFL) numbers.

Original language	English
Article number	041402
Journal	Fluid Dynamics Research
Volume	43
Issue number	4
DOIs	https://doi.org/10.1088/0169-5983/43/4/041402
Publication status	Published - 2011 Aug 1

ASJC Scopus subject areas

Mechanical Engineering
Physics and Astronomy(all)
Fluid Flow and Transfer Processes

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abstract = "A linear stability analysis of the cell-wise relaxation implicit discontinuous Galerkin method proposed in our previous work was carried out for a scalar advection equation using three different generating patterns of triangular cells in two-dimensional space. A detailed mathematical formulation of the stability analysis is presented in this paper. It is shown that the present cell-wise implicit method with spatial accuracies up to fourth order is stable with very large Courant-Friedrichs-Lewy (CFL) numbers.",

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AB - A linear stability analysis of the cell-wise relaxation implicit discontinuous Galerkin method proposed in our previous work was carried out for a scalar advection equation using three different generating patterns of triangular cells in two-dimensional space. A detailed mathematical formulation of the stability analysis is presented in this paper. It is shown that the present cell-wise implicit method with spatial accuracies up to fourth order is stable with very large Courant-Friedrichs-Lewy (CFL) numbers.

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A linear stability analysis of the cell-wise relaxation implicit discontinuous Galerkin method for wave propagation

Abstract

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