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The Montecinos-Balsara ADER-FV polynomial basis: Convergence properties & extension to non-conservative multidimensional systems

Accepted version
Peer-reviewed

Type

Article

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Authors

Abstract

Hyperbolic systems of PDEs can be solved to arbitrary orders of accuracy by using the ADER Finite Volume method. These PDE systems may be non-conservative and non-homogeneous, and contain stiff source terms. ADER-FV requires a spatio-temporal polynomial reconstruction of the data in each spacetime cell, at each time step. This reconstruction is obtained as the root of a nonlinear system, resulting from the use of a Galerkin method. It was proved in Jackson [7] that for traditional choices of basis polynomials, the eigenvalues of certain matrices appearing in these nonlinear systems are always 0, regardless of the number of spatial dimensions of the PDEs or the chosen order of accuracy of the ADER-FV method. This guarantees fast convergence to the Galerkin root for certain classes of PDEs. In Montecinos and Balsara [9] a new, more efficient class of basis polynomials for the one-dimensional ADER-FV method was presented. This new class of basis polynomials, originally presented for conservative systems, is extended to multidimensional, non-conservative systems here, and the corresponding property regarding the eigenvalues of the Galerkin matrices is proved.

Description

Keywords

ADER, Finite Volume, Galerkin, Eigenvalues, Convergence

Journal Title

COMPUTERS & FLUIDS

Conference Name

Journal ISSN

0045-7930
1879-0747

Volume Title

163

Publisher

Elsevier BV

Rights

All rights reserved
Sponsorship
Engineering and Physical Sciences Research Council (EP/L015552/1)