Paper Info
Title
High-order conservative reconstruction schemes for finite volume methods in cylindrical and spherical coordinates.
Abstract
High-order reconstruction schemes for the solution of hyperbolic conservation laws in orthogonal curvilinear coordinates are revised in the finite volume approach. The formulation employs a piecewise polynomial approximation to the zone-average values to reconstruct left and right interface states from within a computational zone to arbitrary order of accuracy by inverting a Vandermonde-like linear system of equations with spatially varying coefficients. The approach is general and can be used on uniform and non-uniform meshes although explicit expressions are derived for polynomials from second to fifth degree in cylindrical and spherical geometries with uniform grid spacing. It is shown that, in regions of large curvature, the resulting expressions differ considerably from their Cartesian counterparts and that the lack of such corrections can severely degrade the accuracy of the solution close to the coordinate origin. Limiting techniques and monotonicity constraints are revised for conventional reconstruction schemes, namely, the piecewise linear method (PLM), third-order weighted essentially non-oscillatory (WENO) scheme and the piecewise parabolic method (PPM).
Year
DOI
Venue
2014
10.1016/j.jcp.2014.04.001
Journal of Computational Physics
Keywords
Field
DocType
Finite volume,Reconstruction methods,Curvilinear geometry,Hydrodynamics,Magnetohydrodynamics (MHD),Methods: numerical
Order of accuracy,Mathematical optimization,System of linear equations,Mathematical analysis,Curvilinear coordinates,Spherical coordinate system,Piecewise linear function,Finite volume method,Piecewise,Mathematics,Cartesian coordinate system
Journal
Volume
ISSN
Citations 
270
0021-9991
4
PageRank 
References 
Authors
0.53
7
1
Name
Order
Citations
PageRank
Andrea Mignone1364.45