UNIFICATION OF SOME ADVECTION SCHEMES IN TWO DIMENSIONS

Authors:
D. Sidilkover;P. L. Roe
Affiliations:
-;-
Venue:
UNIFICATION OF SOME ADVECTION SCHEMES IN TWO DIMENSIONS
Year:
1995

Citing 0
Cited 3

High-order monotonicity-preserving compact schemes for linear scalar advection on 2-D irregular meshes

Journal of Computational Physics
Non-oscillatory third order fluctuation splitting schemes for steady scalar conservation laws

Journal of Computational Physics
Solution of the equation of radiative transfer using a Newton-Krylov approach and adaptive mesh refinement

Journal of Computational Physics

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Abstract

In this paper a relationship between two approaches towards construction of genuinely two-dimensional upwind advection schemes is established. One of these approaches is of the control volume type applicable on structured cartesian meshes. It resulted (see [14], [15]) in the compact high resolution schemes capable of maintaining second order accuracy in both homogeneous and inhomogeneous cases. Another one is the fluctuation splitting approach (see [11], [3], [12], [17]), which is well suited for triangular (and possibly) unstructured meshes. Understanding the relationship between these two approaches allows us to formulate here a new fluctuation splitting high resolution (i.e. possible use of artificial compression, while maintaining positivity property) scheme. This scheme is shown to be linearity preserving in inhomogeneous as well as homogeneous cases.