Computer Methods in Applied Mechanics and Engineering
A positive finite-difference advection scheme
Journal of Computational Physics
Applied Numerical Mathematics
A well-behaved TVD limiter for high-resolution calculations of unsteady flow
Journal of Computational Physics
A method for reducing dispersion in convective difference schemes
Journal of Computational Physics
International Journal of Computational Fluid Dynamics - CFD 2006 Held at Queens University at Kingston, Ontario, Canada, 1519 July 2006
Compact third-order limiter functions for finite volume methods
Journal of Computational Physics
Journal of Computational Physics
The Immersed Structural Potential Method for haemodynamic applications
Journal of Computational Physics
Multi-dimensional limiting for high-order schemes including turbulence and combustion
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.47 |
The design of bounded, higher-order convection schemes is considered with a view to selecting those discretizations giving good resolution of sharp gradients, while at the same time providing competitive accuracy and convergence behaviour when applied to smooth, recirculating flows. The present work contains a detailed classification and analysis and extensive tables of most non-linear scalar convection schemes so far proposed within the cell-centred, finite-volume framework. The analysis includes a review and comparison of the two most frequently-used non-linear approaches, flux limiters (FL) and normalized variables (NV), and the three major boundedness criteria typically employed: total-variation diminishing (TVD), positivity and the convection-boundedness criterion (CBC). All NV schemes considered are converted to FL form to allow direct comparison and classification of a wide range of schemes. Several specific design principles for positive non-linear schemes are considered and it is shown how these can be applied to understand the relative performance of different approaches. Finally the performance of many existing schemes is compared and ranked on the basis of two scalar convection test cases, one smooth and one discontinuous, which demonstrates the wide variation in both accuracy and convergence behaviour of the various schemes and the benefits of the design principles considered.