Abstract
The use of the highest‐order ((N – 1)th‐order) Lagrangian interpolation Polynomial for the approximation of the exact solution in the backward characteristics scheme with N nodes is inefficient owing to the excessive number of terms in the polynomial. New schemes based on a combination of lower‐order polynomials to approximate the exact solution are developed, with the relative weighting of the polynomials determined by Fourier mode analysis. With the addition of a flux limiter and a modified discriminator, the resulting schemes are oscillation‐free, highly accurate, efficient and more cost‐effective as compared with those schemes using the highest‐order Lagrangian polynomial.
Original language | English |
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Pages (from-to) | 997-1012 |
Number of pages | 16 |
Journal | International Journal for Numerical Methods in Fluids |
Volume | 19 |
Issue number | 11 |
DOIs | |
Publication status | Published - 1 Jan 1994 |
Keywords
- Advection
- Finite difference
- Flux limiter
- Method of characteristics
ASJC Scopus subject areas
- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- Computer Science Applications
- Applied Mathematics