Efficient higher‐order backward characteristics schemes for transient advection

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.