AN ACCURATE NUMERICAL ALGORITHM FOR ADVECTIVE TRANSPORT

The paper describes a new numerical algorithm for pure advection at la rge Courant numbers. The DISCUS scheme uses an accurate and proven con trol volume algorithm (QUICKEST) within a Lagrangian treatment of adve ction. By being in sympathy with the information flow dictated by char acteristic lines, the scheme performs exceedingly well at Courant numb ers greater than one. In contrast to existing Lagrangian schemes which use the characteristics to determine the grid points from which conce ntrations are interpolated, in DISCUS the characteristics are used to determine the appropriate location for the control volume. The scheme is of comparable accuracy to Eulerian schemes at Courant numbers less than one, but it increasingly outperforms them as the Courant number i ncreases. Indeed, the results reported illustrate the futility of usin g an Eulerian scheme at high Courant numbers.