Parallel algorithms for semi-lagrangian advection

✍ Scribed by A. V. Malevsky; S. J. Thomas

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 220 KB
• Volume: 25
• Category: Article
• ISSN: 0271-2091
• DOI: 10.1002/(sici)1097-0363(19970830)25:4<455::aid-fld572>3.0.co;2-h

✦ Synopsis

Numerical time step limitations associated with the explicit treatment of advection-dominated problems in computational ¯uid dynamics are often relaxed by employing Eulerian±Lagrangian methods. These are also known as semi-Lagrangian methods in the atmospheric sciences. Such methods involve backward time integration of a characteristic equation to ®nd the departure point of a ¯uid particle arriving at a Eulerian grid point. The value of the advected ®eld at the departure point is obtained by interpolation. Both the trajectory integration and repeated interpolation in¯uence accuracy. We compare the accuracy and performance of interpolation schemes based on piecewise cubic polynomials and cubic B-splines in the context of a distributed memory, parallel computing environment. The computational cost and interprocessor communication requirements for both methods are reported. Spline interpolation has better conservation properties but requires the solution of a global linear system, initially appearing to hinder a distributed memory implementation. The proposed parallel algorithm for multidimensional spline interpolation has almost the same communication overhead as local piecewise polynomial interpolation. We also compare various techniques for tracking trajectories given different values for the Courant number. Large Courant numbers require a high-order ODE solver involving multiple interpolations of the velocity ®eld.