A preliminary investigation on an ELLAM scheme for linear transport equations

• Published in: Numerical methods for partial differential equations Vol. 19; no. 1; pp. 22 - 43
• Main Authors: Al-Lawatia, Mohamed, Wang, Hong
• Format: Journal Article
• Language: English
• Published: New York Wiley Subscription Services, Inc., A Wiley Company 01.01.2003
• Subjects: advection-reaction equations; characteristic methods; comparison of numerical methods; essentially nonoscillatory schemes; Eulerian-Lagrangian methods; transport equations
• ISSN: 0749-159X; 1098-2426
• DOI: 10.1002/num.10042

We present an Eulerian‐Lagrangian localized adjoint method (ELLAM) for linear advection‐reaction partial differential equations in multiple space dimensions. We carry out numerical experiments to investigate the performance of the ELLAM scheme with a range of well‐perceived and widely used methods in fluid dynamics including the monotonic upstream‐centered scheme for conservation laws (MUSCL), the minmod method, the flux‐corrected transport method (FCT), and the essentially non‐oscillatory (ENO) schemes and weighted essentially non‐oscillatory (WENO) schemes. These experiments show that the ELLAM scheme is very competitive with these methods in the context of linear transport PDEs, and suggest/justify the development of ELLAM‐based simulators for subsurface porous medium flows and other applications. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 22–43, 2003