TY - JOUR
T1 - A preliminary investigation on an ELLAM scheme for linear transport equations
AU - Al-Lawatia, Mohamed
AU - Wang, Hong
PY - 2003/1
Y1 - 2003/1
N2 - 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.
AB - 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.
KW - Advection-reaction equations
KW - Characteristic methods
KW - Comparison of numerical methods
KW - Essentially nonoscillatory schemes
KW - Eulerian-Lagrangian methods
KW - Transport equations
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U2 - 10.1002/num.10042
DO - 10.1002/num.10042
M3 - Article
AN - SCOPUS:0037232031
SN - 0749-159X
VL - 19
SP - 22
EP - 43
JO - Numerical Methods for Partial Differential Equations
JF - Numerical Methods for Partial Differential Equations
IS - 1
ER -