TY - JOUR
T1 - Second-order characteristic methods for advection-diffusion equations and comparison to other schemes
AU - Al-Lawatia, Mohamed
AU - Sharpley, Robert C.
AU - Wang, Hong
N1 - Funding Information:
This research was supported in part by DOE Grant No. DE-FG05-95ER25266, by ONR Grant No. N00014-94-1-1163, and by funding from the Mobil Technology Company.
PY - 1999/4/30
Y1 - 1999/4/30
N2 - We develop two characteristic methods for the solution of the linear advection diffusion equations which use a second order Runge-Kutta approximation of the characteristics within the framework of the Eulerian-Lagrangian localized adjoint method. These methods naturally incorporate all three types of boundary conditions in their formulations, are fully mass conservative, and generate regularly structured systems which are symmetric and positive definite for most combinations of the boundary conditions. Extensive numerical experiments are presented which compare the performance of these two Runge-Kutta methods to many other well perceived and widely used methods which include many Galerkin methods and high resolution methods from fluid dynamics.
AB - We develop two characteristic methods for the solution of the linear advection diffusion equations which use a second order Runge-Kutta approximation of the characteristics within the framework of the Eulerian-Lagrangian localized adjoint method. These methods naturally incorporate all three types of boundary conditions in their formulations, are fully mass conservative, and generate regularly structured systems which are symmetric and positive definite for most combinations of the boundary conditions. Extensive numerical experiments are presented which compare the performance of these two Runge-Kutta methods to many other well perceived and widely used methods which include many Galerkin methods and high resolution methods from fluid dynamics.
KW - Characteristics methods
KW - Comparison of numerical methods
KW - Eulerian-Lagranigan methods
KW - Numerical solutions of advection-diffusion equations
KW - Runge-Kutta methods
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U2 - 10.1016/S0309-1708(98)00035-9
DO - 10.1016/S0309-1708(98)00035-9
M3 - Article
AN - SCOPUS:0033617509
SN - 0309-1708
VL - 22
SP - 741
EP - 768
JO - Advances in Water Resources
JF - Advances in Water Resources
IS - 7
ER -