Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 741-768 |
| Number of pages | 28 |
| Journal | Advances in Water Resources |
| Volume | 22 |
| Issue number | 7 |
| DOIs | |
| Publication status | Published - Apr 30 1999 |
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Keywords
- Characteristics methods
- Comparison of numerical methods
- Eulerian-Lagranigan methods
- Numerical solutions of advection-diffusion equations
- Runge-Kutta methods
ASJC Scopus subject areas
- Earth-Surface Processes
Cite this
Second-order characteristic methods for advection-diffusion equations and comparison to other schemes. / Al-Lawatia, Mohamed; Sharpley, Robert C.; Wang, Hong.
In: Advances in Water Resources, Vol. 22, No. 7, 30.04.1999, p. 741-768.Research output: Contribution to journal › Article
}
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
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
UR - http://www.scopus.com/inward/record.url?scp=0033617509&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0033617509&partnerID=8YFLogxK
U2 - 10.1016/S0309-1708(98)00035-9
DO - 10.1016/S0309-1708(98)00035-9
M3 - Article
VL - 22
SP - 741
EP - 768
JO - Advances in Water Resources
JF - Advances in Water Resources
SN - 0309-1708
IS - 7
ER -