TY - JOUR
T1 - A high-order ADI method for parabolic problems with variable coefficients
AU - Karaa, Samir
N1 - Funding Information:
This research was supported by Sultan Qaboos University under Grant IG/SCI/DOMAS/07/08.
PY - 2009/1
Y1 - 2009/1
N2 - A high-order compact alternating direction implicit (ADI) method is proposed for solving two-dimensional (2D) parabolic problems with variable coefficients. The computational problem is reduced to sequence one-dimensional problems which makes the computation cost-effective. The method is easily extendable to multi-dimensional problems. Various numerical tests are performed to test its high-order accuracy and efficiency, and to compare it with the standard second-order Peaceman-Rachford ADI method. The method has been applied to obtain the numerical solutions of the lid-driven cavity flow problem governed by the 2D incompressible Navier-Stokes equations using the stream function-vorticity formulation. The solutions obtained agree well with other results in the literature.
AB - A high-order compact alternating direction implicit (ADI) method is proposed for solving two-dimensional (2D) parabolic problems with variable coefficients. The computational problem is reduced to sequence one-dimensional problems which makes the computation cost-effective. The method is easily extendable to multi-dimensional problems. Various numerical tests are performed to test its high-order accuracy and efficiency, and to compare it with the standard second-order Peaceman-Rachford ADI method. The method has been applied to obtain the numerical solutions of the lid-driven cavity flow problem governed by the 2D incompressible Navier-Stokes equations using the stream function-vorticity formulation. The solutions obtained agree well with other results in the literature.
KW - 2D incompressible Navier-Stokes equations
KW - ADI method
KW - Driven cavity flow
KW - High-order compact scheme
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U2 - 10.1080/00207160802217227
DO - 10.1080/00207160802217227
M3 - Article
AN - SCOPUS:55849125844
SN - 0020-7160
VL - 86
SP - 109
EP - 120
JO - International Journal of Computer Mathematics
JF - International Journal of Computer Mathematics
IS - 1
ER -