TY - JOUR
T1 - A Higher-Order Eulerian-Lagrangian Localized Adjoint Method for Two-Dimensional Unsteady Advection-Diffusion Problems
AU - Mohamed Al-Lawatia
JO - Journal of Computational Mathematics
VL - 3
SP - 324
EP - 336
PY - 2012
DA - 2012/06
SN - 30
DO - http://doi.org/10.4208/jcm.1110-m3465
UR - https://global-sci.org/intro/article_detail/jcm/8433.html
KW - Advection-diffusion equations, Characteristic methods, Eulerian-Lagrangian methods, Biquadratic interpolation.
AB - <p style="text-align: justify;">We present a higher-order in-space characteristic method for the solution of the transient advection diffusion equations in two space dimensions. This method uses biquadratic trial and test functions within the framework of the Eulerian-Lagrangian localized Adjoint Methods (ELLAM). It therefore maintains the advantages of previous ELLAM schemes. Namely, it treats general boundary conditions naturally in a systematic manner, conserves mass, and symmetrizes the governing transport equations. Moreover, it generates accurate numerical solutions even if large time steps are used in the simulation. Numerical experiments are presented to illustrate the performance of this method and establish its order of convergence numerically.</p>