TY - JOUR
T1 - A higher-order eulerian-lagrangian localized adjoint method for two-dimensional unsteady advection-diffusion problems
AU - Al-Lawatia, Mohamed
PY - 2012/5
Y1 - 2012/5
N2 - 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.
AB - 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.
KW - Advection-diffusion equations
KW - Biquadratic interpolation
KW - Characteristic methods
KW - Eulerian-Lagrangian methods
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U2 - 10.4208/jcm.1110-m3465
DO - 10.4208/jcm.1110-m3465
M3 - Article
AN - SCOPUS:84863848892
SN - 0254-9409
VL - 30
SP - 324
EP - 336
JO - Journal of Computational Mathematics
JF - Journal of Computational Mathematics
IS - 3
ER -