A higher-order eulerian-lagrangian localized adjoint method for two-dimensional unsteady advection-diffusion problems

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.