Splitting as an approach to constructing local exact artificial boundary conditions

We employ the technique of splitting for constructing artificial boundary conditions (ABCs) for the linear advection–diffusion–reaction equation when the computational domain is an nD open set with a piecewise smooth artificial boundary. The splitting is performed both by the physical processes and by coordinates. The former permits to construct ABCs for each of the processes separately, which provides local exact boundary conditions; the latter leads to ABCs much less exigent to the shape of artificial boundary in comparison with many others. We also prove that the corresponding boundary value problems are well-posed, and present results of the numerical experiments that confirm the theoretical study.