We present an exact mathematical transformation which converts a wide class of advection-diffusion equations into a form allowing simple and direct spatial discretization in all dimensions, and thus the construction of accurate and more efficient numerical algorithms. These discretized forms can also be viewed as master equations which provide an alternative mesoscopic interpretation of advection-diffusion processes in terms of diffusion with spatially varying hopping rates.
|Journal||Physical Review E: Statistical, Nonlinear, and Soft Matter Physics|
|Publication status||Published - 16 Sep 2004|
Grima, R., & Newman, T. J. (2004). Accurate discretization of advection-diffusion equations. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, 70(3 ), . https://doi.org/10.1103/PhysRevE.70.036703