Accurate discretization of advection-diffusion equations

Details Accurate discretization of advection-diffusion equations Accurate discretization of advection-diffusion equations

2004-12-13

arxiv.org/abs/physics/0412074v1

Physical Review E 70, #036703 (2004)

Physics

Computational Physics

Scientific paper

10.1103/PhysRevE.70.036703

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 provides an alternative mesoscopic interpretation of advection-diffusion processes in terms of diffusion with spatially varying hopping rates.

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