Abstract
A new compact second-order finite-difference method for solving the time-dependent one-dimensional constant-coefficient advection—diffusion equation is developed. It involves a spread of only two grid points in space and two levels in time. It may be evaluated in an explicit marching manner and requires the availability of only upstream boundary values. It is unconditionally stable and has the property of giving ‘non-negative’ values for a large range of Courant and diffusion numbers. For all grid Reynolds numbers greater than 2 it is shown to be more accurate than commonly used second-order methods, all of which involve a spread of three grid points in space.
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