A new second-order accurate, explicit diffusion scheme is presented and discussed. The scheme is derived as a weighted average dimensions, there is a considerable cost both in computaof the conventional, forward-in-time, explicit diffusion scheme over tion time and complexity. So, although this scheme does one grid length and the same scheme, but over two grid lengths. not suffer the problem of having to take many small time-Varying the weighting factors produces a family of schemes. For steps, each time-step it does take is computationally optimum use, a new scheme with the weighting factor dependent very expensive.
on the viscous stability number is proposed. It is slightly more computationally expensive than the conventional explicit scheme
The third shortcoming is that schemes which appear to (typically by 25%) but is numerically stable at viscous stability numhave the benefits of both the simple explicit methods (low bers four times as large. Further, it is about 20% computationally computation time per step) and also of the implicit ones less expensive than the fully implicit scheme even in the simplest (large time-step), have in the past, only achieved this at one-dimensional model. This ''three-level, locally implicit'' scheme some other cost. For example, the scheme described by has been implemented in both a simple one-dimensional diffusion model and also in a complex three-dimensional large-eddy simula-DuFort and Frankel [2] is computationally inexpensive and tion model. It has been found to behave well and is profitable in places no restriction on the time-step, but the solution only both models. แฎ 1996 British Crown Copyright converges to the correct answer as the time-step tends to zero. In practice, this can place as stringent a requirement on the time-step as that encountered with the simple ex-16