Finite volume methods and the equations of finite scale: A mimetic approach

After introducing the general concept of mimetic differencing, we focus on two specific methodologies, nonoscillatory methods and finite volume approximations. We provide a brief historical account of the development of these two mimetic strategies. We then describe the extension of these strategies to new techniques, a discrete operator calculus and implicit large eddy simulation. In each case, we provide illustrative examples. Further abstraction of these ideas leads to the concept of equations of finite scale, which we advocate as a more appropriate PDE model for constructing numerical algorithms. Published in 2007 by John Wiley & Sons, Ltd.