Wk. Dewar et Tj. Mcdougall, The numerical solution of the one-dimensional advection-diffusion equationin layered coordinates, M WEATH REV, 128(7), 2000, pp. 2575-2587
The numerical solution of the vertical advection-diffusion equation in laye
red coordinates is revisited. The objectives of this work are to propose a
generalization of the discontinuous layered representation of the ocean tra
cer held to higher-order, smoother representations (while retaining the qua
si-Lagrangian character of the coordinate) and compare the solutions genera
ted by several approaches in order to illustrate their respective advantage
s and disadvantages. The one-dimensional advection-diffusion equation is ch
osen as a test bed for layered coordinates because ocean simulation for cli
matic purposes requires the inclusion of dianeutral diffusive processes.
The layered approach is generalized by replacing the traditional stack of w
ell-mixed layers by stacks of piecewise smooth profiles. All the well-known
properties of quasi-Lagrangian coordinates are retained. Comparisons of th
e quasi-Lagrangian solutions with coarse- and fine-resolution fixed grid so
lutions illustrates the efficiency of the adaptive, quasi-Lagrangian coordi
nate.