Implicit finite difference methods for modelling discontinuous atmospheric flows
Finite difference schemes are not guaranteed to produce approximate discontinuous flow solutions of differential equations, even if they are consistent and stable. The main purpose of the paper is to find a stable and robust algorithm which is able to approximate discontinuous solutions for the particular cases of flow over a 2-dimensional mountain ridge and for the formation of a front in the atmosphere. It is shown that a carefully designed implicit finite difference scheme can follow a solution in which front are formed and can describe flow over a very peaky mantain barrier. Results from the calculations are illustrated very well by a series of carefully drawn diagrams. The author remarks that the iteration strategy had to be developed empirically and that the theoretical tools for developing an adequate strategy are not yet available.
scientific article; zbMATH DE number 4102650
scientific article