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Two-layer shallow-water flow in two dimensions, a numerical study

Authors
Journal
Journal of Computational Physics
0021-9991
Publisher
Elsevier
Publication Date
Volume
33
Issue
2
Identifiers
DOI: 10.1016/0021-9991(79)90014-7
Disciplines
  • Mathematics

Abstract

Abstract Two-layer shallow-water flow without mixing is discussed. The existence of two types of waves (surface and internal) with rather different velocities of propagation leads to a numerical approach with two separate grids. For that purpose, the differential equations are written in a weak-interaction form. Particular attention is paid to the formulation of boundary conditions leading to a mathematically well-posed and numerically stable problem. A slightly modified leap-frog method is shown to satisfy the requirements. Some examples are given, including salt-water intrusion in a schematic estuary.

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