The problem of boundary conditions for the shallow water equations (Russian)

TL;DR

This paper discusses the challenges and solutions for setting boundary conditions in numerical simulations of shallow water equations over irregular terrains, especially in complex flow regimes like floods and tsunamis.

Contribution

It analyzes various boundary condition methods and advocates for waterfall-type conditions to handle inhomogeneous landforms and critical flow regions effectively.

Findings

Waterfall boundary conditions are advantageous in complex terrain.

Hydraulic jumps near boundaries reduce boundary influence.

Waterfall conditions improve simulation accuracy in inhomogeneous areas.

Abstract

The problem of choice of boundary conditions are discussed for the case of numerical integration of the shallow water equations on a substantially irregular relief. In modeling of unsteady surface water flows has a dynamic boundary partitioning liquid and dry bottom. The situation is complicated by the emergence of sub- and supercritical flow regimes for the problems of seasonal floodplain flooding, flash floods, tsunami landfalls. Analysis of the use of various methods of setting conditions for the physical quantities of liquid when the settlement of the boundary shows the advantages of using the waterfall type conditions in the presence of strong inhomogeneities landforms. When there is a waterfall on the border of the computational domain and heterogeneity of the relief in the vicinity of the boundary portion may occur, which is formed by the region of critical flow with the formation of a hydraulic jump, which greatly weakens the effect of the waterfall on the flow pattern upstream.