Two-Dimensional Horizontal Numerical Model of Open Flow over a Bed with Obstacles

Abstract

An explicit numerical algorithm for solving two-dimensional system of shallow-water equations is presented. The algorithm is based on the control volume method with recording mass and momentum fluxes through the faces of the volume with the use of an approximate solution of the Riemann problem. A numerical solution is compared with analytical solutions for a flow over a bottom step and with data of laboratory experiments in a flume with a sloped bed or a bed with an obstacle.

Multilayer open flow model: A simple pressure correction method for wave problems

“…This is probably related to the fact that at all stages of the calculation algorithm (including pressure calculation), layer interaction was accounted for by using an almost implicit scheme: solving a tridiagonal layer “connection” system. On the other hand, in the CFL condition, diffusion momentum transfer shall also be accounted for.…”

“…This is probably related to the fact that at all stages of the calculation algorithm (including pressure calculation), layer interaction was accounted for by using an almost implicit scheme: solving a tridiagonal layer "connection" system. On the other hand, in the CFL condition, diffusion momentum transfer 21 shall also be accounted for. The Eulerian coordinate system is used on a fixed horizontal control volume grid, while the Lagrange method is used on a moving vertical σ grid (velocities with respect to moving grid).…”

“…To improve the calculation accuracy of vertical advection, the Monotonic Upwind Scheme for Conservation Laws (MUSCL)‐reconstruction technique with the MinMod limiter was applied . Thus, the scheme is of the second‐accuracy order with respect to all 3 coordinates.…”