Cartesian Cut Cell Two-Fluid Solver for Hydraulic Flow Problems

Abstract

A two-fluid solver which can be applied to a variety of hydraulic flow problems has been developed. The scheme is based on the solution of the incompressible Euler equations for a variable density fluid system using the artificial compressibility method. The computational domain encompasses both water and air regions and the interface between the two fluids is treated as a contact discontinuity in the density field which is captured automatically as part of the solution using a high resolution Godunov-type scheme. A time-accurate solution has been achieved by using an implicit dual-time iteration technique. The complex geometry of the solid boundary arising in the real flow problems is represented using a novel Cartesian cut cell technique, which provides a boundary fitted mesh without the need for traditional mesh generation techniques. A number of test cases including the classical low amplitude sloshing tank and dam-break problems, as well as a collapsing water column hitting a downstream obstacle have been calculated using the present approach and the results compare very well with other theoretical and experimental results. Finally, a test case involving regular waves interacting with a sloping beach is also calculated to demonstrate the applicability of the method to real hydraulic problems.