Developments in multi-fluid finite volume free surface capturing methods Recent work at Manchester Metropolitan University has led to the development of AMAZON-SC, a multi-fluid free surface capturing solver for the Euler or Navier-Stokes equations. The free surface is captured automatically as a discontinuity in the density field in a manner similar to shock capturing in compressible flow. No surface tracking or reconstruction procedure is needed. This approach can simulate the breakup and recombination of the free surface and thus can model wave breaking. An artificial compressibility method is used to formulate the incompressible Navier-Stokes equations as a hyperbolic system which is solved using high-resolution Riemann-based upwind methods. Second order accuracy is obtained by using linear interpolation of the stored cell centre data to cell interfaces and slope limiters to eliminate non-physical over/under-shoots in the interpolated data. A time-accurate solution is achieved using an implicit dual-time iteration technique in which the flow solution at each real physical time step is obtained by solving a steady-state problem in a pseudo-time domain. AMAZON-SC has been validated over a range of classical bench-mark problems for free surface flows including a collapsing water column inundating an obstruction, water sloshing in a tank, waves in a flume, slamming of a rigid wedge from air into water and to applications including wave overtopping at sea walls, wave energy devices and floating bodies. AMAZON-SC is implemented on a Cartesian cut cell mesh which automatically and efficiently produces a boundary conforming mesh simply by cutting out solid boundary regions from a fixed background Cartesian mesh. The cut cell technique accommodates moving internal solid boundaries very simply without the necessity to re-mesh globally or even locally. The method extends naturally to 3-D, can handle multi-fluid cases in which there are more than two fluid components as well as, in principle, compliant moving bodies.

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