Implementing a conservative level set method for multiphase simulation in spectral/hp element framework Nektar++

Spectral/hp element methods such as the Nektar++ available in ARCHER2 blend the advantages of h-type geometrical discretisation with the p-type spectral discretisation of Finite Element Methods. In the recent years, the advantages of utilising high degree piecewise polynomial basis functions for spectral (p-type) discretisation have led to the adaptation of spectral/hp element methods for resource intensive computational fluid dynamics simulations. However, they have been primarily limited to single-phase conditions alone. The availability of a robust interface capturing method coupled with Navier-Stokes equations is necessary to propagate spectral/hp element methods to the wider CFD community and their employment in multiphase numerical simulations corresponding to a broader range of practical applications. Through the ARCHER2 eCSE11-5 project, we have implemented a conservative level-set method that exploits the spectral discretisation advantage in Nektar++ to provide better accuracy of the interface at lower computational cost. The benchmark level set method tests of advection (rotating circle) and deformation (vortex) as well as the Zalesak's slotted disk and 3D sphere deformation with the implemented spectral/hp level-set method have all confirmed this when compared against similar level-set methods in CFD and FEM. The current phase of the project aims to couple this conservative level set method with continuum surface tension model and gravity into the incompressible Navier-stokes solver/equations to assemble an effective spectral/hp multiphase solver capable of handling fluids with a density ratio of more than 1000. The poster will showcase some of the current capabilities of our multiphase level-set solver implemented in Nektar++.