Numerical Solution of Incompressible Cahn-Hilliard and Navier-Stokes System with Large Density and Viscosity Ratio Using the Least-Squares Spectral Element Method

There is a growing interest in numerically handling of the interface dynamics in multiphase flows with large density and viscosity ratio in several scientific and engineering applications. We present a parallel space-time implementation of a least-squares spectral element method for the incompressible Cahn-Hilliard and Navier-Stokes equations for different densities and viscosities between phases. The highorder continuity approximation is adopted to support global differentiability of problems, and by using time-stepping procedure and the element-by-element technique the effective usage of memory is resolved. Numerical experiments are conducted in order to verify the spectral/hp least-squares formulation through a convergence analysis. Besides, the efficiency of parallel computing is investigated. As general example, a falling droplet under gravity is solved by our solvers for different density and viscosity ratios, and the positive feedback between velocity field and droplet shape is investigated.