An interface-tracking space-time hybridizable/embedded discontinuous Galerkin method for nonlinear free-surface flows

TL;DR

This paper introduces a novel space-time hybridizable/embedded discontinuous Galerkin method for accurately tracking nonlinear free-surface waves in two-fluid systems, ensuring mass conservation and a sharp interface without smoothing.

Contribution

The paper presents a new compatible discretization combining hybridizable and embedded discontinuous Galerkin methods for free-surface flows, enabling precise interface tracking without additional stabilization.

Findings

Exact mass conservation achieved in simulations

Sharp interface maintained without smoothing techniques

Effective handling of nonlinear free-surface waves

Abstract

We present a compatible space-time hybridizable/embedded discontinuous Galerkin discretization for nonlinear free-surface waves. We pose this problem in a two-fluid (liquid and gas) domain and use a time-dependent level-set function to identify the sharp interface between the two fluids. The incompressible two-fluidd equations are discretized by an exactly mass conserving space-time hybridizable discontinuous Galerkin method while the level-set equation is discretized by a space-time embedded discontinuous Galerkin method. Different from alternative discontinuous Galerkin methods is that the embedded discontinuous Galerkin method results in a continuous approximation of the interface. This, in combination with the space-time framework, results in an interface-tracking method without resorting to smoothing techniques or additional mesh stabilization terms.