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

@article{Jones2021AnIS, title={An interface-tracking space-time hybridizable/embedded discontinuous Galerkin method for nonlinear free-surface flows}, author={Giselle Sosa Jones and Sander Rhebergen}, journal={ArXiv}, year={2021}, volume={abs/2110.13779} }

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-fluid 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…

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SHOWING 1-10 OF 44 REFERENCES

Space-time discontinuous Galerkin method for nonlinear water waves

- Mathematics, Computer ScienceJ. Comput. Phys.
- 2007

A space-time discontinuous Galerkin (DG) finite element method for nonlinear water waves in an inviscid and incompressible fluid is presented and numerical examples are shown on a series of model problems to demonstrate the accuracy and capabilities of the method.

Space--time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows: I. general formulation

- Mathematics
- 2001

A new space-time discontinuous Galerkin finite element method for the solution of the Euler equations of gas dynamics in time-dependent flow domains is presented. The discontinuous Galerkin…

A locally conservative and energy-stable finite-element method for the Navier-Stokes problem on time-dependent domains

- Mathematics, PhysicsInternational Journal for Numerical Methods in Fluids
- 2019

We present a finite element method for the incompressible Navier--Stokes problem that is locally conservative, energy-stable and pressure-robust on time-dependent domains. To achieve this, the…

A space-time Galerkin/least-squares finite element formulation of the Navier-Stokes equations for moving domain problems

- Mathematics
- 1997

A space-time Galerkin/least-squares finite element formulation of the Navier-Stokes equations is presented for the analysis of free surface flows, moving spatial configurations and deforming…

A Hybridizable Discontinuous Galerkin Method for the Navier–Stokes Equations with Pointwise Divergence-Free Velocity Field

- Mathematics, Computer ScienceJ. Sci. Comput.
- 2018

It is shown that with modifications of the function spaces in the method of Labeur and Wells it is possible to formulate a simple method with pointwise divergence-free velocity fields which is momentum conserving, energy stable, and pressure-robust.

A level set discontinuous Galerkin method for free surface flows

- Mathematics
- 2005

We present a discontinuous Galerkin method on a fully unstructured grid for the modeling of unsteady incompressible fluid flows with free surfaces. The surface is modeled by embedding and represented…

High order exactly divergence-free Hybrid Discontinuous Galerkin Methods for unsteady incompressible flows

- Mathematics, Computer ScienceArXiv
- 2015

An efficient discretization method for the solution of the unsteady incompressible Navier–Stokes equations based on a high order (Hybrid) Discontinuous Galerkin formulation is presented and the performance on two and three dimensional benchmark problems is demonstrated.

Hybridizable discontinuous Galerkin method (HDG) for Stokes interface flow

- Mathematics, Computer ScienceJ. Comput. Phys.
- 2013

A hybridizable discontinuous Galerkin (HDG) method for solving the Stokes interface problems with discontinuous viscosity and variable surface tension reduces the number of globally coupled unknowns significantly when high order approximate polynomials are used.

Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows. Part II. Efficient flux quadrature

- Mathematics
- 2001

A new and efficient quadrature rule for the flux integrals arising in the space-time discontinuous Galerkin discretization of the Euler equations in a moving and deforming space-time domain is…