A space-time hybridizable discontinuous Galerkin method for linear free-surface waves

TL;DR

This paper introduces a new space-time hybridizable discontinuous Galerkin method for linear free-surface wave problems, providing a mixed formulation for fluid velocity and explicit error analysis.

Contribution

The paper develops a novel space-time HDG method with a mixed formulation and explicit error estimates for free-surface wave simulations.

Findings

Method verified through numerical examples

Error analysis confirms theoretical predictions

Wave maker simulation demonstrates practical applicability

Abstract

We present and analyze a novel space-time hybridizable discontinuous Galerkin (HDG) method for the linear free-surface problem on prismatic space-time meshes. We consider a mixed formulation which immediately allows us to compute the velocity of the fluid. In order to show well-posedness, our space-time HDG formulation makes use of weighted inner products. We perform an a priori error analysis in which the dependence on the time step and spatial mesh size is explicit. We provide two numerical examples: one that verifies our analysis and a wave maker simulation.