# High-order variational Lagrangian schemes for compressible fluids

## TL;DR

This paper introduces high-order variational Lagrangian finite element methods for compressible fluids that conserve energy and entropy, enabling larger stable time steps especially in challenging flow conditions.

## Contribution

The paper develops a novel high-order variational Lagrangian scheme with energy conservation and entropy stability, using fully implicit time stepping for improved stability in compressible fluid simulations.

## Key findings

- Scheme conserves mass, momentum, and energy.
- Allows larger time steps due to implicit temporal discretization.
- Demonstrates good performance through numerical results.

## Abstract

We present high-order variational Lagrangian finite element methods for compressible fluids using a discrete energetic variational approach. Our spatial discretization is mass/momentum/energy conserving and entropy stable. Fully implicit time stepping is used for the temporal discretization, which allows for a much larger time step size for stability compared to explicit methods, especially for low-Mach number flows and/or on highly distorted meshes. Ample numerical results are presented to showcase the good performance of our proposed scheme.