DeepAI
Log In Sign Up

Efficient parallel 3D computation of the compressible Euler equations with an invariant-domain preserving second-order finite-element scheme

06/30/2020
by   Matthias Maier, et al.
0

We discuss the efficient implementation of a high-performance second-order collocation-type finite-element scheme for solving the compressible Euler equations of gas dynamics on unstructured meshes. The solver is based on the convex limiting technique introduced by Guermond et al. (SIAM J. Sci. Comput. 40, A3211-A3239, 2018). As such it is invariant-domain preserving, i.e., the solver maintains important physical invariants and is guaranteed to be stable without the use of ad-hoc tuning parameters. This stability comes at the expense of a significantly more involved algorithmic structure that renders conventional high-performance discretizations challenging. We develop an algorithmic design that allows SIMD vectorization of the compute kernel, identify the main ingredients for a good node-level performance, and report excellent weak and strong scaling of a hybrid thread/MPI parallelization.

READ FULL TEXT
07/16/2022

Local-in-time structure-preserving finite-element schemes for the Euler-Poisson equations

We discuss structure-preserving numerical discretizations for repulsive ...
11/01/2020

A Riemann Difference Scheme for Shock Capturing in Discontinuous Finite Element Methods

We present a novel structure-preserving numerical scheme for discontinuo...
07/19/2019

An all speed second order IMEX relaxation scheme for the Euler equations

We present an implicit-explicit finite volume scheme for the Euler equat...
10/04/2019

A Compatible Finite Element Discretisation for the Moist Compressible Euler Equations

We present new discretisation of the moist compressible Euler equations,...
03/23/2021

A Massively Parallel Time-Domain Coupled Electrodynamics-Micromagnetics Solver

We present a new, high-performance coupled electrodynamics-micromagnetic...
07/26/2022

Robust second-order approximation of the compressible Euler equations with an arbitrary equation of state

This paper is concerned with the approximation of the compressible Euler...