Edge-based finite element scheme for the Euler equations

AIAA Journal ◽  
1994 ◽  
Vol 32 (6) ◽  
pp. 1183-1190 ◽  
Author(s):  
Hong Luo ◽  
Joseph D. Baum ◽  
Rainald Lohner
Keyword(s):  
Finite Element ◽  
Euler Equations ◽  
Finite Element Scheme ◽  
Element Scheme ◽  
Edge Based

scholarly journals Efficient Parallel 3D Computation of the Compressible Euler Equations with an Invariant-domain Preserving Second-order Finite-element Scheme

2021 ◽  
Vol 8 (3) ◽  
pp. 1-30
Author(s):  
Matthias Maier ◽  
Martin Kronbichler
Keyword(s):  
Finite Element ◽  
Euler Equations ◽  
High Performance ◽  
Ad Hoc ◽  
Second Order ◽  
Compressible Euler Equations ◽  
Finite Element Scheme ◽  
Element Scheme ◽  
Invariant Domain ◽  
Compressible Euler

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.

An adaptive finite element scheme to solve fluid-structure vibration problems on non-matching grids

2001 ◽  
Vol 4 (2) ◽  
pp. 67-78 ◽  
Author(s):  
Ana Alonso ◽  
Anahí Dello Russo ◽  
César Otero-Souto ◽  
Claudio Padra ◽  
Rodolfo Rodríguez
Keyword(s):  
Finite Element ◽  
Adaptive Finite Element ◽  
Finite Element Scheme ◽  
Fluid Structure ◽  
Element Scheme ◽  
Structure Vibration ◽  
Vibration Problems
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