scholarly journals Positivity property of second-order flux-splitting schemes for the compressible Euler equations

2003 ◽  
Vol 3 (2) ◽  
pp. 201-228 ◽  
Author(s):  
Cheng Wang ◽  
◽  
Jian-Guo Liu ◽  
Keyword(s):  
Euler Equations ◽  
Second Order ◽  
Compressible Euler Equations ◽  
Splitting Schemes ◽  
Flux Splitting ◽  
Positivity Property ◽  
Compressible Euler

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.

scholarly journals Explicit Two-Step Peer Methods for the Compressible Euler Equations

2009 ◽  
Vol 137 (7) ◽  
pp. 2380-2392 ◽  
Author(s):  
Stefan Jebens ◽  
Oswald Knoth ◽  
Rüdiger Weiner
Keyword(s):  
Euler Equations ◽  
Linear Method ◽  
Splitting Method ◽  
Second Order ◽  
Compressible Euler Equations ◽  
Runge Kutta Method ◽  
Artificial Damping ◽  
Compressible Euler ◽  
The Common ◽  
Stability And Accuracy

A new time-splitting method for the integration of the compressible Euler equations is presented. It is based on a two-step peer method, which is a general linear method with second-order accuracy in every stage. The scheme uses a computationally very efficient forward–backward scheme for the integration of the high-frequency acoustic modes. With this splitting approach it is possible to stably integrate the compressible Euler equations without any artificial damping. The peer method is tested with the dry Euler equations and a comparison with the common split-explicit second-order three-stage Runge–Kutta method by Wicker and Skamarock shows the potential of the class of peer methods with respect to computational efficiency, stability, and accuracy.

scholarly journals Singularity Formation for the Compressible Euler Equations

2017 ◽  
Vol 49 (4) ◽  
pp. 2591-2614 ◽  
Author(s):  
Geng Chen ◽  
Ronghua Pan ◽  
Shengguo Zhu
Keyword(s):  
Euler Equations ◽  
Compressible Euler Equations ◽  
Singularity Formation ◽  
Compressible Euler
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