A lattice Boltzmann model for the compressible Euler equations with second-order accuracy

2009 ◽  
Vol 60 (1) ◽  
pp. 95-117 ◽  
Author(s):  
Jianying Zhang ◽  
Guangwu Yan ◽  
Xiubo Shi ◽  
Yinfeng Dong
Keyword(s):  
Euler Equations ◽  
Lattice Boltzmann ◽  
Second Order ◽  
Lattice Boltzmann Model ◽  
Compressible Euler Equations ◽  
Order Accuracy ◽  
Compressible Euler ◽  
Boltzmann Model

scholarly journals Multispeed Lattice Boltzmann Model with Space-Filling Lattice for Transcritical Shallow Water Flows

2017 ◽  
Vol 2017 ◽  
pp. 1-5 ◽  
Author(s):  
Y. Peng ◽  
J. P. Meng ◽  
J. M. Zhang
Keyword(s):  
Shallow Water ◽  
Lattice Boltzmann ◽  
Lattice Models ◽  
Second Order ◽  
Lattice Boltzmann Model ◽  
Space Filling ◽  
Order Accuracy ◽  
Water Flows ◽  
Recent Success ◽  
Shallow Water Flows

Inspired by the recent success of applying multispeed lattice Boltzmann models with a non-space-filling lattice for simulating transcritical shallow water flows, the capabilities of their space-filling counterpart are investigated in this work. Firstly, two lattice models with five integer discrete velocities are derived by using the method of matching hydrodynamics moments and then tested with two typical 1D problems including the dam-break flow over flat bed and the steady flow over bump. In simulations, the derived space-filling multispeed models, together with the stream-collision scheme, demonstrate better capability in simulating flows with finite Froude number. However, the performance is worse than the non-space-filling model solved by finite difference scheme. The stream-collision scheme with second-order accuracy may be the reason since a numerical scheme with second-order accuracy is prone to numerical oscillations at discontinuities, which is worthwhile for further study.

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.

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