scholarly journals Nonlinear stability of planar rarefaction wave to the three-dimensional Boltzmann equation

2019 ◽  
Vol 12 (3) ◽  
pp. 637-679 ◽  
Author(s):  
Teng Wang ◽  
◽  
Yi Wang ◽  
◽  
Keyword(s):  
Boltzmann Equation ◽  
Rarefaction Wave ◽  
Nonlinear Stability ◽  
Three Dimensional

scholarly journals Matrix lattice Boltzmann reloaded

2011 ◽  
Vol 369 (1944) ◽  
pp. 2202-2210 ◽  
Author(s):  
Ilya Karlin ◽  
Pietro Asinari ◽  
Sauro Succi
Keyword(s):  
Boltzmann Equation ◽  
Lattice Boltzmann ◽  
Three Dimensional ◽  
Collision Integral ◽  
Lattice Boltzmann Equation ◽  
New Paradigm ◽  
Driven Cavity ◽  
Matrix Lattice ◽  
Stability And Accuracy ◽  
Enhanced Stability

The lattice Boltzmann equation was introduced about 20 years ago as a new paradigm for computational fluid dynamics. In this paper, we revisit the main formulation of the lattice Boltzmann collision integral (matrix model) and introduce a new two-parametric family of collision operators, which permits us to combine enhanced stability and accuracy of matrix models with the outstanding simplicity of the most popular single-relaxation time schemes. The option of the revised lattice Boltzmann equation is demonstrated through numerical simulations of a three-dimensional lid-driven cavity.

Stability of planar rarefaction wave to the 3D bipolar Vlasov–Poisson–Boltzmann system

2019 ◽  
Vol 30 (01) ◽  
pp. 23-104 ◽  
Author(s):  
Shu Wang ◽  
Teng Wang
Keyword(s):  
Wave Propagation ◽  
Boltzmann Equation ◽  
Asymptotic Stability ◽  
Rarefaction Wave ◽  
Stability Result ◽  
Three Dimensions ◽  
Wave Patterns ◽  
Shock Profiles ◽  
Poisson Boltzmann ◽  
Math Phys

We investigate the time-asymptotic stability of planar rarefaction wave for the 3D bipolar Vlasov–Poisson Boltzmann (VPB) system, based on the micro–macro decompositions introduced in [T. P. Liu and S. H. Yu, Boltzmann equation: Micro–macro decompositions and positivity of shock profiles, Comm. Math. Phys. 246 (2004) 133–179; Energy method for the Boltzmann equation, Physica D 188 (2004) 178–192] and our new observations on the underlying wave structures of the equation to overcome the difficulties due to the wave propagation along the transverse directions and its interactions with the planar rarefaction wave. Note that this is the first stability result of basic wave patterns for bipolar VPB system in three dimensions.

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