27 citations · 31 across the 18 of their papers we have counts for
8 papers · 1 filter
Computing statistical Euler limits of the Navier--Stokes equations in three dimensions
Johannes L. Grafen, Tobias Rohner, Stephan Simonis
We develop a Monte Carlo lattice Boltzmann method to compute statistical solutions to the three-dimensional incompressible Navier--Stokes and Euler equations. Entropic space-time a…
Computing statistical solutions of a Mach 2000 astrophysical jet
Stephan Simonis, Gauthier Wissocq
The multi-dimensional compressible Euler equations admit non-unique entropy solutions in turbulent regimes, and extreme-Mach astrophysical flows are a natural setting in which this…
Nonuniqueness of lattice Boltzmann schemes derived from finite difference methods
Eliane Kummer, Stephan Simonis
Recently, the construction of finite difference schemes from lattice Boltzmann schemes has been rigorously analyzed [Bellotti et al. (2022), Numer. Math. 152, pp. 1-40]. It is thus…
Homogenized lattice Boltzmann methods for fluid flow through porous media -- part I: kinetic model derivation
Stephan Simonis, Nicolas Hafen, Julius Jeßberger +3
In this series of studies, we establish homogenized lattice Boltzmann methods (HLBM) for simulating fluid flow through porous media. Our contributions in part I are twofold. First,…
Binary mixture flow with free energy lattice Boltzmann methods
Stephan Simonis, Johannes Nguyen, Samuel J. Avis +2
We use free energy lattice Boltzmann methods (FRE LBM) to simulate shear and extensional flow of a binary mixture in two and three dimensions. To this end, two classical configurat…
Constructing relaxation systems for lattice Boltzmann methods
Stephan Simonis, Martin Frank, Mathias J. Krause
We present the first top-down ansatz for constructing lattice Boltzmann methods (LBM) in d dimensions. In particular, we construct a relaxation system (RS) for a given scalar, line…
Consistent lattice Boltzmann methods for the volume averaged Navier-Stokes equations
Fedor Bukreev, Stephan Simonis, Adrian Kummerländer +2
We derive a novel lattice Boltzmann scheme, which uses a pressure correction forcing term for approximating the volume averaged Navier-Stokes equations (VANSE) in up to three dimen…
Limit Consistency of Lattice Boltzmann Equations
Stephan Simonis, Mathias J. Krause
We establish the notion of limit consistency as a modular part in proving the consistency of lattice Boltzmann equations (LBEs) with respect to a given partial differential equatio…