# An entropy stable discontinuous Galerkin finite-element moment method for the Boltzmann equation

@article{Abdelmalik2016AnES, title={An entropy stable discontinuous Galerkin finite-element moment method for the Boltzmann equation}, author={M. R. A. Abdelmalik and E. H. van Brummelen}, journal={Comput. Math. Appl.}, year={2016}, volume={72}, pages={1988-1999} }

## 11 Citations

Entropy Stable Discontinuous Galerkin Finite Element Moment Methods for Compressible Fluid Dynamics

- Computer Science, Physics
- 2020

This work proposes numerical approximations of the Boltzmann equation that are consistent with the Euler and Navier–Stoke–Fourier solutions and presents a numerical approximation that is based on the discontinuous Galerkin method in position dependence and on the renormalized-moment method in velocity dependence.

Moment closure approximations of the Boltzmann equation based on φ-divergences

- Mathematics
- 2016

This paper is concerned with approximations of the Boltzmann equation based on the method of moments. We propose a generalization of the setting of the moment-closure problem from relative entropy to…

A Discontinuous Galerkin Fast Spectral Method for the Full Boltzmann Equation with General Collision Kernels

- PhysicsJ. Comput. Phys.
- 2019

Error estimation and adaptive moment hierarchies for goal-oriented approximations of the Boltzmann equation

- Computer Science
- 2017

Entropy stable Hermite approximation of the linearised Boltzmann equation for inflow and outflow boundaries

- Computer ScienceJ. Comput. Phys.
- 2018

Simultaneous-approximation-term based boundary discretization for moment equations of rarefied gas dynamics

- MathematicsJ. Comput. Phys.
- 2020

Moment Closure Approximations of the Boltzmann Equation Based on $$\varphi $$φ-Divergences

- Mathematics
- 2015

This paper is concerned with approximations of the Boltzmann equation based on the method of moments. We propose a generalization of the setting of the moment-closure problem from relative entropy to…

Adaptive algorithms for optimal multiscale model hierarchies of the Boltzmann Equation : Galerkin methods for kinetic theory

- Physics
- 2017

This chapter introduces a kinetic description of rarefaction in dilute monatomic fluids. We present a mathematical account of the multi-scale nature of the fluid description – namely, the relation…

Grad's Distribution Function for 13 Moments based Moment Gas Kinetic Solver for Steady and Unsteady Rarefied flows: Discrete and Explicit Forms

- Engineering
- 2022

Eﬃcient modeling of rareﬁed ﬂow has drawn widespread interest for practical engineering applications. In the present work, we proposed the Grad’s distribution function for 13 moments-based moment gas…

Higher-order moment models for laminar multiphase flows with accurate particle-stream crossing

- EngineeringInternational Journal of Multiphase Flow
- 2019

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Moment closure approximations of the Boltzmann equation based on φ-divergences

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This paper is concerned with approximations of the Boltzmann equation based on the method of moments. We propose a generalization of the setting of the moment-closure problem from relative entropy to…

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Moment Closure Approximations of the Boltzmann Equation Based on $$\varphi $$φ-Divergences

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