Interaction of rigid body motion and rarefied gas dynamics based on the BGK model

Sudarshan Tiwari; Axel Klar; Giovanni Russo; Sudarshan Tiwari; Axel Klar; Giovanni Russo

doi:10.3934/mine.2020010

Mathematics in Engineering

2020, Volume 2, Issue 2: 203-229. doi: 10.3934/mine.2020010

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Interaction of rigid body motion and rarefied gas dynamics based on the BGK model

1.
Department of Mathematics, Technische Universität Kaiserslautern, Erwin-Schrödinger-Straße, 67663 Kaiserslautern, Germany
2.
Fraunhofer ITWM, Fraunhoferplatz 1, 67663 Kaiserslautern, Germany
3.
Department of Mathematics and Computer Science, University of Catania, Italy

Received: 22 July 2019 Accepted: 04 December 2019 Published: 31 December 2019

Abstract
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In this paper we present simulations of moving rigid bodies immersed in a rarefied gas. The rarefied gas is simulated by solving the Bhatnager-Gross-Krook (BGK) model for the Boltzmann equation. The Newton-Euler equations are solved to simulate the rigid body motion. The force and the torque on the rigid body is computed from the surrounded gas. An explicit Euler scheme is used for the time integration of the Newton-Euler equations. The BGK model is solved by the semi-Lagrangian method suggested by Russo & Filbet ^[22]. Due to the motion of the rigid body, the computational domain for the rarefied gas (and the interface between the rigid body and the gas domain) changes with respect to time. To allow a simpler handling of the interface motion we have used a meshfree method for the interpolation procedure in the semi-Lagrangian scheme. We have considered a one way, as well as a two-way coupling of rigid body and gas flow. We use diffuse reflection boundary conditions on the rigid body and also on the boundary of the computational domain. In one space dimension the numerical results are compared with analytical as well as with Direct Simulation Monte Carlo (DSMC) solutions of the Boltzmann equation. In the two-dimensional case results are compared with DSMC simulations for the Boltzmann equation and with results obtained by other researchers. Several test problems and applications illustrate the versatility of the approach.
- rigid body motion,
- rarefied gas,
- kinetic equation,
- BGK model,
- meshfree method,
- semi-Lagrangian method
Citation: Sudarshan Tiwari, Axel Klar, Giovanni Russo. Interaction of rigid body motion and rarefied gas dynamics based on the BGK model[J]. Mathematics in Engineering, 2020, 2(2): 203-229. doi: 10.3934/mine.2020010

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Abstract

In this paper we present simulations of moving rigid bodies immersed in a rarefied gas. The rarefied gas is simulated by solving the Bhatnager-Gross-Krook (BGK) model for the Boltzmann equation. The Newton-Euler equations are solved to simulate the rigid body motion. The force and the torque on the rigid body is computed from the surrounded gas. An explicit Euler scheme is used for the time integration of the Newton-Euler equations. The BGK model is solved by the semi-Lagrangian method suggested by Russo & Filbet ^[22]. Due to the motion of the rigid body, the computational domain for the rarefied gas (and the interface between the rigid body and the gas domain) changes with respect to time. To allow a simpler handling of the interface motion we have used a meshfree method for the interpolation procedure in the semi-Lagrangian scheme. We have considered a one way, as well as a two-way coupling of rigid body and gas flow. We use diffuse reflection boundary conditions on the rigid body and also on the boundary of the computational domain. In one space dimension the numerical results are compared with analytical as well as with Direct Simulation Monte Carlo (DSMC) solutions of the Boltzmann equation. In the two-dimensional case results are compared with DSMC simulations for the Boltzmann equation and with results obtained by other researchers. Several test problems and applications illustrate the versatility of the approach.

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