Abstract
Simulations of the discrete Boltzmann Bhatnagar-Gross-Krook equation are an important tool for understanding fluid dynamics in non-continuum regimes. Here, we introduce a discontinuous Galerkin finite element method for spatial discretization of the discrete Boltzmann equation for isothermal flows with high Knudsen numbers [Kn ∼ O (1)]. In conjunction with a high-order Runge-Kutta time marching scheme, this method is capable of achieving high-order accuracy in both space and time, while maintaining a compact stencil. We validate the spatial order of accuracy of the scheme on a two-dimensional Couette flow with Kn = 1 and the D2Q16 velocity discretization. We then apply the scheme to lid-driven micro-cavity flow at Kn = 1, 2, and 8, and we compare the ability of Gauss-Hermite (GH) and Newton-Cotes (NC) velocity sets to capture the high non-linearity of the flow-field. While the GH quadrature provides higher integration strength with fewer points, the NC quadrature has more uniformly distributed nodes with weights greater than machine-zero, helping to avoid the so-called ray-effect. Broadly speaking, we anticipate that the insights from this work will help facilitate the efficient implementation and application of high-order numerical methods for complex high Knudsen number flows.
Original language | English (US) |
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Article number | 032019 |
Journal | Physics of Fluids |
Volume | 33 |
Issue number | 3 |
DOIs | |
State | Published - Mar 1 2021 |
All Science Journal Classification (ASJC) codes
- Computational Mechanics
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Fluid Flow and Transfer Processes