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首页> 外文期刊>Journal of Computational Physics >Double distribution function-based discrete gas kinetic scheme for viscous incompressible and compressible flows
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Double distribution function-based discrete gas kinetic scheme for viscous incompressible and compressible flows

机译：基于双分配功能的离散气体动力动力学方案，用于粘性不可压缩和可压缩流动

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摘要

In this work, we propose a flux solver that relies on a double distribution function (DDF) based discrete gas-kinetic scheme (DGKS) for incompressible and compressible viscous flows. By decomposing the phase space of the Maxwellian distribution function, the double distribution function (DDF) model is established to remove the phase energy variables and develop more compact formulations. It utilizes the density distribution function to recover the macroscopic mass and momentum conservations, and the energy distribution function to derive the macroscopic energy equation. Associated with a modified collision operator for the energy distribution function, the Prandtl number in the recovered energy equation becomes adjustable. The DDF model can be further simplified with the idea of the improved circular function and by replacing the continuous integration with the quadrature algorithm, which yields the discrete DDF model. This model can then be adopted in the reconstruction of numerical fluxes on the cell interface within the framework of the finite volume method, and the improved discrete gas-kinetic scheme (DGKS) is established. In contrast to the previous DGKS [39], the improved flux solver recovers the correct macroscopic equations and allows free adjustment of the Prandtl number. Besides, the introduction of the energy distribution function abbreviates the expression of the energy flux and thus makes the final formulations more compact. Numerical tests, including the compressible Couette flow, lid-driven cavity flow, transonic flow around the airfoil, shock-boundary layer interaction and supersonic flow around a ramp segment, are presented to validate the proposed flux solver in various flow conditions and compare its performance with the previous DGKS methods [39,43]. (C) 2020 Elsevier Inc. All rights reserved.
机译：在这项工作中，我们提出了一种磁通求解器，其依赖于基于双分配功能（DDF）的离散气体动力学方案（DGK），用于不可压缩和可压缩粘性流量。通过分解千年人分布函数的相位空间，建立了双分布函数（DDF）模型以去除相能量变量并开发更紧凑的配方。它利用密度分布函数来恢复宏观质量和动量保守，以及导出宏观能量方程的能量分布函数。与用于能量分布函数的改进的碰撞操作员相关联，恢复的能量方程中的PRANDTL数变得可调。通过改进的圆形功能的思想，可以进一步简化DDF模型，并通过用正交算法替换连续集成，从而产生离散DDF模型。然后可以采用该模型在有限体积法的框架内的单元接口上的数值通量的重建中采用，并且建立了改进的离散气体动力学方案（DGK）。与先前的DGKS相比，改进的磁通件求恢复了正确的宏观方程，并允许自由调整普朗特数。此外，引入能量分配函数缩写了能量通量的表达，从而使最终制剂更紧凑。提供了数值测试，包括可压缩耦合，盖驱动腔流量，围绕翼型，冲击边界层相互作用和超声波围绕斜坡段的超声波流动，以验证各种流动条件中所提出的磁通求解器，并比较其性能使用以前的DGKS方法[39,43]。 （c）2020 Elsevier Inc.保留所有权利。

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